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The barrier heights in Ti/ and Ni/n-SiC Schottky barrier diodes (SBDs) in a wide range of the donor density (N d = 2 × 1017–1 × 1019 cm−3) were investigated. The forward current–voltage characteristics in the heavily-doped SBDs (N d > 2 × 1017 cm−3) are described by the thermionic field emission (TFE) model, which includes an electron tunneling induced by the high electric field (> MV cm−1) at the Schottky interface. The high electric field also causes significant image force lowering (Δϕ ∼ 0.2 eV) in the heavily-doped SBDs (N d = 1 × 1019 cm−3). Through the analysis carefully considering such strong image force lowering, the same slope of the barrier height versus the metal work function plot (S ∼ 0.7) is obtained regardless of N d. This indicates that metal/SiC interfaces are nearly free from Fermi-level pinning independent of N d.

In this paper, by considering higher-order effects of residual attachment modes, a new free-interface component mode synthesis (CMS) method is developed for non-classically damped systems. Firstly, based on the Neumann expansion, the higher-order effects of the residual attachment modes are accurately expressed by the available lower-order modes and the system matrices. Secondly, by using the residual attachment modes and complex modes, the non-classically damped subcomponents are reduced and assembled in the physical space instead of the frequently-used state-space. Then, the new free-interface CMS method is derived and solved built on a frequency shifting technique and an iteration method. Finally, the performances of the presented method are illustrated by two numerical examples and compared with other first- and second-order approximated CMS methods. The results indicate that the presented CMS method for the non-classically damped systems is more accurate than other methods and suitable for the case when both high- and low-order modes are truncated.

We consider the two dimensional gravity water wave equation in a regime where the free interface is allowed to be non-$C^1$. In this regime, only a degenerate Taylor inequality $-\frac{\partial P}{\partial \bf n}\ge 0$ holds, with degeneracy at the singularities. In \cite{kw} an energy functional $\mathcal E(t)$ was constructed and an a-prori estimate was proved. The energy functional $\mathcal E(t)$ is not only finite for interfaces and velocities in Sobolev spaces, but also finite for a class of non-$C^1$ interfaces with angled crests. In this paper we prove the existence, uniqueness and stability of the solution of the 2d gravity water wave equation in the class where $\mathcal E(t), Comment: 81 pages

The paper is devoted to the problem of non-stationary motion of two viscous incompressible fluids separated by a free surface and contained in a bounded vessel. It is assumed that the fluids are subject to mass forces and capillary forces at the interface. We prove the stability of a rest state under the assumption that initial velocities are small, a free interface is close to a sphere at an initial instant of time, and mass forces decay as $t\to\infty$.

In this paper we revisit the derivation of a nonlocal interfacial Hamiltonian model for systems with short-ranged intermolecular forces. Starting from a microscopic Landau-Ginzburg-Wilson Hamiltonian with a double parabola potential, we reformulate the derivation of the interfacial model using a rigorous boundary integral approach. This is done for three scenarios: a single fluid phase in contact with a nonplanar substrate (i.e., wall); a free interface separating coexisting fluid phases (say, liquid and gas); and finally a liquid-gas interface in contact with a nonplanar confining wall, as is applicable to wetting phenomena. For the first two cases our approaches identifies the correct form of the curvature corrections to the free energy and, for the case of a free interface, it allows us to recast these as an interfacial self-interaction as conjectured previously in the literature. When the interface is in contact with a substrate our approach similarly identifies curvature corrections to the nonlocal binding potential, describing the interaction of the interface and wall, for which we propose a generalized and improved diagrammatic formulation., 31 pages, 2 figures, version published in Physical Review E

This chapter reviews the recent activity on the study of glass dynamics in polymers subjected to geometrical confinement. Special attention is dedicated to glassy dynamics in thin polymer films. Nonetheless, other kind of confinement, such as polymer nanocomposites and nanospheres, are dealt with. In this context, it is shown how calorimetric techniques contributed to significant advancement in the topic. After introducing the established phenomenology and the recent findings on the glass transition, the factors that affect the nonequilibrium glass dynamics in confinement, that is, the glass transition temperature (Tg) and the physical aging, are discussed. In light of numerous experimental evidences, it is remarked how arguments exclusively based on the alteration of the rate of spontaneous fluctuations are insufficient to catch the behavior of nonequilibrium dynamics. The role of free interfaces, not enslaved by underlying adsorbed layers, is emphasized for the comprehension of the ability of confined polymer glasses to maintain equilibrium when cooled—testified by a reduction Tg—and accelerated equilibrium recovery in the glassy state. Given the fact that these results imply that confined systems with large free interface are able to access low energy states in short-time scales, the final part of the chapter is dedicated to recent advancements toward the clarification of questions of paramount importance in glass science. In particular, the experimental evidence for the existence of the ideal glass transition is discussed.

Surface freezing is a phenomenon in which crystallization is enhanced at a vapor-liquid interface. In some systems, such as $n$-alkanes, this enhancement is dramatic, and results in the formation of a crystalline layer at the free interface even at temperatures slightly above the equilibrium bulk freezing temperature. There are, however, systems in which the enhancement is purely kinetic, and only involves faster nucleation at or near the interface. The first, thermodynamic, type of surface freezing is easier to confirm in experiments, requiring only the verification of the existence of crystalline order at the interface. The second, kinetic, type of surface freezing is far more difficult to prove experimentally. One material that is suspected of undergoing the second type of surface freezing is liquid water. Despite strong indications that the freezing of liquid water is kinetically enhanced at vapor-liquid interfaces, the findings are far from conclusive, and the topic remains controversial. In this perspective, we present a simple thermodynamic framework to understand conceptually and distinguish these two types of surface freezing. We then briefly survey fifteen years of experimental and computational work aimed at elucidating the surface freezing conundrum in water., 14 pages, 8 figures

We report experiments where a viscoelastic fingering instability develops at the free interface between air and a model viscoelastic fluid confined in a Hele-Shaw cell. The fluid is symmetrically stretched with constant velocity along two opposite directions, leading to the inflation of a two-dimensional air bubble growing from a millimetric centered hole. The instability is observed when the circumferential stretch of the inflating bubble reaches a threshold that depends on the viscoelastic properties of the fluid through the ratio of the material relaxation time to the time elapsed before the fingers start to develop. The critical stretch of the bulk fingering instability of a stretchable elastic solid [B. Saintyves, O. Dauchot, and E. Bouchaud, “Bulk elastic fingering instability in Hele-Shaw cells,” Phys. Rev. Lett. 111, 047801 (2013)] is recovered for large values of this ratio.

A periodic array of interface cracks is subjected to a uniform heat flow in the far field. The crack opening displacements and complex stress intensity factors are determined, using analytic function theory, for the case that the upper half-space is less distortive than the lower half-space.

This paper reports on the development of a new transformation method. In contrast to most existing mode transformation methods in which the first-order state-space equation of the damped vibration system is transformed into a decoupled form with complex coefficient matrices, using the decoupled method presented in this paper, the equation of the damped system can be decomposed into a decoupled equation with real coefficient matrices. Two new free interface component mode synthesis methods are also presented. The equivalent full-mode matrix of the damped structure is used to capture the effects of the higher-order modes. Additionally, this work modifies the compatibility conditions at the junctions that are employed in most of the previous component mode synthesis methods for generally damped systems. The first component mode synthesis method is performed in complex space, whereas the second method can be applied in real space. Because the coefficient matrices of the coupled equation constructed by the second component mode synthesis method are all real-valued, the solution of the eigenproblem for this coupled equation can be performed in real space as well. Additionally, numerical examples demonstrate the accuracy and validity of these two component mode synthesis methods.

We address the local existence of solutions of the 2D and 3D water wave problems. For the space dimension three, we consider the irrotational datum u 0 and prove that the local in time existence holds for initial velocities belonging to H 2.5+? , where ?>0 is arbitrary. For the space dimension two, the data does not need to be irrotational. We prove the local in time existence when u 0 belongs to H 2+? and $\operatorname{curl}u_{0}$ to H 1.5+? , where ?>0 is arbitrary.

We deal with free boundaries evolution in visco-plastic flows. The fluid motion is governed by the incompressible Norton-Hoff operator in the non-cylindrical quasi-static case coupled with the time-dependent convection system. The novelty of this work is that we supply the existence result of an interface between two non-miscible fluids by the use of the non-smooth evolution theory. We argue some numerical examples to illustrate our result.

A new local form of the principle, in which dissipation is estimated only in a small vicinity of a free interface in steady Hele-Shaw flows, is proposed. It is established that for the problem of bubble propulsion the principle proposed is mathematically equivalent to the variational principle formulated by Saffman and Taylor without physical validation. It is shown that the new local form of the minimum dissipation principle effectively solves the problem of selection of a unique selection in the problems of both bubble and finger propulsion.

In this paper, the stress distribution near the singular point in a two dissimilar materials contact problem will be considered, in which the interface is friction free or with friction. The loads may be thermal or mechanical loading. For the type of rω singularity the stress distribution near the singular point is given by σ ij ( r , θ ) = ∑ n = 1 N K n ( r / R ) ω n f ijn ( θ ) + σ 0 f ij 0 ( θ ) The first term is the singular term, and the second term is called the regular term which is especially important for thermal loading. The solutions for determination of the stress exponents, the angular functions and the regular stress term for a friction free interface and an interface with friction will be presented. Finally, the general behavior of the stress exponents for various geometries and material combinations will be discussed.

A simple theoretical approach is used to investigate active colloids at the free interface and near repulsive substrates. We employ dynamical density functional theory to determine the steady-state density profiles in an effective equilibrium system (Farage T. F. F. et al., Phys. Rev. E, 91 (2015) 042310). In addition to the known accumulation at surfaces, we predict wetting and drying transitions at a flat repulsive wall and capillary condensation and evaporation in a slit pore. These new phenomena are closely related to the motility-induced phase separation (MIPS) in the bulk.

Free and forced vibration analyses of the two parallel beams connected to each other by the uniformly distributed vertical springs have been conducted in this contribution. The coupled motion equations were derived by using the free interface substructural method, and both of the free vibration characteristics and the forced vibration responses of the complex double-beam system were obtained. The mode localization and frequency loci veering phenomena would take place in such weakly coupled double beam system when there is a disorder in the system. By comparing with the available data in the literature, our numerical results were verified, and the well agreements were observed. These investigations showed that the proposed method is general and can be extended easily for vibration analysis of coupled double plate system or other complex systems.

Research carried out in this technical paper suggests an application of the widely implemented eye tracking techniques. Traditionally, HCI uses mouse, keyboard as an input devices but this paper presents hand free interface between computer and human. Here providing a novel idea to control computer mouse cursor using human eyes movement. It controls mouse moving by automatically affecting the position where eyesight focused. The project mainly comprises of three sections namely Image Capture, Image Processing, and Cursor Control. After capturing image from webcam, the shape of pupil is recognized using Hough Transform and the center coordinate help to determine the exact point on the screen where the user is looking also coordinate will instruct the computer mouse to move specific location. This system is very helpful for solving the HMI problems of the disabled so that it can provide a way for them to communicate with the outside world.

We address the system of fluid–structure interaction consisting of a compressible Navier–Stokes equation coupled with an elasticity equation, with the velocity and stress continuity requirements across the free moving interface. We prove the a priori estimates for existence of solutions when the initial velocity belongs to H 3 , the initial density is bounded from below and belongs to H 3/2+r , where r> 0, and the initial velocity of the displacement is in H 3/2+r .

Fur die Ausbreitung eines dunnen rotierenden Tropfens wird, unter Ausnutzung der Schmierfilmapproximation, eine Entwicklungsgleichung zur Beschreibung der Position der freien Grenzflache abgeleitet. Die dynamische Benetzung wird mit dem empirischen Tanner'schen Gesetz beschrieben und die Modellierung mit Experimenten aus der Literatur verglichen. Eine lineare Storungsanalyse liefert die instabilen Moden und das Einsetzen von Fingerbildung wahrend der Ausbreitung. Betrachtet wird auch Konvektion aufgrund der temperaturabhangigen Oberflachenspannung und Dichte sowie deren Stabilitat. By applying the lubrication approximation, an evolution equation for the position of the free interface of a rotating thin droplet is derived. The dynamic wetting of the droplet is modeled by using the empiric Tanner's law and the model is compared with experimental results taken from literature. A linear stability analysis gives the unstable modes and the onset of the fingering instability. Also convections due to the temperature dependency of surface tension and density as well as their stability are considered.

In the present article, we have found charged analogues of Henning Knutsen’s interior solutions which join smoothly to the Reissner–Nordstrom metric at the pressure free interface. The solutions are singularity free and analyzed numerically with respect to pressure, energy-density and charge-density in details. The solutions so obtained also present the generalization of A.L. Mehra’s solutions.

We apply density functional theory to study the interfacial properties of a phase-separating binary fluid of ultrasoft particles, whose interaction potentials belong to the family of the so-called generalized exponential models (GEM). By using the formalism of the density functional theory within the mean-field approximation, we investigate the equilibrium density profiles for each component at the free interface as well as at a repulsive, flat wall. We show that the studied system can lead to first-order wetting transition which is characterized by a layering-like behaviour due to the clustering properties of GEM particles.

The p-polyaniline/n-ZnO thin film heterojunction sensor for room temperature LPG detection was fabricated by electrodepositing polyaniline on chemical bath deposited ZnO film. The heterojunction showed rectifying behavior indicating the formation of a diode with ideality factor 1.10. The formation of diffusion free interface of heterojunction was confirmed from cross-sectional FESEM. The heterojunction sensor has quick and high response towards LPG as compared to N2 and CO2 and exhibited maximum response of 81% upon exposure of 1040 ppm of LPG. The LPG sensing mechanism for heterojunction is modeled through change in height of barrier potential.

The study on simulation of compressible gas–liquid flow remains open. Popular methods are either confined to incompressible flow regime, or inevitably induce smear of the free interface. A new finite volume method for compressible two-phase flow simulation is contributed for this subject. First, the “heterogeneous equilibrium” assumption is introduced to the control volume, by hiring free interface reconstruction technology, the distribution of each component in the control volume is achieved. Next, AUSM[Formula: see text]-up (advection upstream splitting method) scheme is employed to calculate the convective fluxes and pressure fluxes, with the contact discontinuity characteristic considered, followed by the update of the whole flow field. The new method features on density-based pattern and interface reconstruction technology from VOF (volume of fluid), thus we name it “[Formula: see text]-VOF method”. Inherited from AUSM families and VOF, [Formula: see text]-VOF behaves as an all-speed method, capable of simulating shock in gas–liquid flow, and preserving the sharpness of the free interface. Gas–liquid shock tube is simulated to evaluate the method, from which good agreement is obtained between the predicted results and those of the cited literature, meanwhile, sharper free interface is identified. Finally, the capability and validity of [Formula: see text]-VOF method can be concluded in compressible gas–liquid flow simulation.

The two-dimensional Kelvin-Helmholtz instability which arises in two immiscible co-currently moving horizontal liquid layers is studied numerically. Two different methods for capturing the free interface movement are applied, namely the volume-of-fluid method and the level-set method. Both methods are very popular and available within commercial computational fluid dynamics tools. The wave is initialized using two different perturbations implemented into the model. As a case study, a system comprising a toluene layer and an aqueous layer is chosen. Numerical results obtained by both methods are in a good agreement with the linear stability theory for small wave amplitudes. The application of both methods is compared and their advantages and drawbacks are highlighted.

Charged analogue of Whittaker’s interior solution is derived which possess constant gravitational mass density (ρ+3p). The solution joins smoothly to Nordstorm solution at the pressure free interface. The solution has increasing energy density away from the center which is unphysical however such model can very well represent the situations when density undergoes abrupt changes during the tug of war between the gravitational attraction and electrostatic repulsion.

A non-local formulation, depending on a free spectral parameter, is presented governing two ideal fluids separated by a free interface and bounded above either by a free surface or by a rigid lid. This formulation is shown to be related to the Dirichlet–Neumann operators associated with the two-fluid equations. As an application, long wave equations are obtained; these include generalizations of the Benney–Luke and intermediate long wave equations, as well as their higher order perturbations. Computational studies reveal that both equations possess lump-type solutions, which indicate the possible existence of fully localized solitary waves in interfacial fluids with sufficient surface tension.

We study regularity and nonexistence properties for some free-interface problems arising in the study of limiting vorticities associated to the Ginzburg‐Landau equations with magnetic field in two dimensions. Our results imply in particular that if these limiting vorticities concentrate on a smooth closed curve then they have a distinguished sign; moreover, if the domain is thin then solutions of the Ginzburg‐Landau equations cannot have a number of vortices much larger than the applied magnetic field.

We present a way to study a wide class of optimal design problems with a perimeter penalization. More precisely, we address existence and regularity properties of saddle points of energies of the form $$ (u,A) \quad \mapsto \quad \int_\Omega 2fu \; \text{d}x \; - \int_{\Omega \cap A} \sigma_1 \mathscr A u \cdot \mathscr A u \; \text{d}x \; - \int_{\Omega \setminus A} \sigma_2\mathscr A u\cdot \mathscr A u \; \text{d}x \; + \; \text{Per}(A;\overline \Omega),$$ where $\Omega$ is a bounded Lipschitz domain, $A\subset \mathbb R^N$ is a Borel set, $u:\Omega \subset \mathbb R^N \to \mathbb R^d$, $\mathscr A$ is an operator of gradient form, and $\sigma_1, \sigma_2$ are two not necessarily well-ordered symmetric tensors. The class of operators of gradient form includes scalar- and vector-valued gradients, symmetrized gradients, and higher order gradients. Therefore, our results may be applied to a wide range of problems in elasticity, conductivity or plasticity models. In this context and under mild assumptions on $f$, we show for a solution $(w,A)$, that the topological boundary of $A \cap \Omega$ is locally a $\rm{C}^1$-hypersurface up to a closed set of zero $\mathscr H^{N-1}$-measure., Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00526-016-1085-5

The problem of stability of uniformly rotating liquid mass consisting of two viscous incompressible capillary self-gravitating liquids separated by a free interface is studied. Bibliography: 12 titles.

Substructure reduction techniques are efficient methods to reduce the size of large models used to analyze the dynamical behavior of complex structures. The most popular approach is a fixed interface method, the Craig-Bampton method (1968), which is based on fixed interface vibration modes and interface constraint modes. In contrast, free interface methods employing free interface vibration modes together with attachment modes are also used, e.g. MacNeal%s method (1971) and Rubin%s method (1975). The methods mentioned so far assemble the substructures using interface displacements (primal assembly). The dual Craig-Bampton method (2004) uses the same ingredients as the two aforementioned free interface methods, but assembles the substructures using interface forces (dual assembly). This method enforces only weak interface compatibility between the substructures, thereby avoiding interface locking problems as sometimes experienced in the primal assembly approaches using free interface modes. The dual Craig-Bampton method leads to simpler reduced matrices compared to other free interface methods and the reduced matrices are sparse, similar to the classical Craig-Bampton matrices. In this contribution we evaluate the primal (classical) formulation of the Craig-Bampton method, the MacNeal method, the Rubin method and the dual formulation of the Craig- Bampton method. The presented theory and the comparison between the four substructuring methods will be illustrated on the Benfield truss, on a three-dimensional beam frame and on a two-dimensional solid plane stress problem Tehnike za redukcijo podstruktur so učinkovita metoda za zmanjševanje velikih modelov, ki se uporabljajo pri analizi dinamičnega vedenja kompleksnih struktur. Najbolj priljubljen pristop je Craig-Bamptonova metoda (1968) s fiksnim stikom, ki temelji na nihajnih oblikah s fiksnim stikom in oblikah omejitev stika. Metode s prostim stikom, kot sta npr. MacNealova (1971) in Rubinova metoda (1975), nasprotno uporabljajo nihajne oblike prostega stika skupaj z oblikami pritrditve. Podstrukture se pri omenjenih metodah sestavljajo z odmiki stikov (glavni sestav). Dvojna Craig-Bamptonova metoda (2004) uporablja enake sestavine kot zgoraj omejeni metodi s prostimi stiki, le da se podstrukture sestavljajo s pomočjo sil na stiku (dvojni sestav). Ta metoda uveljavlja le šibko združljivost stikov med podstrukturami, s čimer se izognemo težavam z zaklepanjem stikov, ki se včasih pojavljajo pri pristopih s primarnimi sestavi in pri uporabi oblik prostega stika. Dvojna Craig-Bamptonova metoda daje v primerjavi z drugimi metodami prostega stika preprostejše reducirane matrike. Te reducirane matrike so redko posejane, podobne kot klasične Craig-Bamptonove matrike. V tem prispevku obravnavamo primarno (klasično) formulacijo Craig-Bamptonove metode, MacNealovo metodo, Rubinovo metodo in dvojno formulacijo Craig-Bamptonove metode. Izpeljava je podana na celovit in dosleden način.

We perform experiments on the sloshing dynamics of liquids in a rectangular container submitted to an impulse. We show that when foam is placed on top of the liquid the oscillations of the free interface are significantly damped. The ability to reduce sloshing and associated splashing could find applications in numerous industrial processes involving liquid transport., Accepted for publication in Journal of Visualization

Fluidigm Corp. released the Topaz™ 1.96 and 4.96 crystallization chips in the fall of 2004. Topaz 1.96 and 4.96 are the latest evolution of Fluidigm’s microfluidics crystallization technologies that enable ultra-low-volume rapid screening for macromolecular crystallization. Topaz 1.96 and 4.96 are similar to each other but represent a major redesign of the Topaz system and have substantially improved ease of automation and ease of use, improved efficiency and even further reduced the amount of material needed. With the release of the new Topaz system, Fluidigm continues to set the standard in low-volume crystallization screening, which is having an increasing impact in the field of structural genomics and more generally in structural biology. It is likely that further optimization and increased utility of the Topaz crystallization system will emerge. It is also probable that further innovation and the emergence of competing technologies will be seen.

The most general accurate solutions for the Buchdhal fluid sphere were obtained and matched with the Schwarzchild's exterior solution at the pressure free interface. Various parameters of the solutions were so adjusted that the energy density, pressure and temperature were positive and decreasing away from the centre, and the velocity of sound was less than unity throughout the spheroid model. Using this procedure, the maximum mass of the fluid sphere with a surface density of2 × 1014gm cm-3 was determined to be 3.82MΘ and 4.57 MΘ for strong and weak energy conditions respectively. PACS number: 0402, 0402J, 0440D, 95301

A precise knowledge of co-axial flow dynamics and a better understanding of the mechanisms that act to destabilize the interface between the two fluids is of fundamental interest in many industrial applications like lubricated transport, injection devices, atomization and controlled microdroplet production. The flow is in general unstable, since at least two mechanisms act to destabilize the cylindrical interface: shear and capillary instabilities. While these two mechanisms are active in a jet issuing from a tap, their respective influence strongly depends on the Reynolds number, the Ohnesorge number, but also on the viscosity, density, and aspect ratios. In this thesis, the global stability characteristics of two-phase co-axial flow are determined. The stability analysis follows two successive steps. First the steady base flow is determined, via the resolution of the nonlinear Navier-Stokes equations together with the location of the free interface. Second, these equations are linearized around the base flow and the dominant eigenmodes determined. The novelty lies in the formulation of models that can describe both the qualitative and quantitative characteristics of the two-phase flow configuration and the adaptation of the tools of global stability analysis for this configuration. We find that the dripping to jetting regime transition depends on the Capillary number, the degree of the confinement and the viscosity ratio, and we show that, surprisingly, the nozzle geometry does not affect the stability properties of the flow. Finally, the influence of surface viscosity on these coaxial flows has been considered. The governing and constitutive equations describing the continuum mechanics of the surface in the axisymmetric case are derived. With the addition of surface viscosity at the interface, the base flow evolves over a lengthscale which is much larger than the entry length in the Stokes regimes and than the typical unstable wavelength. We show that while the flow becomes eventually more convectively unstable once it reaches the fully developed profile, the surface viscosity creates an absolute region at the inlet, that is expected to promote droplet formation.

A level-set method is used for analyzing the behaviors of gas bubbles in two fluids incompressible viscous flow domain. The governing equations are solved by using a finite volume method. The numerical results are verified by comparing with the experimental and other computational results. Computations for the deformations and motions of one or multi-bubbles in the flow domain with the initial undisturbed free interface are conducted. It can be seen that numerical results for different surface tension and density ratio arise very different behaviors of bubbles. When bubbles rise near the free interface, the free interface gives some great influence on the behaviors of bubbles. The present results computed by a level-set method give useful information about the properties of bubble motions and deformations.

In the following work we apply the boundary element method to two-phase flows in shallow microchannels, where one phase is dispersed and does not wet the channel walls. These kinds of flows are often encountered in microfluidic Lab-on-a-Chip devices and characterized by low Reynolds and low capillary numbers. Assuming that these channels are homogeneous in height and have a large aspect ratio, we use depth-averaged equations to describe these two-phase flows using the Brinkman equation, which constitutes a refinement of Darcy's law. These partial differential equations are discretized and solved numerically using the boundary element method, where a stabilization scheme is applied to the surface tension terms, allowing for a less restrictive time step at low capillary numbers. The convergence of the numerical algorithm is checked against a static analytical solution and on a dynamic test case. Finally the algorithm is applied to the non-linear development of the Saffman-Taylor instability and compared to experimental studies of droplet deformation in expanding flows., accepted for publication, Computers and Fluids 2014

This paper describes a simple and reusable microfluidic SlipChip device for studying bacterial chemotaxis based on free interface diffusion. The device consists of two glass plates with reconfigurable microwells and ducts, which can set up 20 parallel chemotaxis units as duplicates. In each unit, three nanoliter microwells and connecting ducts were assembled for pipette loading of a chemoeffector solution, bacterial suspension, and 1X PBS buffer solution. By a simple slipping operation, three microwells were disconnected from other units and interconnected by the ducts, which allowed the formation of diffusion concentration gradients of the chemoeffector for inducing cell migration from the cell microwell towards the other two microwells. The migration of cells in the microwells was monitored and accurately counted to evaluate chemotaxis. Moreover, the migrated cells were easily collected by pipetting for further studies after a slip step to reconnect the chemoeffector microwells. The performance of the device was characterized by comparing chemotaxis of two Escherichia coli species, using aspartic acid as the attractant and nitrate sulfate as the repellent. It also enables the separation of bacterial species from a mixture, based on the difference of chemotactic abilities, and collection of the cells with strong chemotactic phenomena for further studies off the chip.

We construct an asymptotic solution of the phase field system with variable thermal conductivity different in domains occupied by different phases. We show that, depending on relations between parameters characterizing the substance, the dynamics of the free interface between the phases is determined by solutions of the classical or modified Stefan problems.

This paper studies a class of variational problems which involving both bulk and surface energies. The bulk energy is of Dirichlet type though it can be in very general forms allowing unknowns to be scalar or vectors.The surface energy is an arbitrary elliptic parametric integral which is defined on a free interface. One also allows other constraints such as volumes of partitioning sets. One establishes the existence and regularity theory, in particular, the regularity of the free interface of such problems.

We propose a model based on a Ginzburg-Landau approach to study a strain relief mechanism at a free interface of a non-hydrostatically stressed solid, commonly observed in thin-film growth. The evolving instability, known as the Grinfeld instability, is studied numerically in two and three dimensions. Inherent in the description is the proper treatment of nonlinearities. We find these nonlinearities can lead to competitive coarsening of interfacial structures, corresponding to different wavenumbers, as strain is relieved. We suggest ways to experimentally measure this coarsening., Comment: 4 pages (3 figures included)

We consider a new concept of weak solutions to the phase-field equations with a small parameter ε characterizing the length of interaction. For the standard situation of a single free interface, this concept (in contrast with the common one) leads to the well-known Stefan–Gibbs–Thomson problem as ε→0. For the case of a large number M(ε) (M(ε)→∞ as ε→0) of free interfaces, which corresponds to the ‘wave-train’ interpretation of a ‘mushy region’, this concept allows us to obtain the limit problem as ε→0.

ポリマーブレンド薄膜について, 動的平均場法を用いてシミュレーションを行った. 本研究では, 気相との自由界面および固体壁の効果を取り入れ, 両界面を含めた膜の構造について理論的な計算を行った. 動的シミュレーションから, 初期過程においてすでに, 自由界面近傍, 固体壁近傍, 内部に存在するバルクの三つの相分離が起こっていることが示された. 自由界面および固体壁近傍では, ラメラ状の相分離を示し, 特定成分の偏析が見られた. 一方, 内部のバルク領域では, このような秩序構造は示していない. 時間ステップの経過とともに, 内部におけるドメイン成長が起こる. これにより, 空気-ポリマー界面と固体壁の各近傍から膜の内部方向に層の成長が進み, 各ポリマーが界面近傍と膜内部の間で移行していく過程がとらえられた. また, この過程によって誘起されたと考えられる凹凸が自由界面上に観察できた.

The conserved phase field system with a small parameter in the n-dimensional case (n[les ]3) is considered. An asymptotic solution, describing the free interface dynamics, is constructed and justified. As the small parameter tends to zero, the limiting solution satisfies the modified Stefan problem with corrected Gibbs–Thomson law.

Crystallization is a highly demanding and time-consuming task that causes a real bottle-neck in basic research. Great effort has been made to understand the factors and parameters that influence this process and to finely tune them to facilitate crystal growth. Different crystallization techniques have been proposed over the past decades, such as the classical vapor hanging drop method, its variant the sitting drop method, dialysis, cryo-temperature, gel, batch, and the innovative microgravity (space) techniques like free interface diffusion (FID) and counter-ion diffusion (CID). Here, we present a review of the strategies utilizing Langmuir-Blodgett (LB)-based nanotechnologies, and microgravity techniques for obtaining optimal high-quality crystals, as proven by molecular dynamics (MD) and bioinformatics approaches, namely using a clustering algorithm and protein alignment.

Using irreversible thermodynamics we derive the dispersion equation of the growth and decay rate of surface corrugations caused by the simultaneous action of surface and bulk diffusion.

The motions of free interface and its coupling with bubble in oscillating two-phase flow field are simulated numerically by using OpenFOAM. The oscillating two-phase flow field is simulated using the VOF method and the moving grid of the Arbitrary Lagrangian-Eulerian (ALE) method. Firstly, free interface is simulated, and its interface elevation is well coincided with experimental results. Then simulations of free faces with or without bubble near it under oscillating condition are compared. It is found that the free interface between gas and liquid phases is affected largely by the oscillation, and the effect is intensified when bubble is near free surfaces. And local pressure disturbance is found after bubble coalesces with free interface.Copyright © 2013 by ASME