171 results on '"Uwe Thiele"'
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2. From a thin film model for passive suspensions towards the description of osmotic biofilm spreading
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Karin John, Uwe Thiele, and Sarah Trinschek
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thin film hydrodynamics ,biofilms ,active complex fluids ,interfacial flows ,nonlinear science ,Materials of engineering and construction. Mechanics of materials ,TA401-492 - Abstract
Biofilms are ubiquitous macro-colonies of bacteria that develop at various interfaces (solid- liquid, solid-gas or liquid-gas). The formation of biofilms starts with the attachment of individual bac- teria to an interface, where they proliferate and produce a slimy polymeric matrix - two processes that result in colony growth and spreading. Recent experiments on the growth of biofilms on agar substrates under air have shown that for certain bacterial strains, the production of the extracellular matrix and the resulting osmotic influx of nutrient-rich water from the agar into the biofilm are more crucial for the spreading behaviour of a biofilm than the motility of individual bacteria. We present a model which de- scribes the biofilm evolution and the advancing biofilm edge for this spreading mechanism. The model is based on a gradient dynamics formulation for thin films of biologically passive liquid mixtures and suspensions, supplemented by bioactive processes which play a decisive role in the osmotic spreading of biofilms. It explicitly includes the wetting properties of the biofilm on the agar substrate via a dis- joining pressure and can therefore give insight into the interplay between passive surface forces and bioactive growth processes.
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- 2016
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3. First order phase transitions and the thermodynamic limit
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Uwe Thiele, Tobias Frohoff-Hülsmann, Sebastian Engelnkemper, Edgar Knobloch, and Andrew J Archer
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Maxwell construction ,mean-field models ,localized structures ,phase separation ,colloidal crystallization ,Cahn–Hilliard model ,Science ,Physics ,QC1-999 - Abstract
We consider simple mean field continuum models for first order liquid–liquid demixing and solid–liquid phase transitions and show how the Maxwell construction at phase coexistence emerges on going from finite-size closed systems to the thermodynamic limit. The theories considered are the Cahn–Hilliard model of phase separation, which is also a model for the liquid-gas transition, and the phase field crystal model of the solid–liquid transition. Our results show that states comprising the Maxwell line depend strongly on the mean density with spatially localized structures playing a key role in the approach to the thermodynamic limit.
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- 2019
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4. Nonequilibrium configurations of swelling polymer brush layers induced by spreading drops of weakly volatile oil
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Özlem Kap, Simon Hartmann, Harmen Hoek, Sissi de Beer, Igor Siretanu, Uwe Thiele, Frieder Mugele, Physics of Complex Fluids, MESA+ Institute, and Sustainable Polymer Chemistry
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Fluid Dynamics (physics.flu-dyn) ,UT-Hybrid-D ,Soft Condensed Matter (cond-mat.soft) ,FOS: Physical sciences ,General Physics and Astronomy ,Physics - Fluid Dynamics ,Condensed Matter - Soft Condensed Matter ,Physical and Theoretical Chemistry - Abstract
Polymer brush layers are responsive materials that swell in contact with good solvents and their vapors. We deposit drops of an almost completely wetting volatile oil onto an oleophilic polymer brush layer and follow the response of the system upon simultaneous exposure to both liquid and vapor. Interferometric imaging shows that a halo of partly swollen polymer brush layer forms ahead of the moving contact line. The swelling dynamics of this halo is controlled by a subtle balance of direct imbibition from the drop into the brush layer and vapor phase transport and can lead to very long-lived transient swelling profiles as well as nonequilibrium configurations involving thickness gradients in a stationary state. A gradient dynamics model based on a free energy functional with three coupled fields is developed and numerically solved. It describes experimental observations and reveals how local evaporation and condensation conspire to stabilize the inhomogeneous nonequilibrium stationary swelling profiles. A quantitative comparison of experiments and calculations provides access to the solvent diffusion coefficient within the brush layer. Overall, the results highlight the—presumably generally applicable—crucial role of vapor phase transport in dynamic wetting phenomena involving volatile liquids on swelling functional surfaces.
- Published
- 2023
5. Sessile drop evaporation in a gap
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Simon Hartmann, Christian Diddens, Maziyar Jalaal, Uwe Thiele, and Physics of Fluids
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Physics::Fluid Dynamics ,Mechanics of Materials ,lubrication theory ,Mechanical Engineering ,Applied Mathematics ,Fluid Dynamics (physics.flu-dyn) ,Soft Condensed Matter (cond-mat.soft) ,FOS: Physical sciences ,Physics - Fluid Dynamics ,Condensed Matter - Soft Condensed Matter ,Condensed Matter Physics ,condensation/evaporation ,drops - Abstract
We consider the time evolution of a sessile drop of volatile partially wetting liquid on a rigid solid substrate. The drop evaporates under strong confinement, namely, it sits on one of the two parallel plates that form a narrow gap. First, we develop an efficient mesoscopic long-wave description in gradient dynamics form. It couples the diffusive dynamics of the vertically averaged vapour density in the narrow gap to an evolution equation for the profile of the volatile drop. The underlying free energy functional incorporates wetting, interface and bulk energies of the liquid and gas entropy. The model allows us to investigate the transition between diffusion-limited and phase transition-limited evaporation for shallow droplets. Its gradient dynamics character allows for a long-wave as well as a full-curvature formulation. Second, we compare results obtained with the mesoscopic long-wave model to corresponding direct numerical simulations solving the Stokes equation for the drop coupled to the diffusion equation for the vapour as well as to selected experiments. In passing, we discuss the influence of contact line pinning.
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- 2023
6. Non-reciprocity induces resonances in a two-field Cahn–Hilliard model
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Tobias Frohoff-Hülsmann, Uwe Thiele, and Len M. Pismen
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General Mathematics ,General Engineering ,Soft Condensed Matter (cond-mat.soft) ,FOS: Physical sciences ,General Physics and Astronomy ,Pattern Formation and Solitons (nlin.PS) ,Condensed Matter - Soft Condensed Matter ,Nonlinear Sciences - Pattern Formation and Solitons - Abstract
We consider a non-reciprocically coupled two-field Cahn-Hilliard system that has been shown to allow for oscillatory behaviour, a suppression of coarsening as well as the existence of localised states. Here, after introducing the model we first briefly review the linear stability of homogeneous states and show that all instability thresholds are identical to the ones for a corresponding Turing system (i.e., a two-species reaction-diffusion system). Next, we discuss possible interactions of linear modes and analyse the specific case of a ``Hopf-Turing'' resonance by discussing corresponding amplitude equations in a weakly nonlinear approach. The thereby obtained states are finally compared with fully nonlinear simulations for a specific conserved amended FitzHugh-Nagumo system. We conclude by a discussion of the limitations of the weakly nonlinear approach. The published version of this preprint can be found under T. Frohoff-Hu\"ulsmann, U. Thiele and L. M. Pismen. Nonreciprocity induces resonances in two-field Cahn-Hilliard model. Phil. Trans. R. Soc. A. 381: 20220087. 20220087. DOI: 10.1098/rsta.2022.0087
- Published
- 2023
7. Fallbericht aus der Kinder- und Jugendhilfe
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Uwe Thiele, Ina Jahn, and Silke Wiegand-Grefe
- Abstract
Ein 14-jähriger Jugendlicher mit einer meist unverständlichen sprachlichen Ausdrucksweise und einem fehlenden Bezug zu Gleichaltrigen erhält Hilfe durch einen Erziehungsbeistand. Schnell wird klar, dass vor allem die stark belastete Beziehung zur Mutter eine entscheidende Rolle in der Entwicklung des Jugendlichen spielt. Liegt der Schlüssel zum Erfolg in der Aufarbeitung der familiären Geschichte und der Integration in die Gemeinschaft?
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- 2022
8. Stick-slip dynamics in the forced wetting of polymer brushes
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Daniel Greve, Simon Hartmann, and Uwe Thiele
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Fluid Dynamics (physics.flu-dyn) ,FOS: Physical sciences ,Physics - Fluid Dynamics ,General Chemistry ,Condensed Matter Physics - Abstract
We study the static and dynamic wetting of adaptive substrates using a mesoscopic hydrodynamic model for a liquid droplet on a solid substrate covered by a polymer brush. First, we show that on the macroscale Young's law still holds for the equilibrium contact angle and that on the mesoscale a Neumann-type law governs the shape of the wetting ridge. Following an analytic and numeric assessment of the static profiles of droplet and wetting ridge, we examine the dynamics of the wetting ridge for a liquid meniscus that is advanced at constant speed. In other words, we consider an inverse Landau-Levich case where a brush-covered plate is introduced into (and not drawn from) a liquid bath. We find a characteristic stick-slip motion that emerges when the dynamic contact angle of the stationary moving meniscus decreases with increasing velocity, and relate the onset of slip to Gibbs' inequality and to a cross-over in relevant time scales.
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- 2023
9. Derivation and analysis of a phase field crystal model for a mixture of active and passive particles
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Michael te Vrugt, Max Philipp Holl, Aron Koch, Raphael Wittkowski, and Uwe Thiele
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Condensed Matter - Materials Science ,Statistical Mechanics (cond-mat.stat-mech) ,Materials Science (cond-mat.mtrl-sci) ,FOS: Physical sciences ,Pattern Formation and Solitons (nlin.PS) ,Condensed Matter - Soft Condensed Matter ,Condensed Matter Physics ,Nonlinear Sciences - Pattern Formation and Solitons ,Computer Science Applications ,Mechanics of Materials ,Modeling and Simulation ,Soft Condensed Matter (cond-mat.soft) ,General Materials Science ,Condensed Matter - Statistical Mechanics - Abstract
We discuss an active phase field crystal (PFC) model that describes a mixture of active and passive particles. First, a microscopic derivation from dynamical density functional theory (DDFT) is presented that includes a systematic treatment of the relevant orientational degrees of freedom. Of particular interest is the construction of the nonlinear and coupling terms. This allows for interesting insights into the microscopic justification of phenomenological constructions used in PFC models for active particles and mixtures, the approximations required for obtaining them, and possible generalizations. Second, the derived model is investigated using linear stability analysis and nonlinear methods. It is found that the model allows for a rich nonlinear behavior with states ranging from steady periodic and localized states to various time-periodic states. The latter include standing, traveling, and modulated waves corresponding to spatially periodic and localized traveling, wiggling, and alternating peak patterns and their combinations., 25 pages, 7 figures
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- 2022
10. From a microscopic inertial active matter model to the Schr\'odinger equation
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Michael te Vrugt, Tobias Frohoff-Hülsmann, Eyal Heifetz, Uwe Thiele, and Raphael Wittkowski
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Quantum Physics ,Multidisciplinary ,Statistical Mechanics (cond-mat.stat-mech) ,Fluid Dynamics (physics.flu-dyn) ,Soft Condensed Matter (cond-mat.soft) ,FOS: Physical sciences ,General Physics and Astronomy ,General Chemistry ,Physics - Fluid Dynamics ,Condensed Matter - Soft Condensed Matter ,Quantum Physics (quant-ph) ,General Biochemistry, Genetics and Molecular Biology ,Condensed Matter - Statistical Mechanics - Abstract
Field theories for the one-body density of an active fluid, such as the paradigmatic active model B+, are simple yet very powerful tools for describing phenomena such as motility-induced phase separation. No comparable theory has been derived yet for the underdamped case. In this work, we introduce active model I+, an extension of active model B+ to particles with inertia. The governing equations of active model I+ are systematically derived from the microscopic Langevin equations. We show that, for underdamped active particles, thermodynamic and mechanical definitions of the velocity field no longer coincide and that the density-dependent swimming speed plays the role of an effective viscosity. Moreover, active model I+ contains the Schr\"odinger equation in Madelung form as a limiting case, allowing to find analoga of the quantum-mechanical tunnel effect and of fuzzy dark matter in the active fluid. We investigate the active tunnel effect analytically and via numerical continuation., Comment: 16 pages, 1 figure
- Published
- 2022
11. Time Integration and Steady-State Continuation for 2d Lubrication Equations.
- Author
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Philippe Beltrame and Uwe Thiele
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- 2010
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12. Gradient-dynamics model for liquid drops on elastic substrates
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Uwe Thiele, Christopher Henkel, Jacco H. Snoeijer, MESA+ Institute, and Physics of Fluids
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Materials science ,Contact line ,Dynamics (mechanics) ,Fluid Dynamics (physics.flu-dyn) ,FOS: Physical sciences ,General Chemistry ,Substrate (electronics) ,Mechanics ,Physics - Fluid Dynamics ,Condensed Matter - Soft Condensed Matter ,Condensed Matter Physics ,Dynamic contact ,Contact angle ,Condensed Matter::Soft Condensed Matter ,Physics::Fluid Dynamics ,Soft Condensed Matter (cond-mat.soft) ,Wetting ,Elasticity (economics) ,Statics - Abstract
The wetting of soft elastic substrates exhibits many features that have no counterpart on rigid surfaces. Modelling the detailed elastocapillary interactions is challenging, and has so far been limited to single contact lines or single drops. Here we propose a reduced long-wave model that captures the main qualitative features of statics and dynamics of soft wetting, but which can be applied to ensembles of droplets. The model has the form of a gradient dynamics on an underlying free energy that reflects capillarity, wettability and compressional elasticity. With the model we first recover the double transition in the equilibrium contact angles that occurs when increasing substrate softness from ideally rigid towards very soft (i.e., liquid). Second, the spreading of single drops of partially and completely wetting liquids is considered showing that known dependencies of the dynamic contact angle on contact line velocity are well reproduced. Finally, we go beyond the single droplet picture and consider the coarsening for a two-drop system as well as for a large ensemble of drops. It is shown that the dominant coarsening mode changes with substrate softness in a nontrivial way.
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- 2021
13. Bifurcation study for a surface-acoustic-wave-driven meniscus
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Uwe Thiele, Ofer Manor, and Kevin David Joachim Mitas
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Fluid Flow and Transfer Processes ,Materials science ,Surface acoustic wave ,Computational Mechanics ,FOS: Physical sciences ,Pattern Formation and Solitons (nlin.PS) ,Acoustic wave ,Mechanics ,Nonlinear Sciences - Pattern Formation and Solitons ,Condensed Matter::Soft Condensed Matter ,Physics::Fluid Dynamics ,symbols.namesake ,Modeling and Simulation ,symbols ,Meniscus ,Weber number ,Deposition (phase transition) ,Wetting ,Rayleigh scattering ,Bifurcation - Abstract
A thin-film model for a meniscus driven by Rayleigh surface acoustic waves (SAW) is analysed, a problem closely related to the classical Landau-Levich or dragged-film problem where a plate is withdrawn at constant speed from a bath. We consider a mesoscopic hydrodynamic model for a partially wetting liquid, were wettability is incorporated via a Derjaguin (or disjoining) pressure and combine SAW driving with the elements known from the dragged-film problem. For a one-dimensional substrate, i.e., neglecting transverse perturbations, we employ numerical path continuation to investigate in detail how the various occurring steady and time-periodic states depend on relevant control parameters like the Weber number and SAW strength. The bifurcation structure related to qualitative transitions caused by the SAW is analysed with particular attention on the {appearance and interplay of Hopf bifurcations where branches of time-periodic states emerge. The latter correspond to the regular shedding of liquid ridges from the meniscus. The obtained information is relevant to the entire class of dragged-film problems.
- Published
- 2021
14. Symmetry-breaking, motion and bistability of active drops through polarization-surface coupling
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Fenna Stegemerten, Karin John, and Uwe Thiele
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Physics::Fluid Dynamics ,Motion ,Biological Physics (physics.bio-ph) ,Soft Condensed Matter (cond-mat.soft) ,FOS: Physical sciences ,General Chemistry ,Physics - Biological Physics ,Myosins ,Condensed Matter - Soft Condensed Matter ,Condensed Matter Physics ,Cytoskeleton - Abstract
Cell crawling crucially depends on the collective dynamics of the acto-myosin cytoskeleton. However, it remains an open question to what extent cell polarization and persistent motion depend on continuous regulatory mechanisms and autonomous physical mechanisms. Experiments on cell fragments and theoretical considerations for active polar liquids have highlighted that physical mechanisms induce motility through splay and bend configurations in a nematic director field. Here, we employ a simple model, derived from basic thermodynamic principles, for active polar free-surface droplets to identify a different mechanism of motility. Namely, active stresses drive drop motion through spatial variations of polarization strength. This robustly induces parity-symmetry breaking and motility even for liquid ridges (2D drops) and adds to splay- and bend-driven pumping in 3D geometries. Intriguingly, then, stable polar moving and axisymmetric resting states may coexist, reminiscent of the interconversion of moving and resting keratocytes by external stimuli. The identified additional motility mode originates from a competition between the elastic bulk energy and the polarity control exerted by the drop surface. As it already breaks parity-symmetry for passive drops, the resulting back-forth asymmetry enables active stresses to effectively pump liquid and drop motion ensues., Comment: 9 pages 7 figures
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- 2021
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15. Two-dimensional localized states in an active phase-field-crystal model
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Uwe Thiele, Lukas Ophaus, Svetlana V. Gurevich, and Edgar Knobloch
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Physics ,FOS: Physical sciences ,Pattern Formation and Solitons (nlin.PS) ,Condensed Matter - Soft Condensed Matter ,01 natural sciences ,Instability ,Nonlinear Sciences - Pattern Formation and Solitons ,010305 fluids & plasmas ,Numerical continuation ,Mean field theory ,Crystal model ,0103 physical sciences ,Soft Condensed Matter (cond-mat.soft) ,Homoclinic orbit ,Statistical physics ,010306 general physics ,Bifurcation ,Multistability ,Linear stability - Abstract
The active phase-field-crystal (active PFC) model provides a simple microscopic mean field description of crystallization in active systems. It combines the PFC model (or conserved Swift-Hohenberg equation) of colloidal crystallization and aspects of the Toner-Tu theory for self-propelled particles. We employ the active PFC model to study the occurrence of localized and periodic active crystals in two spatial dimensions. Due to the activity, crystalline states can undergo a drift instability and start to travel while keeping their spatial structure. Based on linear stability analyses, time simulations and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of resting and traveling states. We explore, for instance, how the slanted homoclinic snaking of steady localized states found for the passive PFC model is modified by activity. The analysis is carried out for the model in two spatial dimensions. Morphological phase diagrams showing the regions of existence of various solution types are presented merging the results from all the analysis tools employed. We also study how activity influences the crystal structure with transitions from hexagons to rhombic and stripe patterns. This in-depth analysis of a simple PFC model for active crystals and swarm formation provides a clear general understanding of the observed multistability and associated hysteresis effects, and identifies thresholds for qualitative changes in behavior.
- Published
- 2020
16. Efficient calculation of phase coexistence and phase diagrams: application to a binary phase-field-crystal model
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Max Philipp Holl, Andrew J. Archer, and Uwe Thiele
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Physics ,Phase transition ,Maxwell construction ,Diagram ,Thermodynamics ,FOS: Physical sciences ,02 engineering and technology ,Condensed Matter - Soft Condensed Matter ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,01 natural sciences ,Thermodynamic system ,Numerical continuation ,Phase (matter) ,Metastability ,0103 physical sciences ,Soft Condensed Matter (cond-mat.soft) ,General Materials Science ,010306 general physics ,0210 nano-technology ,Phase diagram - Abstract
We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems described by a suitable free energy functional. In particular, this involves the determination of lines of phase coexistence related to first order phase transitions and the continuation of triple points. To illustrate the method we apply it to a binary phase-field-crystal model for the crystallisation of a mixture of two types of particles. The resulting phase diagram is determined for one- and two-dimensional domains. In the former case it is compared to the diagram obtained from a one-mode approximation. The various observed liquid and crystalline phases and their stable and metastable coexistence are discussed as well as the temperature-dependence of the phase diagrams. This includes the (dis)appearance of critical points and triple points. We also relate bifurcation diagrams for finite-size systems to the thermodynamics of phase transitions in the infinite-size limit.
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- 2020
17. Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling
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Jana Wrembel, Tobias Frohoff-Hülsmann, and Uwe Thiele
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Coupling ,Physics ,Conservation law ,FOS: Physical sciences ,Condensed Matter - Soft Condensed Matter ,01 natural sciences ,Instability ,010305 fluids & plasmas ,Nonlinear system ,Classical mechanics ,0103 physical sciences ,Homogeneous space ,Soft Condensed Matter (cond-mat.soft) ,010306 general physics ,Ternary operation ,Turing ,computer ,Bifurcation ,computer.programming_language - Abstract
We investigate a generic two-field Cahn-Hilliard model with variational and nonvariational coupling. It describes, for instance, passive and active ternary mixtures, respectively. Already a linear stability analysis of the homogeneous mixed state shows that activity not only allows for the usual large-scale stationary (Cahn-Hilliard) instability of the well-known passive case but also for small-scale stationary (Turing) and large-scale oscillatory (Hopf) instabilities. In consequence of the Turing instability, activity may completely suppress the usual coarsening dynamics. In a fully nonlinear analysis, we first briefly discuss the passive case before focusing on the active case. Bifurcation diagrams and selected direct time simulations are presented that allow us to establish that nonvariational coupling (i) can partially or completely suppress coarsening and (ii) may lead to the emergence of drifting and oscillatory states. Throughout, we emphasize the relevance of conservation laws and related symmetries for the encountered intricate bifurcation behavior.
- Published
- 2020
18. Adaptive stochastic continuation with a modified lifting procedure applied to complex systems
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Clemens Willers, Oliver Kamps, Uwe Thiele, David J. B. Lloyd, and Andrew J. Archer
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Computer science ,Complex system ,Microscopic level ,FOS: Physical sciences ,Observable ,Fixed point ,01 natural sciences ,Nonlinear Sciences - Adaptation and Self-Organizing Systems ,010305 fluids & plasmas ,Continuation ,Lattice (order) ,0103 physical sciences ,Applied mathematics ,Ising model ,010306 general physics ,Adaptation and Self-Organizing Systems (nlin.AO) ,Bifurcation - Abstract
Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on the level of macroscopic observables, one has to rely on equation-free methods like stochastic continuation. Here, we investigate how to improve stochastic continuation techniques by adaptively choosing the parameters of the algorithm. This allows one to obtain bifurcation diagrams quite accurately, especially near bifurcation points. We introduce lifting techniques which generate microscopic states with a naturally grown structure, which can be crucial for a reliable evaluation of macroscopic quantities. We show how to calculate fixed points of fluctuating functions by employing suitable linear fits. This procedure offers a simple measure of the statistical error. We demonstrate these improvements by applying the approach in analyses of (i) the Ising model in two dimensions, (ii) an active Ising model, and (iii) a stochastic Swift-Hohenberg model. We conclude by discussing the abilities and remaining problems of the technique.
- Published
- 2020
19. Thin-film modeling of resting and moving active droplets
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Sarah Trinschek, Karin John, Uwe Thiele, Fenna Stegemerten, DYnamique des Fluides COmplexes et Morphogénèse [Grenoble] (DYFCOM-LIPhy ), Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères] (LIPhy ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), and Campus France (PRO- COPE 2020 Grant No. 57511756), Studienstiftung des deutschen Volkes, doctoral school 'Active living fluids' funded by the German French University (Grant No. CDFA-01-14), and the DAAD
- Subjects
Materials science ,Drop (liquid) ,Surface force ,Contact line ,Fluid Dynamics (physics.flu-dyn) ,FOS: Physical sciences ,Physics - Fluid Dynamics ,Polarization (waves) ,01 natural sciences ,010305 fluids & plasmas ,Physics::Fluid Dynamics ,Biological Physics (physics.bio-ph) ,Chemical physics ,Free surface ,0103 physical sciences ,Polar ,Physics - Biological Physics ,Wetting ,Thin film ,010306 general physics ,[PHYS.COND.CM-SCM]Physics [physics]/Condensed Matter [cond-mat]/Soft Condensed Matter [cond-mat.soft] - Abstract
We propose a generic model for thin films and shallow drops of a polar active liquid that have a free surface and are in contact with a solid substrate. The model couples evolution equations for the film height and the local polarization profile in the form of a gradient dynamics supplemented with active stresses and fluxes. A wetting energy for a partially wetting liquid is incorporated allowing for motion of the liquid-solid-gas contact line. This gives a consistent basis for the description of drops of dense bacterial suspensions or compact aggregates of living cells on solid substrates. As example, we analyze the dynamics of two-dimensional active drops (i.e., ridges) and demonstrate how active forces compete with passive surface forces to shape droplets and drive contact line motion. The model reproduces moving and resting states of polarized droplets: Drops containing domains of opposite polarization are stationary and evolve after long transients into drops with a uniform polarization moving actively over the substrate. In our simple two-dimensional scenario droplet motion sets in at infinitely small self-propulsion force, i.e., it does not need to overcome a critical threshold., Comment: 17 pages, 16 figures
- Published
- 2020
20. Bifurcations of front motion in passive and active Allen-Cahn-type equations
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Fenna Stegemerten, Uwe Thiele, and Svetlana V. Gurevich
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Physics ,Field (physics) ,Applied Mathematics ,Mathematical analysis ,Front (oceanography) ,Fluid Dynamics (physics.flu-dyn) ,General Physics and Astronomy ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Physics - Fluid Dynamics ,Pattern Formation and Solitons (nlin.PS) ,Type (model theory) ,Bifurcation diagram ,01 natural sciences ,Nonlinear Sciences - Pattern Formation and Solitons ,010305 fluids & plasmas ,Continuation ,Simple (abstract algebra) ,0103 physical sciences ,Path (graph theory) ,010306 general physics ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematical Physics ,Bifurcation - Abstract
The well-known cubic Allen–Cahn (AC) equation is a simple gradient dynamics (or variational) model for a nonconserved order parameter field. After revising main literature results for the occurrence of different types of moving fronts, we employ path continuation to determine their bifurcation diagram in dependence of the external field strength or chemical potential. We then employ the same methodology to systematically analyze fronts for more involved AC-type models. In particular, we consider a cubic–quintic variational AC model and two different nonvariational generalizations. We determine and compare the bifurcation diagrams of front solutions in the four considered models.
- Published
- 2020
21. Phase-field crystal description of active crystallites: elastic and inelastic collisions
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Johannes Kirchner, Uwe Thiele, Svetlana V. Gurevich, and Lukas Ophaus
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Physics ,Condensed matter physics ,Plane (geometry) ,Applied Mathematics ,Inelastic collision ,General Physics and Astronomy ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Pattern Formation and Solitons (nlin.PS) ,Collision ,Nonlinear Sciences - Pattern Formation and Solitons ,01 natural sciences ,010305 fluids & plasmas ,0103 physical sciences ,Bound state ,Path (graph theory) ,Crystallite ,010306 general physics ,Focus (optics) ,Mathematical Physics ,Phase diagram - Abstract
The active Phase-Field-Crystal (aPFC) model combines elements of the Toner-Tu theory for self-propelled particles and the classical Phase-Field-Crystal (PFC) model that describes the transition between liquid to crystalline phases. In the liquid-crystal coexistence region of the PFC model, crystalline clusters exist in the form of localized states that coexist with the homogeneous background. At sufficiently strong self-propulsion strength (or activity) they start to travel. We employ numerical path continuation and direct time simulations to first investigate the existence regions of different types of localized states for a one-dimensional system. The results are summarized in morphological phase diagrams in the parameter plane spanned by activity and mean concentration. Then we focus on the interaction of traveling localized states studying their collision behavior. As a result we distinguish 'elastic' and 'inelastic' collisions. In the former, localized states recover their properties after a collision while in the latter they may annihilate or form resting or traveling bound states. In passing, we describe oscillating and modulated traveling localized states that have as the steadily traveling localized states no counterpart in the classical PFC model.
- Published
- 2020
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22. Localized states in passive and active phase-field-crystal models
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Max Philipp Holl, Svetlana V. Gurevich, Uwe Thiele, Andrew J. Archer, Lukas Ophaus, and Edgar Knobloch
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Physics ,Physics::Computational Physics ,Field (physics) ,Applied Mathematics ,Dynamics (mechanics) ,FOS: Physical sciences ,Condensed Matter - Soft Condensed Matter ,Polarization (waves) ,01 natural sciences ,010305 fluids & plasmas ,Crystal ,Coupling (physics) ,Numerical continuation ,Classical mechanics ,0103 physical sciences ,Soft Condensed Matter (cond-mat.soft) ,Homoclinic orbit ,010306 general physics ,Bifurcation - Abstract
The passive conserved Swift-Hohenberg equation (or phase-field-crystal [PFC] model) corresponds to a gradient dynamics for a single order parameter field related to density. It provides a simple microscopic description of the thermodynamic transition between liquid and crystalline states. In addition to spatially extended periodic structures, the model describes a large variety of steady spatially localized structures. In appropriate bifurcation diagrams the corresponding solution branches exhibit characteristic slanted homoclinic snaking. In an active PFC model, encoding for instance the active motion of self-propelled colloidal particles, the gradient dynamics structure is broken by a coupling between density and an additional polarization field. Then, resting and traveling localized states are found with transitions characterized by parity-breaking drift bifurcations. Here, we first briefly review the snaking behavior of localized states in passive and active PFC models before discussing the bifurcation behavior of localized states in systems of (i) two coupled passive PFC equations described by common gradient dynamics, (ii) two coupled passive PFC where the coupling breaks the gradient dynamics structure, and (iii) a passive PFC coupled to an active PFC., Comment: submitted to the IMA Journal of Applied Mathematics' Special Issue on Homoclinic Snaking at 21, in memory of Patrick Woods
- Published
- 2020
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23. Localized states in coupled Cahn-Hilliard equations
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Tobias Frohoff-Hülsmann and Uwe Thiele
- Subjects
Physics ,Conservation law ,Spinodal ,Applied Mathematics ,Drop (liquid) ,FOS: Physical sciences ,Pattern Formation and Solitons (nlin.PS) ,Condensed Matter - Soft Condensed Matter ,Nonlinear Sciences - Pattern Formation and Solitons ,01 natural sciences ,Instability ,010305 fluids & plasmas ,Coupling (physics) ,Classical mechanics ,Phase (matter) ,0103 physical sciences ,Soft Condensed Matter (cond-mat.soft) ,Homoclinic orbit ,010306 general physics ,Nonlinear Sciences::Pattern Formation and Solitons ,Bifurcation - Abstract
The classical Cahn–Hilliard (CH) equation corresponds to a gradient dynamics model that describes phase decomposition in a binary mixture. In the spinodal region, an initially homogeneous state spontaneously decomposes via a large-scale instability into drop, hole or labyrinthine concentration patterns of a typical structure length followed by a continuously ongoing coarsening process. Here, we consider the coupled CH dynamics of two concentration fields and show that non-reciprocal (or active or non-variational) coupling may induce a small-scale (Turing) instability. At the corresponding primary bifurcation, a branch of periodically patterned steady states emerges. Furthermore, there exist localized states that consist of patterned patches coexisting with a homogeneous background. The branches of steady parity-symmetric and parity-asymmetric localized states form a slanted homoclinic snaking structure typical for systems with a conservation law. In contrast to snaking structures in systems with gradient dynamics, here, Hopf instabilities occur at a sufficiently large activity, which results in oscillating and travelling localized patterns.
- Published
- 2020
- Full Text
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24. Recent advances in and future challenges for mesoscopic hydrodynamic modelling of complex wetting
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Uwe Thiele
- Subjects
Physics ,Mesoscopic physics ,Fluid Dynamics (physics.flu-dyn) ,FOS: Physical sciences ,Physics - Fluid Dynamics ,Condensed Matter - Soft Condensed Matter ,01 natural sciences ,010305 fluids & plasmas ,Physics::Fluid Dynamics ,Colloid and Surface Chemistry ,0103 physical sciences ,Soft Condensed Matter (cond-mat.soft) ,Wetting ,Statistical physics ,010306 general physics ,Energy functional - Abstract
We highlight some recent developments that widen the scope and reach of mesoscopic thin-film (or long-wave) hydrodynamic models employed to describe the dynamics of thin films, drops and contact lines of simple and complex liquids on solid substrates. The basis of the discussed developments is the reformulation of various mesoscopic thin-film hydrodynamic models as gradient dynamics on underlying energy functionals. After briefly presenting the general approach, the following sections discuss how to improve these models by amending the energy functional and the mobility function, how to obtain gradient dynamics models for some complex liquids, and how to incorporate processes beyond relaxational dynamics.
- Published
- 2018
25. Self-organized dip-coating patterns of simple, partially wetting, nonvolatile liquids
- Author
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Svetlana V. Gurevich, Uwe Thiele, Walter Tewes, and Markus Wilczek
- Subjects
Fluid Flow and Transfer Processes ,SIMPLE (dark matter experiment) ,Materials science ,Fluid Dynamics (physics.flu-dyn) ,Computational Mechanics ,FOS: Physical sciences ,Physics - Fluid Dynamics ,Substrate (printing) ,Ridge (differential geometry) ,01 natural sciences ,Dip-coating ,010305 fluids & plasmas ,Condensed Matter::Soft Condensed Matter ,Physics::Fluid Dynamics ,Liquid film ,Solid substrate ,Modeling and Simulation ,0103 physical sciences ,Meniscus ,Wetting ,Composite material ,010306 general physics - Abstract
When a solid substrate is withdrawn from a bath of simple, partially wetting, nonvolatile liquid, one typically distinguishes two regimes, namely, after withdrawal the substrate is macroscopically dry or homogeneously coated by a liquid film. In the latter case, the coating is called a Landau-Levich film. Its thickness depends on the angle and velocity of substrate withdrawal. We predict by means of a numerical and analytical investigation of a hydrodynamic thin-film model the existence of a third regime. It consists of the deposition of a regular pattern of liquid ridges oriented parallel to the meniscus. We establish that the mechanism of the underlying meniscus instability originates from competing film dewetting and Landau-Levich film deposition. Our analysis combines a marginal stability analysis, numerical time simulations and a numerical bifurcation study via path-continuation.
- Published
- 2019
26. On the multiple solutions of coating and rimming flows on rotating cylinders
- Author
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André Von Borries Lopes, Andrew L. Hazel, and Uwe Thiele
- Subjects
Materials science ,Mechanical Engineering ,engineering.material ,Condensed Matter Physics ,01 natural sciences ,Lubrication theory ,010305 fluids & plasmas ,Physics::Fluid Dynamics ,Coating ,Mechanics of Materials ,0103 physical sciences ,engineering ,Thin film ,Composite material ,010306 general physics - Abstract
We consider steady solutions of the Stokes equations for the flow of a film of fluid on the outer or inner surface of a cylinder that rotates with its axis perpendicular to the direction of gravity. We find that previously unobserved stable and unstable steady solutions coexist over an intermediate range of rotation rates for sufficiently high values of the Bond number (ratio of gravitational forces relative to surface tension). Furthermore, we compare the results of the Stokes calculations to the classic lubrication models of Pukhnachev (J. Appl. Mech. Tech. Phys., vol 18, 1977, pp. 344–351) and Reisfeld & Bankoff (J. Fluid Mech., vol. 236, 1992, pp. 167–196); an extended lubrication model of Benilov & O’Brien (Phys. Fluids, vol. 17, 2005, 052106) and Evans et al. (Phys. Fluids, vol. 16, 2004, pp. 2742–2756); and a new lubrication approximation formulated using gradient dynamics. We quantify the range of validity of each model and confirm that the gradient-dynamics model is most accurate over the widest range of parameters, but that the new steady solutions are not captured using any of the simplified models because they contain features that can only be described by the full Stokes equations.
- Published
- 2017
27. Effect of driving on coarsening dynamics in phase-separating systems
- Author
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Uwe Thiele, M. Alesemi, Dmitri Tseluiko, and Te-Sheng Lin
- Subjects
Convection ,Work (thermodynamics) ,Spinodal decomposition ,Applied Mathematics ,Chaotic ,FOS: Physical sciences ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Pattern Formation and Solitons (nlin.PS) ,Dynamical Systems (math.DS) ,Mechanics ,01 natural sciences ,Instability ,Nonlinear Sciences - Pattern Formation and Solitons ,010305 fluids & plasmas ,Phase (matter) ,0103 physical sciences ,FOS: Mathematics ,Symmetry breaking ,Mathematics - Dynamical Systems ,010306 general physics ,Cahn–Hilliard equation ,Mathematical Physics ,Mathematics - Abstract
We consider the Cahn–Hilliard (CH) equation with a Burgers-type convective term that is used as a model of coarsening dynamics in laterally driven phase-separating systems. In the absence of driving, it is known that solutions to the standard CH equation are characterized by an initial stage of phase separation into regions of one phase surrounded by the other phase (i.e. clusters or drops/holes or islands are obtained) followed by the coarsening process, where the average size of the structures grows in time and their number decreases. Moreover, two main coarsening modes have been identified in the literature, namely, coarsening due to volume transfer and due to translation. In the opposite limit of strong driving, the well-known Kuramoto–Sivashinsky equation is recovered, which may produce complicated chaotic spatio-temporal oscillations. The primary aim of the present work is to perform a detailed and systematic investigation of the transitions in the solutions of the convective CH equation for a wide range of parameter values, and, in particular, to understand in detail how the coarsening dynamics is affected by an increase of the strength of the lateral driving force. Considering symmetric two-drop states, we find that one of the coarsening modes is stabilized at relatively weak driving, and the type of the remaining mode may change as driving increases. Furthermore, there exist intervals in the driving strength where coarsening is completely stabilized. In the intervals where the symmetric two-drop states are unstable they can evolve, for example, into one-drop states, two-drop states of broken symmetry or even time-periodic two-drop states that consist of two traveling drops that periodically exchange mass. We present detailed stability diagrams for symmetric two-drop states in various parameter planes and corroborate our findings by selected time simulations.
- Published
- 2019
28. Correction to 'Equilibrium Contact Angle and Adsorption Layer Properties with Surfactants'
- Author
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Jacco H. Snoeijer, Uwe Thiele, Sarah Trinschek, and Karin John
- Subjects
Surface tension ,Contact angle ,Materials science ,Adsorption ,Pulmonary surfactant ,Electrochemistry ,Thermodynamics ,General Materials Science ,Surfaces and Interfaces ,Condensed Matter Physics ,Layer (electronics) ,Spectroscopy ,Line (formation) - Abstract
The last line in eq 27 on page 7213 should read (Formula Presented) In the caption for Figure 2a on page 7213 it should read (a) In the macroscopic approach, the equilibrium contact angle is determined by the solid-liquid interfacial tension γsl and the liquid-gas and solid-gas interfacial tensions γ and γ sg that depend on the respective surfactant concentrations Gd and Ga on the droplet and the adsorption layer. (Formula Presented).
- Published
- 2019
29. Effects of time-periodic forcing in a Cahn-Hilliard model for Langmuir-Blodgett transfer
- Author
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Phong-Minh Timmy Ly, Uwe Thiele, Svetlana V. Gurevich, and Lifeng Chi
- Subjects
Physics ,Time periodic ,FOS: Physical sciences ,Oblique case ,Pattern formation ,Geometry ,Pattern Formation and Solitons (nlin.PS) ,01 natural sciences ,Langmuir–Blodgett film ,Nonlinear Sciences - Pattern Formation and Solitons ,010305 fluids & plasmas ,Spatial direction ,0103 physical sciences ,Perpendicular ,010306 general physics ,Entrainment (chronobiology) - Abstract
The influence of a temporal forcing on the pattern formation in Langmuir-Blodgett transfer is studied employing a generalized Cahn-Hilliard model. The occurring frequency locking effects allow for controlling the pattern formation process. In the case of one-dimensional (i.e., stripe) patterns one finds various synchronization phenomena such as entrainment between the distance of deposited stripes and the forcing frequency. In two dimensions, the temporal forcing gives rise to the formation of intricate complex patterns such as vertical stripes, oblique stripes and lattice structures. Remarkably, it is possible to influence the system in the spatial direction perpendicular to the forcing direction leading to synchronization in two spatial dimensions., Added sentences in reference to remarks from editors and fixed numbering, formatting issues
- Published
- 2019
30. The collective behaviour of ensembles of condensing liquid drops on heterogeneous inclined substrates
- Author
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Uwe Thiele and Sebastian Engelnkemper
- Subjects
Mesoscopic physics ,Drop size ,Materials science ,Condensation ,Fluid Dynamics (physics.flu-dyn) ,FOS: Physical sciences ,General Physics and Astronomy ,Mechanics ,Substrate (electronics) ,Physics - Fluid Dynamics ,01 natural sciences ,Instability ,010305 fluids & plasmas ,Physics::Fluid Dynamics ,0103 physical sciences ,Outflow ,010306 general physics ,Stationary state ,Bifurcation - Abstract
Employing a long-wave mesoscopic hydrodynamic model for the film height evolution we study ensembles of pinned and sliding drops of a volatile liquid that continuously condense onto a chemically heterogeneous inclined substrate. Our analysis combines, on the one hand, path continuation techniques to determine bifurcation diagrams for the depinning of single drops of nonvolatile liquid on single hydrophilic spots on a partially wettable substrate and, on the other hand, time simulations of growth and depinning of individual condensing drops as well as of the long-time behaviour of large ensembles of such drops. Pinned drops grow on the hydrophilic spots, depin and slide along the substrate while merging with other pinned drops and smaller drops that slide more slowly, and possibly undergo a pearling instability. As a result, the collective behaviour converges to a stationary state where condensation and outflow balance. The main features of the emerging drop size distribution can then be related to single-drop bifurcation diagrams.
- Published
- 2019
31. Gradient dynamics model for drops spreading on polymer brushes
- Author
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Uwe Thiele and Simon Hartmann
- Subjects
Materials science ,Liquid drop ,General Physics and Astronomy ,FOS: Physical sciences ,02 engineering and technology ,Condensed Matter - Soft Condensed Matter ,010402 general chemistry ,Polymer brush ,01 natural sciences ,digestive system ,law.invention ,law ,medicine ,General Materials Science ,Physical and Theoretical Chemistry ,Energy functional ,chemistry.chemical_classification ,Drop (liquid) ,Fluid Dynamics (physics.flu-dyn) ,Brush ,Physics - Fluid Dynamics ,Polymer ,Mechanics ,021001 nanoscience & nanotechnology ,0104 chemical sciences ,chemistry ,Soft Condensed Matter (cond-mat.soft) ,Wetting ,Swelling ,medicine.symptom ,0210 nano-technology - Abstract
When a liquid drop spreads on an adaptive substrate the latter changes its properties what may result in an intricate coupled dynamics of drop and substrate. Here we present a generic mesoscale hydrodynamic model for such processes that is written as a gradient dynamics on an underlying energy functional. We specify the model details for the example of a drop spreading on a dry polymer brush. There, liquid absorption into the brush results in swelling of the brush causing changes in the brush topography and wettability. The liquid may also advance within the brush via diffusion (or wicking) resulting in coupled drop and brush dynamics. The specific model accounts for coupled spreading, absorption and wicking dynamics when the underlying energy functional incorporates capillarity, wettability and brush energy. After employing a simple version of such a model to numerically simulate a droplet spreading on a swelling brush we conclude with a discussion of possible model extensions.
- Published
- 2019
- Full Text
- View/download PDF
32. Two-dimensional patterns in dip coating - first steps on the continuation path
- Author
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Kevin David Joachim Mitas, Phong-Minh Timmy Ly, Uwe Thiele, and Svetlana V. Gurevich
- Subjects
Materials science ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Pattern Formation and Solitons (nlin.PS) ,Mechanics ,engineering.material ,Condensed Matter Physics ,Nonlinear Sciences - Pattern Formation and Solitons ,01 natural sciences ,Dip-coating ,010305 fluids & plasmas ,Physics::Fluid Dynamics ,Continuation ,Coating ,0103 physical sciences ,engineering ,Thin-film equation ,010306 general physics ,Nonlinear Sciences::Pattern Formation and Solitons ,Bifurcation - Abstract
We present a brief comparative investigation of the bifurcation structure related to the formation of two-dimensional deposition patterns as described by continuum models of Cahn–Hilliard type. These are, on the one hand a driven Cahn–Hilliard model for Langmuir–Blodgett transfer of a surfactant layer from the surface of a bath onto a moving plate and on the other hand a driven thin-film equation modelling the surface acoustic wave-driven coating of a plate by a simple liquid. In both cases, we present selected two-dimensional steady states corresponding to deposition patterns and discuss the main structure of the corresponding bifurcation diagrams.
- Published
- 2020
33. Continuation for Thin Film Hydrodynamics and Related Scalar Problems
- Author
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Hannes Uecker, Daniel Wetzel, Svetlana V. Gurevich, Uwe Thiele, and Sebastian Engelnkemper
- Subjects
Mathematical analysis ,Scalar (mathematics) ,Time evolution ,01 natural sciences ,010305 fluids & plasmas ,Physics::Fluid Dynamics ,Nonlinear system ,Continuation ,Numerical continuation ,0103 physical sciences ,Boundary value problem ,010306 general physics ,Nonlinear Sciences::Pattern Formation and Solitons ,Scalar field ,Bifurcation ,Mathematics - Abstract
This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution of a single scalar field like a density or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn–Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift–Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto–Sivashinsky equation, convective Allen–Cahn and Cahn–Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues.
- Published
- 2018
34. Resting and Traveling Localized States in an Active Phase-Field-Crystal Model
- Author
-
Svetlana V. Gurevich, Lukas Ophaus, and Uwe Thiele
- Subjects
Physics ,Field (physics) ,FOS: Physical sciences ,Pattern Formation and Solitons (nlin.PS) ,Nonlinear Sciences - Pattern Formation and Solitons ,01 natural sciences ,010305 fluids & plasmas ,law.invention ,Nonlinear system ,Numerical continuation ,Classical mechanics ,law ,Crystal model ,0103 physical sciences ,Homoclinic orbit ,Crystallization ,010306 general physics ,Bifurcation ,Linear stability - Abstract
The conserved Swift-Hohenberg equation (or phase-field-crystal [PFC] model) provides a simple microscopic description of the thermodynamic transition between fluid and crystalline states. Combining it with elements of the Toner-Tu theory for self-propelled particles, Menzel and Lowen [Phys. Rev. Lett. 110, 055702 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.055702] obtained a model for crystallization (swarm formation) in active systems. Here, we study the occurrence of resting and traveling localized states, i.e., crystalline clusters, within the resulting active PFC model. Based on linear stability analyses and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of periodic and localized, resting and traveling states in a one-dimensional active PFC model. This allows us, for instance, to explore how the slanted homoclinic snaking of steady localized states found for the passive PFC model is amended by activity. A particular focus lies on the onset of motion, where we show that it occurs either through a drift-pitchfork or a drift-transcritical bifurcation. A corresponding general analytical criterion is derived.
- Published
- 2018
- Full Text
- View/download PDF
35. Modelling of surfactant-driven front instabilities in spreading bacterial colonies
- Author
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Karin John, Sarah Trinschek, Uwe Thiele, LIPHY-DYFCOM, Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères] (LIPhy), Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematical Sciences [Loughborough], and Loughborough University
- Subjects
Materials science ,FOS: Physical sciences ,Condensed Matter - Soft Condensed Matter ,Surface concentration ,01 natural sciences ,Instability ,Models, Biological ,010305 fluids & plasmas ,Surface tension ,Surface-Active Agents ,Pulmonary surfactant ,0103 physical sciences ,Physics - Biological Physics ,010306 general physics ,Marangoni effect ,Bacteria ,Front (oceanography) ,Substrate (chemistry) ,General Chemistry ,Condensed Matter Physics ,Chemical physics ,Biological Physics (physics.bio-ph) ,Wettability ,Soft Condensed Matter (cond-mat.soft) ,Wetting ,[PHYS.COND.CM-SCM]Physics [physics]/Condensed Matter [cond-mat]/Soft Condensed Matter [cond-mat.soft] - Abstract
International audience; The spreading of bacterial colonies at solid-air interfaces is determined by the physico-chemical properties of the involved interfaces. The production of surfactant molecules by bacteria is a widespread strategy that allows the colony to efficiently expand over the substrate. On the one hand, surfactant molecules lower the surface tension of the colony, effectively increasing the wettability of the substrate, which facilitates spreading. On the other hand, gradients in the surface concentration of surfactant molecules result in Marangoni flows that drive spreading. These flows may cause an instability of the circular colony shape and the subsequent formation of fingers. In this work, we study the effect of bacterial surfactant production and substrate wettability on colony growth and shape within the framework of a hydrodynamic thin film model. We show that variations in the wettability and surfactant production are sufficient to reproduce four different types of colony growth, which have been described in the literature, namely, arrested and continuous spreading of circular colonies, slightly modulated front lines and the formation of pronounced fingers.
- Published
- 2018
- Full Text
- View/download PDF
36. Connecting monotonic and oscillatory motions of the meniscus of a volatile polymer solution to the transport of polymer coils and deposit morphology
- Author
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Ofer Manor, Uwe Thiele, Anna Zigelman, Mohammad Abo Jabal, and Ala Egbaria
- Subjects
Morphology (linguistics) ,Materials science ,Evaporation ,FOS: Physical sciences ,02 engineering and technology ,Condensed Matter - Soft Condensed Matter ,01 natural sciences ,Physics::Fluid Dynamics ,chemistry.chemical_compound ,0103 physical sciences ,Electrochemistry ,Deposition (phase transition) ,General Materials Science ,Physics::Chemical Physics ,Methyl methacrylate ,010306 general physics ,Spectroscopy ,Phase diagram ,chemistry.chemical_classification ,Surfaces and Interfaces ,Polymer ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,Toluene ,Condensed Matter::Soft Condensed Matter ,chemistry ,Chemical physics ,Meniscus ,Soft Condensed Matter (cond-mat.soft) ,0210 nano-technology - Abstract
We study the deposition mechanisms of polymer from a confined meniscus of volatile liquid. In particular, we investigate the physical processes that are responsible for qualitative changes in the pattern deposition of polymer and the underlying interplay of the state of pattern deposition, motion of the meniscus, and the transport of polymer within the meniscus. As a model system we evaporate a solution of poly(methyl methacrylate) (PMMA) in toluene. Different deposition patterns are observed when varying the molecular mass, the initial concentration of the solute, and temperature; these are systematically presented in the form of morphological phase diagrams. The modi of deposition and meniscus motion are correlated. They vary with the ratio between the evaporation-driven convective flux and the diffusive flux of the polymer coils in the solution. In the case of a diffusion-dominated solute transport, the solution monotonically dewets the solid substrate by evaporation, supporting continuous contact line motion and continuous polymer deposition. However, a convection-dominated transport results in an oscillatory ratcheting dewetting-wetting motion of the contact line with more pronounced dewetting phases. The deposition process is then periodic and produces a stripe pattern. The oscillatory motion of the meniscus differs from the well documented stick-slip motion of the meniscus, observed as well, and is attributed to the opposing influences of evaporation and Marangoni stresses, which alternately dominate the deposition process.
- Published
- 2018
- Full Text
- View/download PDF
37. Modelling Pattern Formation in Dip-Coating Experiments
- Author
-
Michael H. Köpf, Walter Tewes, Uwe Thiele, Markus Wilczek, Lifeng Chi, and Svetlana V. Gurevich
- Subjects
Materials science ,Mathematical model ,Applied Mathematics ,FOS: Physical sciences ,35Q35, 65Z05 ,Pattern formation ,Pattern Formation and Solitons (nlin.PS) ,Mechanics ,Substrate (printing) ,Condensed Matter - Soft Condensed Matter ,Nonlinear Sciences - Pattern Formation and Solitons ,Dip-coating ,Modeling and Simulation ,Soft Condensed Matter (cond-mat.soft) ,Thin-film equation ,Focus (optics) ,Cahn–Hilliard equation - Abstract
We briefly review selected mathematical models that describe the dynamics of pattern formation phenomena in dip-coating and Langmuir-Blodgett transfer experiments, where solutions or suspensions are transferred onto a substrate producing patterned deposit layers with structure length from hundreds of nanometres to tens of micrometres. The models are presented with a focus on their gradient dynamics formulations that clearly shows how the dynamics is governed by particular free energy functionals and facilitates the comparison of the models. In particular, we include a discussion of models based on long-wave hydrodynamics as well as of more phenomenological models that focus on the pattern formation processes in such systems. The models and their relations are elucidated and examples of resulting patterns are discussed before we conclude with a discussion of implications of the gradient dynamics formulation and of some related open issues.
- Published
- 2015
38. An introduction to inhomogeneous liquids, density functional theory, and the wetting transition
- Author
-
Adam P. Hughes, Andrew J. Archer, and Uwe Thiele
- Subjects
Physics ,Surface tension ,Density distribution ,Wetting transition ,Lattice (order) ,General Physics and Astronomy ,Density functional theory ,Ising model ,Statistical mechanics ,Wetting ,Statistical physics - Abstract
Classical density functional theory (DFT) is a statistical mechanical theory for calculating the density profiles of the molecules in a liquid. It is widely used, for example, to study the density distribution of the molecules near a confining wall, the interfacial tension, wetting behavior, and many other properties of nonuniform liquids. DFT can, however, be somewhat daunting to students entering the field because of the many connections to other areas of liquid-state science that are required and used to develop the theories. Here, we give an introduction to some of the key ideas, based on a lattice-gas (Ising) model fluid. This approach builds on knowledge covered in most undergraduate statistical mechanics and thermodynamics courses, so students can quickly get to the stage of calculating density profiles, etc., for themselves. We derive a simple DFT for the lattice gas and present some typical results that can readily be calculated using the theory.
- Published
- 2014
39. Continuous versus Arrested Spreading of Biofilms at Solid-Gas Interfaces: The Role of Surface Forces
- Author
-
Karin John, Uwe Thiele, Sigolene Lecuyer, Sarah Trinschek, LIPHY-DYFCOM, Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères] (LIPhy), Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Department of Mathematical Sciences [Loughborough], Loughborough University, and Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)
- Subjects
0301 basic medicine ,Osmosis ,Solid gas ,Materials science ,Surface Properties ,Surface force ,Biofilm ,General Physics and Astronomy ,02 engineering and technology ,Models, Theoretical ,biochemical phenomena, metabolism, and nutrition ,021001 nanoscience & nanotechnology ,Surface tension ,03 medical and health sciences ,030104 developmental biology ,Chemical physics ,Biofilms ,Wettability ,Wetting ,0210 nano-technology ,[PHYS.COND.CM-SCM]Physics [physics]/Condensed Matter [cond-mat]/Soft Condensed Matter [cond-mat.soft] ,ComputingMilieux_MISCELLANEOUS ,Bacillus subtilis - Abstract
We introduce and analyze a model for osmotically spreading bacterial colonies at solid-air interfaces that includes wetting phenomena, i.e., surface forces. The model is based on a hydrodynamic description for liquid suspensions which is supplemented by bioactive processes. We show that surface forces determine whether a biofilm can expand laterally over a substrate and provide experimental evidence for the existence of a transition between continuous and arrested spreading for Bacillus subtilis biofilms. In the case of arrested spreading, the lateral expansion of the biofilm is confined, albeit the colony is biologically active. However, a small reduction in the surface tension of the biofilm is sufficient to induce spreading. The incorporation of surface forces into our hydrodynamic model allows us to capture this transition in biofilm spreading behavior.
- Published
- 2017
40. Collective Cell Migration in Embryogenesis Follows the Laws of Wetting
- Author
-
Sarah Trinschek, Uwe Thiele, Timo Betz, Sargon Yigit, and Bernhard Wallmeyer
- Subjects
0301 basic medicine ,Physics ,Work (thermodynamics) ,Tension (physics) ,Dynamics (mechanics) ,Biophysics ,Epiboly ,Embryonic Development ,Mechanics ,01 natural sciences ,Interfacial Force ,Models, Biological ,Surface tension ,Contact angle ,03 medical and health sciences ,030104 developmental biology ,Cell Movement ,Cell Biophysics ,0103 physical sciences ,Wettability ,Wetting ,010306 general physics - Abstract
Collective cell migration is a fundamental process during embryogenesis and its initial occurrence, called epiboly, is an excellent in vivo model to study the physical processes involved in collective cell movements that are key to understanding organ formation, cancer invasion, and wound healing. In zebrafish, epiboly starts with a cluster of cells at one pole of the spherical embryo. These cells are actively spreading in a continuous movement toward its other pole until they fully cover the yolk. Inspired by the physics of wetting, we determine the contact angle between the cells and the yolk during epiboly. By choosing a wetting approach, the relevant scale for this investigation is the tissue level, which is in contrast to other recent work. Similar to the case of a liquid drop on a surface, one observes three interfaces that carry mechanical tension. Assuming that interfacial force balance holds during the quasi-static spreading process, we employ the physics of wetting to predict the temporal change of the contact angle. Although the experimental values vary dramatically, the model allows us to rescale all measured contact-angle dynamics onto a single master curve explaining the collective cell movement. Thus, we describe the fundamental and complex developmental mechanism at the onset of embryogenesis by only three main parameters: the offset tension strength, α, that gives the strength of interfacial tension compared to other force-generating mechanisms; the tension ratio, δ, between the different interfaces; and the rate of tension variation, λ, which determines the timescale of the whole process.
- Published
- 2017
41. Nudged elastic band calculation of the binding potential for liquids at interfaces
- Author
-
Svetlana V. Gurevich, Walter Tewes, Andreas Heuer, Andrew J. Archer, Oleg Buller, and Uwe Thiele
- Subjects
Materials science ,Statistical Mechanics (cond-mat.stat-mech) ,010304 chemical physics ,FOS: Physical sciences ,General Physics and Astronomy ,Binding potential ,Thermodynamics ,Lattice density functional theory ,Condensed Matter - Soft Condensed Matter ,01 natural sciences ,Liquid film ,0103 physical sciences ,Soft Condensed Matter (cond-mat.soft) ,Wetting ,Physical and Theoretical Chemistry ,Microscopic theory ,010306 general physics ,Condensed Matter - Statistical Mechanics - Abstract
The wetting behavior of a liquid on solid substrates is governed by the nature of the effective interaction between the liquid-gas and the solid-liquid interfaces, which is described by the binding or wetting potential $g(h)$ which is an excess free energy per unit area that depends on the liquid film height $h$. Given a microscopic theory for the liquid, to determine $g(h)$ one must calculate the free energy for liquid films of any given value of $h$; i.e. one needs to create and analyze out-of-equilibrium states, since at equilibrium there is a unique value of $h$, specified by the temperature and chemical potential of the surrounding gas. Here we introduce a Nudged Elastic Band (NEB) approach to calculate $g(h)$ and illustrate the method by applying it in conjunction with a microscopic lattice density functional theory for the liquid. We show too that the NEB results are identical to those obtained with an established method based on using a fictitious additional potential to stabilize the non-equilibrium states. The advantages of the NEB approach are discussed., 5 pages, 2 figures
- Published
- 2017
42. Patterns and pathways in nanoparticle self-organization
- Author
-
Uwe Thiele, Bosiljka Tadić, Matthew O. Blunt, C. P. Martin, Emmanuelle Pauliac-Vaujour, Milovan Šuvakov, Ioan Vancea, Philip Moriarty, and Andrew Stannard
- Subjects
Self-organization ,Materials science ,Nanoparticle ,Nanotechnology ,Self-assembly - Abstract
This article reviews relatively recent forms of self-assembly and self-organization that have demonstrated particular potential for the assembly of nanostructured matter, namely biorecognition and solvent-mediated dynamics. It first considers the key features of self-assembled and self-organized nanoparticle arrays, focusing on the self-assembly of nanoparticle superlattices, the use of biorecognition for nanoparticle assembly, and self-organizing nanoparticles. It then describes the mechanisms and pathways for charge transport in nanoparticle assemblies, with particular emphasis on the relationship between the current–voltage characteristics and the topology of the lattice. It also discusses single-electron conduction in nanoparticle films as well as pattern formation and self-organization in dewetting nanofluids.
- Published
- 2017
43. Sliding drops - ensemble statistics from single drop bifurcations
- Author
-
Markus Wilczek, Sebastian Engelnkemper, Walter Tewes, Svetlana V. Gurevich, and Uwe Thiele
- Subjects
Physics ,Coalescence (physics) ,Drop size ,Break-Up ,Drop (liquid) ,Fluid Dynamics (physics.flu-dyn) ,General Physics and Astronomy ,FOS: Physical sciences ,Statistical model ,Mechanics ,Physics - Fluid Dynamics ,Bifurcation diagram ,01 natural sciences ,010305 fluids & plasmas ,010101 applied mathematics ,Physics::Fluid Dynamics ,Classical mechanics ,0103 physical sciences ,Evolution equation ,0101 mathematics ,Stationary state - Abstract
Ensembles of interacting drops that slide down an inclined plate show a dramatically different coarsening behavior as compared to drops on a horizontal plate: As drops of different size slide at different velocities, frequent collisions result in fast coalescence. However, above a certain size individual sliding drops are unstable and break up into smaller drops. Therefore, the long-time dynamics of a large drop ensemble is governed by a balance of merging and splitting. We employ a long-wave film height evolution equation and determine the dynamics of the drop size distribution towards a stationary state from direct numerical simulations on large domains. The main features of the distribution are then related to the bifurcation diagram of individual drops obtained by numerical path continuation. The gained knowledge allows us to develop a Smoluchowski-type statistical model for the ensemble dynamics that well compares to full direct simulations.
- Published
- 2017
- Full Text
- View/download PDF
44. Nonequilibrium Gibbs’ Criterion for Completely Wetting Volatile Liquids
- Author
-
Yannis Tsoumpas, Uwe Thiele, Heidi Ottevaere, Sam Dehaeck, Mariano Galvagno, Alexey Rednikov, Pierre Colinet, Applied Physics and Photonics, and Brussels Photonics Team
- Subjects
Total internal reflection ,Materials science ,Contact line ,Fluid Dynamics (physics.flu-dyn) ,Evaporation ,FOS: Physical sciences ,Non-equilibrium thermodynamics ,Thermodynamics ,CONTACT ANGLES ,EVAPORATING DROPLETS ,Physics - Fluid Dynamics ,Surfaces and Interfaces ,RESISTANCE ,SURFACES ,LINE ,Condensed Matter Physics ,Critical value ,Contact angle ,Electrochemistry ,General Materials Science ,Wetting ,Spectroscopy ,Line (formation) - Abstract
During the spreading of a liquid over a solid substrate, the contact line can stay pinned at sharp edges until the contact angle exceeds a critical value. At (or sufficiently near) equilibrium, this is known as Gibbs' criterion. Here, we show both experimentally and theoretically that, for completely wetting volatile liquids, there also exists a dynamically-produced contribution to the critical angle for depinning, which increases with the evaporation rate. This suggests that one may introduce a simple modification of the Gibbs' criterion for (de)pinning that accounts for the nonequilibrium effect of evaporation.
- Published
- 2014
45. Morphological transitions of sliding drops: Dynamics and bifurcations
- Author
-
Uwe Thiele, Sebastian Engelnkemper, Svetlana V. Gurevich, and Markus Wilczek
- Subjects
Fluid Flow and Transfer Processes ,Physics ,Hopf bifurcation ,Fluid Dynamics (physics.flu-dyn) ,Computational Mechanics ,FOS: Physical sciences ,Physics - Fluid Dynamics ,Mechanics ,Breakup ,Bifurcation diagram ,01 natural sciences ,Instability ,010305 fluids & plasmas ,Physics::Fluid Dynamics ,symbols.namesake ,Hysteresis ,Cascade ,Modeling and Simulation ,0103 physical sciences ,symbols ,010306 general physics ,Focus (optics) ,Linear stability - Abstract
We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we focus on qualitative changes in the morphology and behavior of stationary sliding drops. We employ the inclination angle of the substrate as control parameter and use continuation techniques to analyze for several fixed droplet sizes the bifurcation diagram of stationary droplets, their linear stability, and relevant eigenmodes. The obtained predictions on existence ranges and instabilities are tested via direct numerical simulations that are also used to investigate a branch of time-periodic behavior (corresponding to repeated breakup-coalescence cycles, where the breakup is also denoted as pearling) which emerges at a global instability, the related hysteresis in behavior, and a period-doubling cascade. The nontrivial oscillatory behavior close to a Hopf bifurcation of drops with a finite-length tail is also studied. Finally, it is shown that the main features of the bifurcation diagram follow scaling laws over several decades of the droplet size.
- Published
- 2016
46. Films, layers and droplets: The effect of near-wall fluid structure on spreading dynamics
- Author
-
Uwe Thiele, Hanyu Yin, Andrew J. Archer, and David N. Sibley
- Subjects
Thin layers ,Diffusion equation ,Materials science ,Statistical Mechanics (cond-mat.stat-mech) ,Fluid Dynamics (physics.flu-dyn) ,FOS: Physical sciences ,02 engineering and technology ,Physics - Fluid Dynamics ,Condensed Matter - Soft Condensed Matter ,021001 nanoscience & nanotechnology ,01 natural sciences ,Surface tension ,Physics::Fluid Dynamics ,Condensed Matter::Soft Condensed Matter ,Adsorption ,Chemical physics ,0103 physical sciences ,Lubrication ,Soft Condensed Matter (cond-mat.soft) ,Wetting ,010306 general physics ,0210 nano-technology ,Hydrodynamic theory ,Layer (electronics) ,Condensed Matter - Statistical Mechanics - Abstract
We present a study of the spreading of liquid droplets on a solid substrate at very small scales. We focus on the regime where effective wetting energy (binding potential) and surface tension effects significantly influence steady and spreading droplets. In particular, we focus on strong packing and layering effects in the liquid near the substrate due to underlying density oscillations in the fluid caused by attractive substrate-liquid interactions. We show that such phenomena can be described by a thin-film (or long-wave or lubrication) model including an oscillatory Derjaguin (or disjoining/conjoining) pressure, and explore the effects it has on steady droplet shapes and the spreading dynamics of droplets on both, an adsorption (or precursor) layer and completely dry substrates. At the molecular scale, commonly used two-term binding potentials with a single preferred minimum controlling the adsorption layer height are inadequate to capture the rich behaviour caused by the near-wall layered molecular packing. The adsorption layer is often sub-monolayer in thickness, i.e., the dynamics along the layer consists of single-particle hopping, leading to a diffusive dynamics, rather than the collective hydrodynamic motion implicit in standard thin-film models. We therefore modify the model in such a way that for thicker films the standard hydrodynamic theory is realised, but for very thin layers a diffusion equation is recovered., 17 pages, 21 figures
- Published
- 2016
47. Modelling spreading dynamics of nematic liquid crystals in three spatial dimensions
- Author
-
Lou Kondic, Uwe Thiele, Linda Cummings, and Te-Sheng Lin
- Subjects
Yield (engineering) ,Materials science ,Mechanical Engineering ,Fluid Dynamics (physics.flu-dyn) ,FOS: Physical sciences ,Anchoring ,Physics - Fluid Dynamics ,Mechanics ,Substrate (electronics) ,Condensed Matter - Soft Condensed Matter ,Condensed Matter Physics ,01 natural sciences ,Parabolic partial differential equation ,010305 fluids & plasmas ,Condensed Matter::Soft Condensed Matter ,Nonlinear system ,Mechanics of Materials ,Liquid crystal ,Free surface ,0103 physical sciences ,Soft Condensed Matter (cond-mat.soft) ,010306 general physics ,Scaling - Abstract
We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth-order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The influence of elastic distortion energy and of imposed anchoring variations at the substrate are explored through linear stability analysis and scaling arguments, which yield useful insight and predictions for the behaviour of spreading droplets. This behaviour is captured by fully nonlinear time-dependent simulations of three-dimensional droplets spreading in the presence of anchoring variations that model simple defects in the nematic orientation at the substrate.
- Published
- 2013
48. Effect of Au Nanoparticle Spatial Distribution on the Stability of Thin Polymer Films
- Author
-
Colm O'Dwyer, Ullrich Steiner, David Corcoran, George Amarandei, Uwe Thiele, and Arousian Arshak
- Subjects
musculoskeletal diseases ,chemistry.chemical_classification ,Spinodal ,Materials science ,Dewetting ,technology, industry, and agriculture ,Nanoparticle ,Nanotechnology ,Surfaces and Interfaces ,Polymer ,Condensed Matter Physics ,Stability (probability) ,Solid substrate ,chemistry ,Colloidal gold ,Thin polymer film ,Electrochemistry ,Gold nanoparticles ,General Materials Science ,sense organs ,Stability ,Spectroscopy - Abstract
The stability of thin poly(methyl-methacrylate) (PMMA) films of low molecular weight on a solid substrate is controlled by the areal coverage of gold nanoparticles (NPs) present at the air-polymer interface. As the polymer becomes liquid the Au NPs are free to diffuse, coalesce, and aggregate while the polymer film can change its morphology through viscous flow. These processes lead at the same time to the formation of a fractal network of Au NPs and to the development of spinodal instabilities of the free surface of the polymer films. For thinner films a single wavelength is observed, while for thicker films two wavelengths compete. With continued heating the aggregation process results in a decrease in coverage, the networks evolve into disordered particle assemblies, while the polymer films flatten again. The disordering occurs first on the smallest scales and coincides (in thicker films) with the disappearance of the smaller wavelength. The subsequent disordering on larger scales causes the films to flatten.
- Published
- 2013
49. A homotopy continuation approach for analysing finite-time singularities in thin liquid films
- Author
-
Uwe Thiele, Josh Baxter, and Dmitri Tseluiko
- Subjects
Surface tension ,symbols.namesake ,Planar ,Applied Mathematics ,Homotopy ,Numerical analysis ,Free surface ,Mathematical analysis ,symbols ,Gravitational singularity ,van der Waals force ,Bifurcation ,Mathematics - Abstract
We consider self-similar solutions related to rupture of thin liquid films on a solid substrate that evolve solely under the stabilizing influence of surface tension and the destabilizing influence of effective van der Waals interactions between the free surface of the film and the substrate. Such solutions have been previously analysed in the literature and various numerical approaches to obtain such solutions have been proposed. Such approaches are based either on shooting or finite-difference schemes and require well-chosen initial guesses for solutions. We propose an alternative numerical method, which is based on a homotopy approach and continuation techniques and allows one to reach self-similar solutions from analytically known small-amplitude steady solutions of the related thin-film equation. We argue that this method is more robust than previously proposed methods and does not require initial guesses to obtain solutions. Although the present study focuses on the particular case of self-similar solutions related to planar rupture that have square-root far-field behaviour, our approach can also be used to obtain planar solutions having a different far-field behaviour and radially symmetric self-similar solutions for the considered thin-film equation. We expect the approach to be also valid for other equations of similar type that show a subcritical primary bifurcation and finite-time singularities.
- Published
- 2013
50. Two-dimensional steady states in off-critical mixtures with high interface tension
- Author
-
Santiago Madruga, Uwe Thiele, and Fathi Bribesh
- Subjects
Materials science ,Tension (physics) ,General Physics and Astronomy ,Oblique case ,Nanotechnology ,Function (mathematics) ,Bifurcation diagram ,01 natural sciences ,Molecular physics ,010305 fluids & plasmas ,Solid substrate ,Free surface ,0103 physical sciences ,General Materials Science ,Polymer blend ,Physical and Theoretical Chemistry ,010306 general physics ,Layer (electronics) - Abstract
We present 2D steady concentration profiles of confined layers of off-critical polymer blends. The layer rests on a solid substrate and has a flat free surface due to very high surface tension. The profiles correspond to non-linear steady solutions of the Cahn-Hilliard equation in a rectangular domain. The free polymer-gas interface is considered to be sharp, while the internal interfaces are diffuse. We explore the rich solution structure (including laterally structured layers, stratified layers, checkerboard structures, oblique states and droplets) as a function of mean concentration.
- Published
- 2013
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