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The relation between dynamics and structure in systems of bidisperse 2D hard disks with apparent arrested dynamics is considered using numerical simulations and Voronoi analysis. Surprisingly, the suspensions systematically appear to fall out of equilibrium at an area fraction of {\phi} {\approx} 0.777 over a wide range of disk-size ratios. This is in close agreement with the experimental findings of [Lozano et al., Nat. Mater. 18, 1118 (2019)] for a single large-to-small size ratio of {\approx} 1.4. Even inside the crystalline region of the state diagram there are weak structural signatures present for this area fraction. Adopting a granocentric viewpoint, this allows for the identification of a geometric feature - a floret pentagonal tiling - that could underlie the observations. That is, this tiling has an area fraction of {\phi} {\approx} 0.777343, which closely matches the apparent 'glass transition' value of {\phi}. The connection suggests that a zero-entropy, ground-state tiling can influence the dynamics of the system at finite temperature, in a manner that may be similar to the way in which geometry in foam-like tissue models induces a jamming transition. A geometric ground-state argument also appears to explain the change in local dynamics observed by [Li et al., Nature 587, 225 (2020)], when a honeycomb lattice is used as the reference. Combined these findings change how to view high-{\phi} 2D fluids, namely as being influenced by the presence of zero-entropy geometric ground states. The proposed connection leads to an unexpected (dynamic) transition in the finite-temperature system, which can be mistaken for a(n onset) glass transition, but is in a class of its own. There is also a tentative connection to random loose packing for frictional systems. An outlook is provided on how this concept may be extended to soft-particle systems and into higher dimensions., Comment: 26 pages, 12 figures

Colloidal gels have strong industrial relevance as they can behave liquid- and solid-like. The latter allows them to support the buoyant weight against gravity. However, the system is intrinsically out-of-equilibrium, which means that the colloids must eventually settle out of the suspension. The process of settling has been captured theoretically, but the presence of a delay time during which the gel appears relatively unaffected by gravity has not. Here, we modify existing frameworks to capture this delay, by treating the gel as a continuum with viscoelastic response that is based on the local bond density. We can solve our model numerically to obtain the evolution of the colloid density profile and recover qualitatively the accumulation of a dense layer on top of the settling gel, as is experimentally observed in depletion gels. This numerical study is complemented by a theoretical analysis that allows us to identify an emergent time and length scale that set the dynamics of the gel. Our model provides a solid foundation for future studies that incorporate hydrodynamic erosion and tackle industrially relevant geometries.

The Cellular Potts model, also known as the Glazier-Graner-Hogeweg model, is a lattice-based approach by which biological tissues at the level of individual cells can be numerically studied. Traditionally, a square or hexagonal underlying lattice structure is assumed for two-dimensional systems, and this is known to introduce artifacts in the structure and dynamics of the model tissues. That is, on regular lattices, cells can assume shapes that are dictated by the symmetries of the underlying lattice. Here, we developed a variant of this method that can be applied to a broad class of (ir)regular lattices. We show that on an irregular lattice deriving from a fluid-like configuration, two types of artifacts can be removed. We further report on the transition between a fluid-like disordered and a solid-like hexagonally ordered phase present for monodisperse confluent cells as a function of their surface tension. This transition shows the hallmarks of a first-order phase transition and is different from the glass/jamming transitions commonly reported for the vertex and active Voronoi models. We emphasize this by analyzing the distribution of shape parameters found in our state space. Our analysis provides a useful reference for the future study of epithelia using the (ir)regular Cellular Potts model., Comment: This paper has been accepted for publication in Soft Matter as an open-access article, available at the DOI provided. A major revision was made during the review process, changing the method for capturing the transition point using the effective self-diffusion coefficient instead of the mean square displacement scaling exponent. We thank the reviewers for their constructive feedback

Colloidal gels are elasto-plastic materials composed of an out-of-equilibrium, self-assembled network of micron-sized (solid) particles suspended in a fluid. Recent work has shown that far-field hydrodynamic interactions do not change gel structure, only the rate at which the network forms and ages. However, during gel formation, the interplay between short-ranged attractions leading to gelation and equally short-ranged hydrodynamic lubrication interactions remains poorly understood. Here, we therefore study gelation using a range of hydrodynamic descriptions: from single-body (Brownian Dynamics), to pairwise (Rotne-Prager-Yamakawa), to (non-)lubrication-corrected many-body (Stokesian Dynamics). We confirm the current understanding informed by simulations accurate in the far-field. Yet, we find that accounting for lubrication can strongly impact structure at low colloid volume fraction. Counterintuitively, strongly dissipative lubrication interactions also accelerate the aging of a gel, irrespective of colloid volume fraction. Both elements can be explained by lubrication forces facilitating collective dynamics and therefore phase-separation. Our findings indicate that despite the computational cost, lubricated hydrodynamic modeling with many-body far-field interactions is needed to accurately capture the evolution of the gel structure.

Attractive colloids diffuse and aggregate to form gels, solid-like particle networks suspended in a fluid. Gravity is known to strongly impact the stability of gels once they are formed. However, its effect on the process of gel formation has seldom been studied. Here, we simulate the effect of gravity on gelation using both Brownian dynamics and a lattice-Boltzmann algorithm that accounts for hydrodynamic interactions. We work in a confined geometry to capture macroscopic, buoyancy-induced flows driven by the density mismatch between fluid and colloids. These flows give rise to a stability criterion for network formation, based on an effective accelerated sedimentation of nascent clusters at low volume fractions that disrupts gelation. Above a critical volume fraction, mechanical strength in the forming gel network dominates the dynamics: the interface between the colloid-rich and colloid-poor region moves downward at an ever decreasing rate. Finally, we analyze the asymptotic state, the colloidal gel-like sediment, which we find not to be appreciably impacted by the vigorous flows that can occur during the settling of the colloids. Our findings represent the first steps toward understanding how flow during formation affects the life span of colloidal gels., Comment: 14 pages, 15 figures, 3 movies

Locally (re)structuring colloidal gels $\unicode{x2013}$ micron-sized particles forming a connected network with arrested dynamics $\unicode{x2013}$ enables precise tuning of the micromechanical and -rheological properties of the system. A recent experimental study [B. Saint-Michel, G. Petekidis, and V. Garbin, Soft Matter $\boldsymbol{18}$, 2092 (2022)] showed that rapid restructuring can occur by acoustically modulating an embedded microbubble. Here, we perform Brownian dynamics simulations to understand the mechanical effect of an oscillating microbubble on the structure of the embedding colloidal gel. Our simulations reveal a hexagonal-close-packed restructuring in a range that is comparable to the amplitude of the oscillations. However, we were unable to reproduce the unexpectedly long-ranged modification of the gel structure $\unicode{x2013}$ dozens of amplitudes $\unicode{x2013}$ observed in experiment. This suggests including long-ranged effects, such as fluid flow, should be considered in future work., Comment: 7 pages, 6 figures

One of the major challenges in modern robotics is controlling micromanipulation by active and adaptive materials. In the respiratory system, such actuation enables pathogen clearance by means of motile cilia. While various types of artificial cilia have been engineered recently, they often involve complex manufacturing protocols and focus on transporting liquids only. Here, we create soft magnetic carpets via an easy self-assembly route based on the Rosensweig instability. These carpets can transport liquids but also solid objects that are larger and heavier than the artificial cilia, using a crowd-surfing effect. This amphibious transportation is locally and reconfigurably tuneable by simple micromagnets or advanced programmable magnetic fields with a high degree of spatial resolution. We identify and model two surprising cargo reversal effects due to collective ciliary motion and non-trivial elastohydrodynamics. While our active carpets are generally applicable to integrated control systems for transport, mixing and sorting, these effects could also be exploited for microfluidic viscosimetry and elastometry.

Unrestricted particle transport through microfluidic channels is of paramount importance to a wide range of applications, including lab-on-a-chip devices. In this article, we study using video microscopy the electro-osmotic aggregation of colloidal particles at the opening of a micrometer-sized silica channel in presence of a salt gradient. Particle aggregation eventually leads to clogging of the channel, which may be undone by a time-adjusted reversal of the applied electric potential. We numerically model our system via the Stokes-Poisson-Nernst-Planck equations in a geometry that approximates the real sample. This allows us to identify the transport processes induced by the electric field and salt gradient and to provide evidence that a balance thereof leads to aggregation. We further demonstrate experimentally that a net flow of colloids through the channel may be achieved by applying a square-waveform electric potential with an appropriately tuned duty cycle. Our results serve to guide the design of microfluidic and nanofluidic pumps that allow for controlled particle transport and provide new insights for anti-fouling in ultra-filtration., Comment: 9 pages, 7 figures

Cooperative motion in biological microswimmers is crucial for their survival as it facilitates adhesion to surfaces, formation of hierarchical colonies, efficient motion, and enhanced access to nutrients. Synthetic microswimmers currently lack truly cooperative behavior that originates from activity-induced interactions. Here, we demonstrate that catalytic microswimmers show a variety of cooperative behaviors along one-dimensional paths. We show that their speed increases with the number of swimmers, while the activity induces a preferred distance between swimmers. Using a minimal model, we ascribe this behavior to an effective activity-induced potential that stems from a competition between chemical and hydrodynamic coupling. These interactions further induce active self-assembly into trains as well as compact chains that can elongate, break-up, become immobilized and remobilized. We identify the crucial role that environment morphology and swimmer directionality play on these highly dynamic chain behaviors. These activity-induced interactions open the door towards exploiting cooperation for increasing the efficiency of, as well as provide temporal and spatial control over, microswimmer motion, thereby enabling them to perform intricate tasks inside complex environments.

Recent experiments show a strong rotational-diffusion enhancement for self-propelled microrheological probes in colloidal glasses. Here, we provide microscopic understanding using simulations with a frictional probe-medium coupling that converts active translation into rotation. Diffusive enhancement emerges from the medium's disordered structure and peaks at a second-order transition in the number of contacts. Our results reproduce the salient features of the colloidal glass experiment and support an effective description that is applicable to a broader class of viscoelastic suspensions., Comment: 5 pages, 4 figures

Geometric confinement strongly influences the behavior of microparticles in liquid environments. However, to date, nonspherical particle behaviors close to confining boundaries, even as simple as planar walls, remain largely unexplored. Here, we measure the height distribution and orientation of colloidal dumbbells above walls by means of digital in-line holographic microscopy. We find that while larger dumbbells are oriented almost parallel to the wall, smaller dumbbells of the same material are surprisingly oriented at preferred angles. We determine the total height-dependent force acting on the dumbbells by considering gravitational effects and electrostatic particle-wall interactions. Our modeling reveals that at specific heights both net forces and torques on the dumbbells are simultaneously below the thermal force and energy, respectively, which makes the observed orientations possible. Our results highlight the rich near-wall dynamics of nonspherical particles, and can further contribute to the development of quantitative frameworks for arbitrarily-shaped microparticle dynamics in confinement., Comment: Ruben W. Verweij and Stefania Ketzetzi contributed equally to this work. 17 pages and 7 figures

Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in how they deal with complex flow geometries and suspended particles. Here, we present a lattice Boltzmann solver for Oldroyd-B fluids that can handle arbitrarily-shaped fixed and moving boundary conditions, which makes it ideally suited for the simulation of confined colloidal suspensions. We validate our method using several standard rheological setups, and additionally study a single sedimenting colloid, also finding good agreement with literature. Our approach can readily be extended to constitutive equations other than Oldroyd-B. This flexibility and the handling of complex boundaries holds promise for the study of microswimmers in viscoelastic fluids., Comment: 13 pages, 11 figures

Microswimmers typically move near walls, which can strongly influence their motion. However, direct experimental measurements of swimmer-wall separation remain elusive to date. Here, we determine this separation for model catalytic microswimmers from the height dependence of the passive component of their mean-squared displacement. We find that swimmers exhibit "ypsotaxis", a tendency to assume a fixed height above the wall for a range of salt concentrations, swimmer surface charges, and swimmer sizes. Our findings indicate that ypsotaxis is activity-induced, posing restrictions on future modeling of their still debated propulsion mechanism.

Self-propelled particles have been experimentally shown to orbit spherical obstacles and move along surfaces. Here, we theoretically and numerically investigate this behavior for a hydrodynamic squirmer interacting with spherical objects and flat walls using three different methods of approximately solving the Stokes equations: The method of reflections, which is accurate in the far field; lubrication theory, which describes the close-to-contact behavior; and a lattice Boltzmann solver that accurately accounts for near-field flows. The method of reflections predicts three distinct behaviors: orbiting/sliding, scattering, and hovering, with orbiting being favored for lower curvature as in the literature. Surprisingly, it also shows backward orbiting/sliding for sufficiently strong pushers, caused by fluid recirculation in the gap between the squirmer and the obstacle leading to strong forces opposing forward motion. Lubrication theory instead suggests that only hovering is a stable point for the dynamics. We therefore employ lattice Boltzmann to resolve this discrepancy and we qualitatively reproduce the richer far-field predictions. Our results thus provide insight into a possible mechanism of mobility reversal mediated solely through hydrodynamic interactions with a surface., Comment: 13 pages, 12 figures

The squirmer is a simple yet instructive model for microswimmers, which employs an effective slip velocity on the surface of a spherical swimmer to describe its self-propulsion. We solve the hydrodynamic flow problem with the lattice Boltzmann (LB) method, which is well-suited for time-dependent problems involving complex boundary conditions. Incorporating the squirmer into LB is relatively straight-forward, but requires an unexpectedly fine grid resolution to capture the physical flow fields and behaviors accurately. We demonstrate this using four basic hydrodynamic tests: Two for the far-field flow---accuracy of the hydrodynamic moments and squirmer-squirmer interactions---and two that require the near field to be accurately resolved---a squirmer confined to a tube and one scattering off a spherical obstacle---which LB is capable of doing down to the grid resolution. We find good agreement with (numerical) results obtained using other hydrodynamic solvers in the same geometries and identify a minimum required resolution to achieve this reproduction. We discuss our algorithm in the context of other hydrodynamic solvers and present an outlook on its application to multi-squirmer problems., Comment: 9 pages, 7 figures

Catalytic colloidal swimmers that propel due to self-generated fluid flows exhibit strong affinity for surfaces. We here report experimental measurements of significantly different velocities of such microswimmers in the vicinity of substrates made from different materials. We find that velocities scale with the solution contact angle $\theta$ on the substrate, which in turn relates to the associated hydrodynamic substrate slip length, as $V\propto(\cos\theta+1)^{-3/2}$. We show that such dependence can be attributed to osmotic coupling between swimmers and substrate. Our work points out that hydrodynamic slip at the wall, though often unconsidered, can significantly impact the self-propulsion of catalytic swimmers.

We consider sedimentation of a rigid helical filament in a viscous fluid under gravity. In the Stokes limit, the drag forces and torques on the filament are approximated within the resistive-force theory. We develop an analytic approximation to the exact equations of motion that works well in the limit of a sufficiently large number of turns in the helix (larger than two, typically). For a wide range of initial conditions, our approximation predicts that the centre of the helix itself follows a helical path with the symmetry axis of the trajectory being parallel to the direction of gravity. The radius and the pitch of the trajectory scale as non-trivial powers of the number of turns in the original helix. For the initial conditions corresponding to an almost horizontal orientation of the helix, we predict trajectories that are either attracted towards the horizontal orientation, in which case the helix sediments in a straight line along the direction of gravity, or trajectories that form a helical-like path with many temporal frequencies involved. Our results provide new insight into the sedimentation of chiral objects and might be used to develop new techniques for their spatial separation., Comment: 25 pages, 10 figures; accepted for publication in Physical Review Fluids

ESPResSo 4.0 is an extensible simulation package for research on soft matter. This versatile molecular dynamics program was originally developed for coarse-grained simulations of charged systems Limbach et al., Comput. Phys. Commun. 174, 704 (2006). The scope of the software has since broadened considerably: ESPResSo can now be used to simulate systems with length scales spanning from the molecular to the colloidal. Examples include, self-propelled particles in active matter, membranes in biological systems, and the aggregation of soot particles in process engineering. ESPResSo also includes solvers for hydrodynamic and electrokinetic problems, both on the continuum and on the explicit particle level. Since our last description of version 3.1 Arnold et al., Meshfree Methods for Partial Differential Equations VI, Lect. Notes Comput. Sci. Eng. 89, 1 (2013), the software has undergone considerable restructuring. The biggest change is the replacement of the Tcl scripting interface with a much more powerful Python interface. In addition, many new simulation methods have been implemented. In this article, we highlight the changes and improvements made to the interface and code, as well as the new simulation techniques that enable a user of ESPResSo 4.0 to simulate physics that is at the forefront of soft matter research.

A locally heated Janus colloid can achieve motion in a fluid through the coupling of dissolved ions and the medium's polarizibility to an imposed temperature gradient, an effect known as self-thermo(di)electrophoresis. We numerically study the self-propulsion of such a "hot swimmer" in a monovalent electrolyte solution using the finite-element method. The effect of electrostatic screening for intermediate and large Debye lengths is charted and we report on the fluid flow generated by self-thermoelectrophoresis. We obtain excellent agreement between our analytic theory and numerical calculations in the limit of high salinity, validating our approach. At low salt concentrations, we consider two analytic approaches and use Teubner's integral formalism to arrive at expressions for the speed. These expressions agree semi-quantitatively with our numerical results for conducting swimmers, providing further validation. Our numerical approach provides a solid framework against the strengths and weaknesses of analytic theory can be appreciated and which should benefit the realization and analysis of further experiments on hot swimming., Comment: 15 pages, 6 figures

Colloidal particles with strong, short-ranged attractions can form a gel. We simulate this process without and with hydrodynamic interactions (HI), using the lattice-Boltzmann method to account for presence of a thermalized solvent. We show that HI speed up and slow down gelation at low and high volume fractions, respectively. The transition between these two regimes is linked to the existence of a percolating cluster shortly after quenching the system. However, when we compare gels at matched 'structural age', we find nearly indistinguishable structures with and without HI. Our result explains longstanding, unresolved conflicts in the literature., Comment: 7 pages, 4 figures

An ion-exchange-resin-based microfluidic pump is introduced that utilizes trace amounts of ions to generate fluid flows. We show experimentally that our pump operates in almost deionized water for periods exceeding 24h and induces fluid flows of um/s over hundreds of um. This flow displays a far-field, power-law decay which is characteristic of two-dimensional (2D) flow when the system is strongly confined and of three-dimensional (3D) flow when it is not. Using theory and numerical calculations we demonstrate that our observations are consistent with electroosmotic pumping driven by umol/L ion concentrations in the sample cell that serve as 'fuel' to the pump. Our study thus reveals that trace amounts of charge carriers can produce surprisingly strong fluid flows; an insight that should benefit the design of a new class of microfluidic pumps that operate at very low fuel concentrations., Comment: 15 pages, 10 figures, 1 table

Hydrodynamic interactions in systems comprised of self-propelled particles, such as swimming microorganisms, and passive tracers have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force/counter-force based lattice-Boltzmann (LB) algorithm [J. de Graaf~\textit{et al.}, J. Chem. Phys.~\textbf{144}, 134106 (2016)] in order to validate its ability to capture the relevant low-Reynolds-number physics. We show that the LB algorithm reproduces far-field theoretical results well, both in a system with periodic boundary conditions and in a spherical cavity with no-slip walls, for which we derive expressions here. The force-lattice coupling of the LB algorithm leads to a "smearing out" of the flow field, which strongly perturbs the tracer trajectories at close swimmer-tracer separations, and we analyze how this effect can be accurately captured using a simple renormalized hydrodynamic theory. Finally, we show that care must be taken when using LB algorithms to simulate systems of self-propelled particles, since its finite momentum transport time can lead to significant deviations from theoretical predictions based on Stokes flow. These insights should prove relevant to the future study of large-scale microswimmer suspensions using these methods.

The motion of ionic solutes and charged particles under the influence of an electric field and the ensuing hydrodynamic flow of the underlying solvent is ubiquitous in aqueous colloidal suspensions. The physics of such systems is described by a coupled set of differential equations, along with boundary conditions, collectively referred to as the electrokinetic equations. Capuani et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for solving this system of equations, which builds upon the lattice Boltzmann algorithm for the simulation of hydrodynamic flow and exploits computational locality. However, thus far, a description of how to incorporate moving boundary conditions into the Capuani scheme has been lacking. Moving boundary conditions are needed to simulate multiple arbitrarily-moving colloids. In this paper, we detail how to introduce such a particle coupling scheme, based on an analogue to the moving boundary method for the pure LB solver. The key ingredients in our method are mass and charge conservation for the solute species and a partial-volume smoothing of the solute fluxes to minimize discretization artifacts. We demonstrate our algorithm's effectiveness by simulating the electrophoresis of charged spheres in an external field; for a single sphere we compare to the equivalent electro-osmotic (co-moving) problem. Our method's efficiency and ease of implementation should prove beneficial to future simulations of the dynamics in a wide range of complex nanoscopic and colloidal systems that was previously inaccessible to lattice-based continuum algorithms.

Recent years have seen a surge of interest in nanopores because such structures show a strong potential for characterizing nanoparticles, proteins, DNA, and even single molecules. These systems have been extensively studied in experiment as well as by all-atom and coarse-grained simulations, with a strong focus on DNA translocation. However, the equally interesting problem of particle characterization using nanopores has received far less attention. Here, we theoretically investigate the translocation of a nanoparticle through a conical nanocapillary. We use a model based on numerically solving the coupled system of electrokinetic continuum equations, which we introduce in detail. Based on our findings, we formulate basic guidelines for obtaining the maximum current signal during the translocation event, which should be transferable to other nanopore geometries. In addition, the dependence of the signal strength on particle properties, such as surface charge and size, is evaluated. Finally, we identify conditions under which the translocation is prevented by the formation of a strong electro-osmotic barrier and show that the particle may even become trapped at the pore orifice, without imposing an external hydrostatic pressure difference., Comment: 13 pages, 7 figures

Self-propelled particles can spontaneously form dense phases from a dilute suspension in a process referred to as motility-induced phase separation. The properties of the out-of-equilibrium structures that are formed are governed by the specifics of the particle interactions and the strength of the activity. Thus far, most studies into the formation of these structures have focused on spherical colloids, dumbbells, and rod-like particles endowed with various interaction potentials. Only a few studies have examined the collective behavior of more complex particle shapes. Here, we increase the geometric complexity and use Molecular Dynamics simulations to consider the structures formed by triangular self-propelled particles with surface roughness. These triangles either move towards their apex or towards their base, i.e., they possess a polarity. We find that apex-directed triangles cluster more readily, more stably, and have a smoother cluster interface than their base-directed counterparts. A difference between the two polarities is in line with the results of [H.H. Wensink, et al., Phys. Rev. E 89, 010302(R) (2014)], however, we obtain the reversed result when it comes to clustering, namely that apex-directed particles cluster more readily. We further show that reducing the surface roughness negatively impacts the stability of the base-directed structures, suggesting that their formation is in large part due to surface roughness. Our results lay a solid foundation for future experimental and computational studies into the effect of roughness on the collective dynamics of swimmers., Comment: 15 pages, 10 figures

The interaction between swimming microorganisms or artificial self-propelled colloids and passive (tracer) particles in a fluid leads to enhanced diffusion of the tracers. This enhancement has attracted strong interest, as it could lead to new strategies to tackle the difficult problem of mixing on a microfluidic scale. Most of the theoretical work on this topic has focused on hydrodynamic interactions between the tracers and swimmers in a bulk fluid. However, in simulations, periodic boundary conditions (PBCs) are often imposed on the sample and the fluid. Here, we theoretically analyze the effect of PBCs on the hydrodynamic interactions between tracer particles and microswimmers. We formulate an Ewald sum for the leading-order stresslet singularity produced by a swimmer to probe the effect of PBCs on tracer trajectories. We find that introducing periodicity into the system has a surprisingly significant effect, even for relatively small swimmer-tracer separations. We also find that the bulk limit is only reached for very large system sizes, which are challenging to simulate with most hydrodynamic solvers., Comment: 11 pages, 4 figures

We show experimentally that a cheap glass microcapillary can accumulate {\lambda}-phage DNA at its tip and deliver the DNA into the capillary using a combination of electro-osmotic flow, pressure-driven flow, and electrophoresis. We develop an efficient simulation model for this phenomenon based on the electrokinetic equations and the finite-element method. Using our model, we explore the large parameter space of the trapping mechanism by varying the salt concentration, the capillary surface charge, the applied voltage, the pressure difference, and the mobility of the analyte molecules. Our simulation results show that this system can be tuned to capture a wide range of analyte molecules, such as DNA or proteins, based on their electrophoretic mobility. Our method for separation and pre-concentration of analytes has implications for the development of low-cost lab-on-a-chip devices., Comment: 9 pages, 4 figures

Self-propelled colloids (swimmers) in confining geometries follow trajectories determined by hydrodynamic interactions with the bounding surfaces. However, typically these interactions are ignored or truncated to lowest order. We demonstrate that higher-order hydrodynamic moments cause rod-like swimmers to follow oscillatory trajectories in quiescent fluid between two parallel plates, using a combination of lattice-Boltzmann simulations and far-field calculations. This behavior occurs even far from the confining walls and does not require lubrication results. We show that a swimmer's hydrodynamic quadrupole moment is crucial to the onset of the oscillatory trajectories. This insight allows us to develop a simple model for the dynamics near the channel center based on these higher hydrodynamic moments, and suggests opportunities for trajectory-based experimental characterization of swimmers' hydrodynamic properties., Comment: 12 pages, 9 figures, 2 tables

Electrokinetic transport phenomena can strongly influence the behaviour of macromolecules and colloidal particles in solution, with applications in, e.g., DNA translocation through nanopores, electro-osmotic flow in nanocapillaries, and electrophoresis of charged macromolecules. Numerical simulations are an important tool to investigate these electrokinetic phenomena, but are often plagued by spurious fluxes and spurious flows that can easily exceed physical fluxes and flows. Here, we present a method that reduces one of these spurious currents, spurious flow, by several orders of magnitude. We demonstrate the effectiveness and generality of our method for both electrokinetic lattice-Boltzmann and finite-element-method based algorithms by simulating a charged sphere in an electrolyte solution, and flow through a nanopore. We also show that previous attempts to suppress these spurious currents introduce other sources of error., Comment: 13 pages, 7 figures

We consider the efficiency of self-phoretic colloidal particles (swimmers) as a function of the heterogeneity in the surface reaction rate. The set of fluid, species, and electrostatic continuity equations is solved analytically using a linearization and numerically using a finite-element method. To compare spherical swimmers of different size and with heterogeneous catalytic conversion rates, a 'swimmer efficiency' functional $\eta$ is introduced. It is proven, that in order to obtain maximum swimmer efficiency the reactivity has to be localized at the pole(s). Our results also shed light on the sensitivity of the propulsion speed to details of the surface reactivity, a property that is notoriously hard to measure. This insight can be utilized in the design of new self-phoretic swimmers., Comment: 10 pages, 4 figures

A plethora of active matter models exist that describe the behavior of self-propelled particles (or swimmers), both with and without hydrodynamics. However, there are few studies that consider shape-anisotropic swimmers and include hydrodynamic interactions. Here, we introduce a simple method to simulate self-propelled colloids interacting hydrodynamically in a viscous medium using the lattice-Boltzmann technique. Our model is based on raspberry-type viscous coupling and a force/counter-force formalism which ensures that the system is force free. We consider several anisotropic shapes and characterize their hydrodynamic multipolar flow field. We demonstrate that shape-anisotropy can lead to the presence of a strong quadrupole and octupole moments, in addition to the principle dipole moment. The ability to simulate and characterize these higher-order moments will prove crucial for understanding the behavior of model swimmers in confining geometries., Comment: 11 pages, 3 figures, 3 tables

Water is a polar solvent and hence supports the bulk dissociation of itself and its solutes into ions, and the re-association of these ions into neutral molecules in a dynamic equilibrium, e.g., ${\rm H_2O_2}\leftrightharpoons {\rm H^+~+~HO_2^-}$. Using continuum theory, we study the influence of these reactions on the self-propulsion of colloids driven by surface chemical reactions (chemical swimmers) in aqueous solution. The association-dissociation reactions are here shown to have a strong influence on the swimmers' behaviour, and must therefore be included in future modelling. In particular, such bulk reactions permit charged swimmers to propel electrophoretically even if all species involved in the surface reactions are neutral. The bulk reactions also significantly modify the predicted speed of chemical swimmers propelled by ionic currents, by up to an order of magnitude. For swimmers whose surface reactions produce both anions and cations (ionic self-diffusiophoresis), the bulk reactions produce an additional reactive screening length, analogous to the Debye length in electrostatics. This in turn leads to an inverse relationship between swimmer radius and swimming speed, which could provide an alternative explanation for recent experimental observations on Pt-polystyrene Janus swimmers [S. Ebbens et al., Phys. Rev. E 85, 020401 (2012)]. We also use our continuum theory to investigate the effect of the Debye screening length itself, going beyond the infinitely thin limit approximation used by previous analytical theories. We identify significant departures from this limiting behavior for micron-sized swimmers under typical experimental conditions, and find that the limiting behavior fails entirely for nanoscale swimmers., Comment: 25 pages, 12 figures

The so-called 'raspberry' model refers to the hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by [V. Lobaskin and B. D\"unweg, New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. This technique has been used in many simulation studies on the behavior of colloids. However, there are fundamental questions with regards to the use of this model. In this paper, we examine the accuracy with which the raspberry method is able to reproduce Stokes-level hydrodynamic interactions when compared to analytic expressions for solid spheres in simple-cubic crystals. To this end, we consider the quality of numerical experiments that are traditionally used to establish these properties and we discuss their shortcomings. We show that there is a discrepancy between the translational and rotational mobility reproduced by the simple raspberry model and present a way to numerically remedy the problem by adding internal coupling points. Finally, we examine a non-convex shape, namely a colloidal dumbbell, and show that the filled raspberry model replicates the desired hydrodynamic behavior in bulk for this more complicated shape. Our investigation is continued in [J. de Graaf, et al., J. Chem. Phys. 143, 084107 (2015)], wherein we consider the raspberry model in the confining geometry of two parallel plates., Comment: 25 pages, 11 figures

The so-called 'raspberry' model refers to the hybrid lattice-Boltzmann (LB) and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by [V. Lobaskin and B. D\"unweg, New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. In this paper, we present a follow up to our study of the effectiveness of the raspberry model in reproducing hydrodynamic interactions in the Stokes regime for spheres arranged in a simple-cubic crystal [L. Fischer, et al., J. Chem. Phys. 143, 084108 (2015)]. Here, we consider the accuracy with which the raspberry model is able to reproduce such interactions for particles confined between two parallel plates. To this end, we compare our LB simulation results to established theoretical expressions and finite-element calculations. We show that there is a discrepancy between the translational and rotational mobility when only surface coupling points are used, as also found in Part I of our joint publication. We demonstrate that adding internal coupling points to the raspberry, can be used to correct said discrepancy in confining geometries as well. Finally, we show that the raspberry model accurately reproduces hydrodynamic interactions between a spherical colloid and planar walls up to roughly one LB lattice spacing., Comment: 13 pages, 8 figures

Colloidal spheres with a partial platinum surface coating perform auto-phoretic motion when suspended in hydrogen peroxide solution. We present a theoretical analysis of the self-propulsion velocity of these particles using a continuum multi-component, self-diffusiophoretic model. With this model as a basis, we show how the slip-layer approximation can be derived and in which limits it holds. First, we consider the differences between the full multi-component model and the slip-layer approximation. Then the slip model is used to demonstrate and explore the sensitive nature of the particle's velocity on the details of the molecule-surface interaction. We find a strong asymmetry in the dependence of the colloid's velocity as a function of the level of catalytic coating, when there is a different interaction between the solute and solvent molecules and the inert and catalytic part of the colloid, respectively. The direction of motion can even be reversed by varying the level of the catalytic coating. Finally, we investigate the robustness of these results with respect to variations in the reaction rate near the edge between the catalytic and inert parts of the particle. Our results are of significant interest to the interpretation of experimental results on the motion of self-propelled particles., Comment: 20 pages, 8 figures

In continuation of our work in [A.P. Gantapara et al., Phys. Rev. Lett. 111, 015501 (2013)], we investigate here the thermodynamic phase behavior of a family of truncated hard cubes, for which the shape evolves smoothly from a cube via a cuboctahedron to an octahedron. We used Monte Carlo simulations and free-energy calculations to establish the full phase diagram. This phase diagram exhibits a remarkable richness in crystal and mesophase structures, depending sensitively on the precise particle shape. In addition, we examined in detail the nature of the plastic crystal (rotator) phases that appear for intermediate densities and levels of truncation. Our results allow us to probe the relation between phase behavior and building-block shape and to further the understanding of rotator phases. Furthermore, the phase diagram presented here should prove instrumental for guiding future experimental studies on similarly-haped nanoparticles and the creation of new materials., Comment: 19 pages, 12 figures

In this paper we study the electrostatic properties of `Janus' spheres with unequal charge densities on both hemispheres. We introduce a method to compare primitive-model Monte Carlo simulations of the ionic double layer with predictions of (mean-field) nonlinear Poisson-Boltzmann theory. We also derive practical DLVO-like expressions that describe the Janus-particle pair interactions by mean-field theory. Using a large set of parameters, we are able to probe the range of validity of the Poisson-Boltzmann approximation, and thus of DLVO-like theories, for such particles. For homogeneously charged spheres this range corresponds well to the range that was predicted by field-theoretical studies of homogeneously charged flat surfaces. Moreover, we find similar ranges for colloids with a Janus-type charge distribution. The techniques and parameters we introduce show promise for future studies of an even wider class of charged-patterned particles., Comment: 14 pages, 6 figures

The phase diagram of colloidal hard superballs, of which the shape interpolates between cubes and octahedra via spheres, is determined by free-energy calculations in Monte Carlo simulations. We discover not only a stable face-centered cubic (fcc) plastic crystal phase for near-spherical particles, but also a stable body-centered cubic (bcc) plastic crystal close to the octahedron shape, and in fact even coexistence of these two plastic crystals with a substantial density gap. The plastic fcc and bcc crystals are, however, unstable in the cube and octahedron limit, suggesting that the rounded corners of superballs play an important role in stablizing the rotator phases. In addition, we observe a two-step melting phenomenon for hard octahedra, in which the Minkowski crystal melts into a metastable bcc plastic crystal before melting into the fluid phase.

We present a new numerical scheme to study systems of non-convex, irregular, and punctured particles in an efficient manner. We employ this method to analyze regular packings of odd-shaped bodies, not only from a nanoparticle but also both from a computational geometry perspective. Besides determining close-packed structures for many shapes, we also discover a new denser configuration for Truncated Tetrahedra. Moreover, we consider recently synthesized nanoparticles and colloids, where we focus on the excluded volume interactions, to show the applicability of our method in the investigation of their crystal structures and phase behavior. Extensions to the presented scheme include the incorporation of soft particle-particle interactions, the study of quasicrystalline systems, and random packings., Comment: 4 pages, 3 figures

We introduce a new numerical technique, namely triangular tessellation, to calculate the free energy associated with the adsorption of a colloidal particle at a flat interface. The theory and numerical scheme presented here are sufficiently general to handle non-convex patchy colloids with arbitrary surface patterns characterized by a wetting angle, e.g., amphiphilicity. We ignore interfacial deformation due to capillary, electrostatic, or gravitational forces, but the method can be extended to take such effects into account. It is verified that the numerical method presented is accurate and sufficiently stable to be applied to more general situations than presented in this paper. The merits of the tessellation method prove to outweigh those of traditionally used semi-analytic approaches, especially when it comes to generality and applicability., Comment: 21 pages, 11 figures, 0 tables

We calculate ion distributions near a planar oil-water interface within non-linear Poisson-Boltzmann theory, taking into account the Born self-energy of the ions in the two media. For unequal self-energies of cations and anions, a spontaneous charge separation is found such that the water and oil phase become oppositely charged, in slabs with a typical thickness of the Debye screening length in the two media. From the analytical solutions, the corresponding interfacial charge density and the contribution to the interfacial tension is derived, together with an estimate for the Yukawa-potential between two spherical water droplets in oil. The parameter regime is explored where the plasma coupling parameter exceeds the crystallization threshold, i.e. where the droplets are expected to form crystalline structures due to a strong Yukawa repulsion, as recently observed experimentally. Extensions of the theory that we discuss briefly include numerical calculations on spherical water droplets in oil, and analytical calculations of the linear PB-equation for a finite oil-water interfacial width., Comment: 9 pages, 4 figures, accepted by JPCM for proceedings of LMC7

The interfacial tension of a liquid droplet surrounded by another liquid in the presence of microscopic ions is studied as a function of the droplet radius. An analytical expression for the interfacial tension is obtained within a linear Poisson-Boltzmann theory and compared with numerical results from non-linear Poisson-Boltzmann theory. The excess liquid-liquid interfacial tension with respect to the pure, salt-free liquid-liquid interfacial tension is found to decompose into a curvature-independent part due to short-ranged interfacial effects and a curvature-dependent electrostatic contribution. Several curvature-dependent regimes of different scaling of the electrostatic excess interfacial tension are identified. Symmetry relations of the interfacial tension upon swapping droplet and bulk liquid are found to hold in the low-curvature limit, which, e.g., lead to a sign change of the excess Tolman length. For some systems a low-curvature expansion up to second order turns out to be applicable if and only if the droplet size exceeds the Debye screening length in the droplet, independent of the Debye length in the bulk., Comment: submitted

We study the spontaneous charging and the crystallization of spherical micron-sized water-droplets dispersed in oil by numerically solving, within a Poisson-Boltzmann theory in the geometry of a spherical cell, for the density profiles of the cations and anions in the system. We take into account screening, ionic Born self-energy differences between oil and water, and partitioning of ions over the two media. We find that the surface charge density of the droplet as induced by the ion partitioning is significantly affected by the droplet curvature and by the finite density of the droplets. We also find that the salt concentration and the dielectric constant regime in which crystallization of the water droplets is predicted is enhanced substantially compared to results based on the planar oil-water interface, thereby improving quantitative agreement with recent experiments., Comment: 10 pages, 7 figures, submitted for publication

In many applications it will be useful to know those patterns that occur with a balanced interval, e.g., a certain combination of phone numbers are called almost every Friday or a group of products are sold a lot on Tuesday and Thursday. In previous work we proposed a new measure of support (the number of occurrences of a pattern in a dataset), where we count the number of times a pattern occurs (nearly) in the middle between two other occurrences. If the number of non-occurrences between two occurrences of a pattern stays almost the same then we call the pattern balanced. It was noticed that some very frequent patterns obviously also occur with a balanced interval, meaning in every transaction. However more interesting patterns might occur, e.g., every three transactions. Here we discuss a solution using standard deviation and average. Furthermore we propose a simpler approach for pruning patterns with a balanced interval, making estimating the pruning threshold more intuitive.