Direct numerical simulations of electrophoresis of charged colloids

Impact of Inverse Squeezing Flow on the Self-Assembly of Oppositely Charged Colloidal Particles under Electric Field

Hydrodynamic interactions (HIs) play a critical role in the self-organization of colloidal suspensions and biological solutions. However, their roles have remained elusive particularly for charged soft matter systems. Here we consider the role of HIs in the self-assembly of oppositely charged colloidal particles, which is a promising candidate for electrical tunable soft materials. We employ the fluid particle dynamics method to consider many-body HIs and the coupling between the colloid, ion, and fluid motions. We find that, under a constant electric field, oppositely charged colloidal particles form clusters and percolate into a gel network, unlike bundlelike aggregates aligned in the field direction observed by Brownian dynamics simulations neglecting HIs. We reveal that the cluster-forming tendency originates from the incompressibility-induced "inverse squeezing flow" effect that dramatically slows down the disaggregation of attached colloids. Our findings indicate that the HI selects a unique kinetic pathway to the nonequilibrium colloidal self-assembly.

Phonon transport properties of particulate physical gels

Particulate physical gels are sparse, low-density amorphous materials in which clusters of glasses are connected to form a heterogeneous network structure. This structure is characterized by two length scales, ξ s and ξ G: ξ s measures the length of heterogeneities in the network structure and ξ G is the size of glassy clusters. Accordingly, the vibrational states (eigenmodes) of such a material also exhibit a multiscale nature with two characteristic frequencies, [Formula: see text] and ω G, which are associated with ξ s and ξ G, respectively: (i) phonon-like vibrations in the homogeneous medium at [Formula: see text], (ii) phonon-like vibrations in the heterogeneous medium at [Formula: see text], and (iii) disordered vibrations in the glassy clusters at ω > ω G. Here, we demonstrate that the multiscale characteristics seen in the static structures and vibrational states also extend to the phonon transport properties. Phonon transport exhibits two distinct crossovers at frequencies ω* and ω G (or at wavenumbers of [Formula: see text] and [Formula: see text]). In particular, both transverse and longitudinal phonons cross over between Rayleigh scattering at [Formula: see text] and diffusive damping at [Formula: see text]. Remarkably, the Ioffe–Regel limit is located at the very low frequency of ω*. Thus, phonon transport is localized above ω*, even where phonon-like vibrational states persist. This markedly strong scattering behavior is caused by the sparse, porous structure of the gel.

Colloidal density control with Bessel-Gauss beams

Optical manipulation of colloidal systems is of high interest for both fundamental studies and practical applications. It has been shown that optically induced thermophoresis and nonlinear interactions can significantly affect the properties of dense colloidal media. However, macroscopic scale phenomena can also be generated at thermal equilibrium. Here, we demonstrate that steady-state variations of particle density can be created over large, three-dimensional regions by appropriately structured external optical fields. We prove analytically and experimentally that an optical vortex beam can dynamically control the spatial density of microscopic particles along the direction of its propagation. We show that these artificial steady-states can be generated at will and can be maintained indefinitely, which can be beneficial for applications such as path clearing and mass transportation.

Smoothed profile method for direct numerical simulations of hydrodynamically interacting particles

A general method is presented for computing the motions of hydrodynamically interacting particles in various kinds of host fluids for arbitrary Reynolds numbers. The method follows the standard procedure for performing direct numerical simulations (DNS) of particulate systems, where the Navier-Stokes equation must be solved consistently with the motion of the rigid particles, which defines the temporal boundary conditions to be satisfied by the Navier-Stokes equation. The smoothed profile (SP) method provides an efficient numerical scheme for coupling the continuum fluid mechanics with the dispersed moving particles, which are allowed to have arbitrary shapes. In this method, the sharp boundaries between solid particles and the host fluid are replaced with a smeared out thin shell (interfacial) region, which can be accurately resolved on a fixed Cartesian grid utilizing a SP function with a finite thickness. The accuracy of the SP method is illustrated by comparison with known exact results. In the present paper, the high degree of versatility of the SP method is demonstrated by considering several types of active and passive particle suspensions.

The first normal stress difference of non-Brownian hard-sphere suspensions in the oscillatory shear flow near the liquid and crystal coexistence region

We carry out a numerical study to investigate the dynamics of non-Brownian hard-sphere suspensions near the liquid and crystal coexistence region in small to large amplitude oscillatory shear flow. The first normal stress difference (N1) and related rheological functions are carefully analyzed, focusing on the strain stiffening phenomenon, which occurs in the large strain amplitude region. Under oscillatory shear, we observe several unique behaviors of N1. A negative nonzero mean value of N1 (N1,0) is observed for the applied strain amplitudes. The change of the sign, from negative to positive, at the maximum value of N1 (N1,max) is observed at a specific point, which is not consistent with the critical strain amplitude (γ0,c) at which the modulus begins to deviate from linear viscoelasticity. The behavior of N1 in the oscillatory shear flow is different from that of N1 in steady shear flow, that is, the characteristics of N1 in strain stiffening and shear thickening are quite distinguished from each other. We also perform structural analysis to confirm the relationship between the rheological properties and microstructure of the suspension. A strong correlation is observed between the global bond order parameter (Ψ6) and the distortions in both nonlinear shear and normal stresses. The most noticeable characteristic is captured through the maximum of the global bond order parameter (Ψ6,max). The strain amplitude at the slope change of Ψ6,max corresponds to the point where a unique behavior of N1 is observed, i.e. the change of the sign in N1,max, but a strong correlation is not captured at γ0,c. This demonstrates that the normal stress responds to particle ordering more sensitively than other rheological functions based on shear stress like dynamic moduli. As far as we are concerned, the behavior of N1 has rarely been fully explored and related with the strain stiffening of non-Brownian suspensions so far. Therefore, this study has significance as the first report to strictly analyze strain stiffening along with the first normal stress difference N1.

Particle dynamics at fluid interfaces studied by the color gradient lattice Boltzmann method coupled with the smoothed profile method

We suggest a numerical method to describe particle dynamics at the fluid interface. We adopt a coupling strategy by combining the color gradient lattice Boltzmann method (CGLBM) and smoothed profile method (SPM). The proposed scheme correctly resolves the momentum transfer among the solid particles and fluid phases while effectively controlling the wetting condition. To validate the present algorithm (CGLBM-SPM), we perform several simulation tests like wetting a single solid particle and capillary interactions in two solid particles floating at the fluid interface. Simulation results show a good agreement with the analytical solutions available and look qualitatively reasonable. From these analyses, we conclude that the key features of the particle dynamics at the fluid interface are correctly resolved in our simulation method. In addition, we apply the present method for spinodal decomposition of a ternary mixture, which contains two-immiscible fluids with solid particles. By adding solid particles, fluid segregation is much suppressed than in the binary liquid mixture case. Furthermore, it has different morphology, such as with the jamming structure of the particles at the fluid interface, and captured images are similar to bicontinuous interfacially jammed emulsion gels in literature. From these results, we confirm the feasibility of the present method to describe soft matters; in particular, emulsion systems that contain solid particles at the interface.

Self-assembly of charged colloidal cubes

In this work, we show how and why the interactions between charged cubic colloids range from radially isotropic to strongly directionally anisotropic, depending on tuneable factors. Using molecular dynamics simulations, we illustrate the effects of typical solvents to complement experimental investigations of cube assembly. We find that in low-salinity water solutions, where cube self-assembly is observed, the colloidal shape anisotropy leads to the strongest attraction along the corner-to-corner line, followed by edge-to-edge, with a face-to-face configuration of the cubes only becoming energetically favorable after the colloids have collapsed into the van der Waals attraction minimum. Analysing the potential of mean force between colloids with varied cubicity, we identify the origin of the asymmetric microstructures seen in experiment.

Effects of viscoelasticity on shear-thickening in dilute suspensions in a viscoelastic fluid

We investigate previously unclarified effects of fluid elasticity on shear-thickening in dilute suspensions in an Oldroyd-B viscoelastic fluid using a novel direct numerical simulation based on the smoothed profile method. Fluid elasticity is determined by the Weissenberg number Wi and by viscosity ratio 1 - β = ηp/(ηs + ηp) which measures the coupling between the polymer stress and flow: ηp and ηs are the polymer and solvent viscosity, respectively. As 1 - β increases, while the stresslet does not change significantly compared to that in the β → 1 limit, the growth rate of the normalized polymer stress with Wi was suppressed. Analysis of flow and conformation dynamics around a particle for different β reveals that at large 1 - β, polymer stress modulates flow, leading to suppression of polymer stretch. This effect of β on polymer stress development indicates complex coupling between fluid elasticity and flow, and is essential to understand the rheology and hydrodynamic interactions in suspensions in viscoelastic media.

Bridging the gap between molecular dynamics and hydrodynamics in nanoscale Brownian motions

Through molecular dynamics simulations, we examined the hydrodynamic behavior of the Brownian motion of fullerene particles based on molecular interactions. The solvation free energy and velocity autocorrelation function (VACF) were calculated by using the Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) potentials for the solute-solvent and solvent-solvent interactions and by changing the size of the fullerene particles. We also measured the diffusion constant of the fullerene particles and the shear viscosity of the host fluid, and then the hydrodynamic radius aHD was quantified from the Stokes-Einstein relation. The aHD value exceeds that of the gyration radius of the fullerene when the solvation free energy exhibits largely negative values using the LJ potential. In contrast, aHD is similar to the size of bare fullerene when the solvation free energy is positive using the WCA potential. Furthermore, the VACF of the fullerene particles is directly comparable with the analytical expressions utilizing the Navier-Stokes equations both in incompressible and compressible forms. A hydrodynamic long-time tail t-3/2 is demonstrated for timescales longer than the kinematic time of the momentum diffusion over the particle size. However, the VACF at shorter timescales deviates from the hydrodynamic description, particularly for smaller fullerene particles and for the LJ potential. This occurs even though the compressible effect is considered when characterizing the decay of the VACF around the sound-propagation timescale over the particle size. These results indicate that the nanoscale Brownian motion is influenced by the solvation structure around the solute particles originating from the molecular interaction.

Mechanism of diffusiophoresis with chemical reaction on a colloidal particle

A mechanism for diffusiophoresis of a charged colloidal particle undergoing surface chemical reaction is proposed. A theoretical model is constructed to describe the dynamics of the particle and the surrounding solution of a weak electrolyte. Theoretical analysis and numerical simulations of the model reveal that phoretic motion of the particle emerges in response to a concentration gradient of electrolyte. The concentration gradient breaks the spherical symmetry of the surface charge distribution, which gives rise to a net force on the particle and leads to directional motion of the particle.

Hydrodynamic simulations of charge-regulation effects in colloidal suspensions

Self-organization of charged soft matter is of crucial importance in biology. However, it is an extremely complex phenomenon due to dynamical couplings between the hydrodynamic flow, ions, and charges of soft matter. For colloidal suspensions, the coupling between the former two has already been studied by numerical simulations, with the colloid surface charge being fixed. However, the self-organization of colloids and/or the application of an external electric field make the electrostatic environment of each colloid inhomogeneous in both space and time. Thus, this leads to inhomogenisation of the surface charge of each colloid under ionisation equilibrium conditions. This effect is known as "charge regulation" and is of great importance in various electrostatic and electrokinetic phenomena not only in colloid suspensions but also in solutions of biomolecules. However, there has so far been no success in taking the charge regulation effect into account in numerical simulations of colloidal electrokinetics. Here, we extend the fluid particle dynamics (FPD) method to incorporate the charge regulation effect. We present a theoretical formulation of the method and its application to two types of problems, where charge regulation plays an important role: (i) cluster formation of colloid particles and (ii) a single colloid particle under an external field. By these examples, we show not only the importance of considering charge-regulation effects in the self-organization of charged systems but also the applicability of our simulation method to more complex problems of charged soft matter systems.

Field-induced dipolar attraction between like-charged colloids

The field induced anisotropic interactions between like-charged colloidal particles is studied using direct numerical simulations, where the polarization of the electric double layer is explicitly computed under external AC electric fields. These interactions are found to depend on the magnitude E0 and frequency ω of the applied field, as well as the zeta potential, the Debye length, and the relative orientation of the particles. We also determined the range of E0 and ω over which a dipolar attraction is induced between a pair of like-charged colloids. Finally, we performed simulations for systems of six and twelve colloidal particles to study the stability of pear-chain-like configurations.

Physical foundation of the fluid particle dynamics method for colloid dynamics simulation

Colloid dynamics is significantly influenced by many-body hydrodynamic interactions mediated by a suspending fluid. However, theoretical and numerical treatments of such interactions are extremely difficult. To overcome this situation, we developed a fluid particle dynamics (FPD) method [H. Tanaka and T. Araki, Phys. Rev. Lett., 2000, 35, 3523], which is based on two key approximations: (i) a colloidal particle is treated as a highly viscous particle and (ii) the viscosity profile is described by a smooth interfacial profile function. Approximation (i) makes our method free from the solid-fluid boundary condition, significantly simplifying the treatment of many-body hydrodynamic interactions while satisfying the incompressible condition without the Stokes approximation. Approximation (ii) allows us to incorporate an extra degree of freedom in a fluid, e.g., orientational order and concentration, as an additional field variable. Here, we consider two fundamental problems associated with these approximations. One is the introduction of thermal noise and the other is the incorporation of coupling of the colloid surface with an order parameter introduced into a fluid component, which is crucial when considering colloidal particles suspended in a complex fluid. Here, we show that our FPD method makes it possible to simulate colloid dynamics properly while including full hydrodynamic interactions, inertia effects, incompressibility, thermal noise, and additional degrees of freedom of a fluid, which may be relevant for wide applications in colloidal and soft matter science.

Reynolds-number-dependent dynamical transitions on hydrodynamic synchronization modes of externally driven colloids

The collective dynamics of externally driven N_{p}-colloidal systems (1≤N_{p}≤4) in a confined viscous fluid have been investigated using three-dimensional direct numerical simulations with fully resolved hydrodynamics. The dynamical modes of collective particle motion are studied by changing the particle Reynolds number as determined by the strength of the external driving force and the confining wall distance. For a system with N_{p}=3, we found that at a critical Reynolds number a dynamical mode transition occurs from the doublet-singlet mode to the triplet mode, which has not been reported experimentally. The dynamical mode transition was analyzed in detail from the following two viewpoints: (1) spectrum analysis of the time evolution of a tagged particle velocity and (2) the relative acceleration of the doublet cluster with respect to the singlet particle. For a system with N_{p}=4, we found similar dynamical mode transitions from the doublet-singlet-singlet mode to the triplet-singlet mode and further to the quartet mode.

Purely hydrodynamic origin for swarming of swimming particles

Three-dimensional simulations with fully resolved hydrodynamics are performed to study the collective motion of model swimmers in bulk and confinement. Calculating the dynamic structure factor, we clarified that the swarming in bulk systems can be understood as a pseudoacoustic mode. Under confinement between flat parallel walls, this pseudoacoustic mode leads to a traveling wavelike motion. This swarming behavior is due purely to the hydrodynamic interactions between the swimmers and depends strongly on the type and strength of swimming (i.e., pusher or puller).

Celebrating Soft Matter's 10th Anniversary: Influencing the charge of poly(methyl methacrylate) latexes in nonpolar solvents

Sterically-stabilized poly(methyl methacrylate) (PMMA) latexes dispersed in nonpolar solvents are a classic, well-studied system in colloid science. This is because they can easily be synthesized with a narrow size distribution and because they interact essentially as hard spheres. These PMMA latexes can be charged using several methods (by adding surfactants, incorporating ionizable groups, or dispersing in autoionizable solvents), and due to the low relative permittivity of the solvents (εr ≈ 2 for alkanes to εr ≈ 8 for halogenated solvents), the charges have long-range interactions. The number of studies of these PMMA particles as charged species has increased over the past ten years, after few studies immediately following their discovery. A large number of variations in both the physical and chemical properties of the system (size, concentration, surfactant type, or solvent, as a few examples) have been studied by many groups. By considering the literature on these particles as a whole, it is possible to determine the variables that have an effect on the charge of particles. An understanding of the process of charge formation will add to understanding how to control charge in nonaqueous solvents as well as make it possible to develop improved technologically relevant applications for charged polymer nanoparticles.

Full Characterization of Colloidal Dynamics at Low Péclet Numbers

Although critical in applications, the dynamics of colloidal systems at low Péclet numbers is poorly understood. Here we introduce an optical technique that permits for the first time a complete characterization of this regime through a continuous and independent measurement of both the diffusive and the advective components of a system's dynamics. For the particular example of gravity-driven colloids, we demonstrate experimentally that the hydrodynamic size and the mass density of particulate suspensions can be measured simultaneously. The proven capabilities are of particular interest for studying the spatial and temporal properties of inhomogeneous colloidal systems where aggregation and structural evolution play major roles.

Computer simulations of single particles in external electric fields

Applying electric fields is an attractive way to control and manipulate single particles or molecules, e.g., in lab-on-a-chip devices. However, the response of nanosize objects in electrolyte solution to external fields is far from trivial. It is the result of a variety of dynamical processes taking place in the ion cloud surrounding charged particles and in the bulk electrolyte, and it is governed by an intricate interplay of electrostatic and hydrodynamic interactions. Already systems composed of one single particle in electrolyte solution exhibit a complex dynamical behaviour. In this review, we discuss recent coarse-grained simulations that have been performed to obtain a molecular-level understanding of the dynamic and dielectric response of single particles and single macromolecules to external electric fields. We address both the response of charged particles to constant fields (DC fields), which can be characterized by an electrophoretic mobility, and the dielectric response of both uncharged and charged particles to alternating fields (AC fields), which is described by a complex polarizability. Furthermore, we give a brief survey of simulation algorithms and highlight some recent developments.

Self-consistent description of electrokinetic phenomena in particle-based simulations

A new computational method is presented for study suspensions of charged particles undergoing fluctuating hydrodynamic and electrostatic interactions. The proposed model is appropriate for polymers, proteins, and porous particles embedded in a continuum electrolyte. A self-consistent Langevin description of the particles is adopted in which hydrodynamic and electrostatic interactions are included through a Green's function formalism. An Ewald-like split is adopted in order to satisfy arbitrary boundary conditions for the Stokeslet and Poisson Green functions, thereby providing a formalism that is applicable to any geometry and that can be extended to deformable objects. The convection-diffusion equation for the continuum ions is solved simultaneously considering Nernst-Planck diffusion. The method can be applied to systems at equilibrium and far from equilibrium. Its applicability is demonstrated in the context of electrokinetic motion, where it is shown that the ionic clouds associated with individual particles can be severely altered by the flow and concentration, leading to intriguing cooperative effects.

Rheology and microstructure of non-Brownian suspensions in the liquid and crystal coexistence region: strain stiffening in large amplitude oscillatory shear

Concentrated hard-sphere suspensions in the liquid and crystal coexistence region show a unique nonlinear behavior under a large amplitude oscillatory shear flow, the so-called strain stiffening, in which the viscosity or modulus suddenly starts to increase near a critical strain amplitude. Even though this phenomenon has been widely reported in experiments, its key mechanism has never been investigated in a systematic way. To have a good understanding of this behavior, a numerical simulation was performed using the lattice Boltzmann method (LBM). Strain stiffening was clearly observed at large strain amplitudes, and the critical strain amplitude showed an angular frequency dependency. The distortion of the shear stress appeared near the critical strain amplitude, and the nonlinear behavior was quantified by the Fourier transformation (FT) and the stress decomposition methods. Above the critical strain amplitude, an increase in the global bond order parameter Ψ(6) was observed at the flow reversal. The maximum of Ψ(6) and the maximum shear stress occurred at the same strain. These results show how strongly the ordered structure of the particles is related to the stress distortion. The ordered particles maintained a bond number of "two" with alignment with the compressive axis, and they were distributed over a narrow range of angular distribution (110°-130°). In addition, the ordered structure was formed near the lowest shear rate region (the flow reversal). The characteristics of the ordered structure were remarkably different from those of the hydroclusters which are regarded as the origin of shear thickening. It is clear that strain stiffening and shear thickening originate from different mechanisms. Our results clearly demonstrate how the ordering of the particles induces strain stiffening in the liquid and crystal coexistence region.

Local shear stress and its correlation with local volume fraction in concentrated non-Brownian suspensions: lattice Boltzmann simulation

The local shear stress of non-Brownian suspensions was investigated using the lattice Boltzmann method coupled with the smoothed profile method. Previous studies have only focused on the bulk rheology of complex fluids because the local rheology of complex fluids was not accessible due to technical limitations. In this study, the local shear stress of two-dimensional solid particle suspensions in Couette flow was investigated with the method of planes to correlate non-Newtonian fluid behavior with the structural evolution of concentrated particle suspensions. Shear thickening was successfully captured for highly concentrated suspensions at high particle Reynolds number, and both the local rheology and local structure of the suspensions were analyzed. It was also found that the linear correlation between the local particle stress and local particle volume fraction was dramatically reduced during shear thickening. These results clearly show how the change in local structure of suspensions influences the local and bulk rheology of the suspensions.

Dynamic electrophoresis of charged colloids in an oscillating electric field

The dynamics of charged colloids in an electrolyte solution is studied using direct numerical simulations via the smoothed profile method. We calculated the complex electrophoretic mobility μ(ω) of the charged colloids under an oscillating electric field of frequency ω. We show the existence of three dynamically distinct regimes, determined by the momentum diffusion and ionic diffusion time scales. The present results agree well with approximate theories based on the cell model in dilute suspensions; however, systematic deviations between the simulation results and theoretical predictions are observed as the volume fraction of colloids is increased, similar to the case of constant electric fields.

Computing the electrophoretic mobility of large spherical colloids by combining explicit ion simulations with the standard electrokinetic model

The electrophoretic mobility of large spherical colloids in different salt solutions of varying valency and concentration is studied via a combination approach of numerically solving the standard electrokinetic model with a ζ potential that has been obtained from explicit ion simulations of the restricted primitive model, thus going beyond the standard mean-field treatment. We compare our theoretical mobility curves to two distinct sets of experimental results and obtain good agreement for monovalent and divalent salt solutions. For the case of the trivalent La(3+) salt, the experimentally obtained mobility reversal at high ionic strengths can be obtained only by adding an additional attractive interaction of 4k(B)T to the potential between the colloid and La(3+), hinting at the presence of a nonelectrostatic binding term for this ion. It is also shown that, contrary to intuition, charge inversion does not necessarily result in mobility reversal.

Mathematical modeling of blood clot fragmentation during flow-mediated thrombolysis

A microscale mathematical model of blood clot dissolution based on coarse-grained molecular dynamics is presented. In the model, a blood clot is assumed to be an assembly of blood cells interconnected with elastic fibrin bonds, which are cleaved either biochemically (bond degradation) or mechanically (bond overstretching) during flow-mediated thrombolysis. The effect of a thrombolytic agent on biochemical bond degradation was modeled phenomenologically by assuming that the decay rate of an individual bond is a function of the remaining noncleaved bonds in the vicinity of that bond (spatial corrosion) and the relative stretching of the bond (deformational corrosion). The results of simulations indicate that the blood clot dissolution process progresses by a blood-flow-promoted removal of clot fragments, the sizes of which are flow-dependent. These findings are in good agreement with the results of our recent optical-microscopy experimental studies on a model of blood clot dissolution, as well as with clinical observations. The findings of this study may contribute to a better understanding of the clot fragmentation process and may therefore also help in designing new, safer thrombolytic approaches.

Numerical electrokinetics

A new lattice method is presented in order to efficiently solve the electrokinetic equations, which describe the structure and dynamics of the charge cloud and the flow field surrounding a single charged colloidal sphere, or a fixed array of such objects. We focus on calculating the electrophoretic mobility in the limit of small driving field, and systematically linearize the equations with respect to the latter. This gives rise to several subproblems, each of which is solved by a specialized numerical algorithm. For the total problem we combine these solvers in an iterative procedure. Applying this method, we study the effect of the screening mechanism (salt screening versus counterion screening) on the electrophoretic mobility, and find a weak non-trivial dependence, as expected from scaling theory. Furthermore, we find that the orientation of the charge cloud (i.e. its dipole moment) depends on the value of the colloid charge, as a result of a competition between electrostatic and hydrodynamic effects.

Electrokinetics on superhydrophobic surfaces

On a superhydrophobic surface a liquid is exposed to a large air-water interface. The reduced wall friction is expected to cause a higher electro-osmotic mobility. On the other hand, the low charge density of a superhydrophobic surface reduces the electro-osmotic mobility. Due to a lack of experimental data it has not been clear so far whether the reduced wall friction or the reduced charge density dominate the electrokinetic mobilities. To separate the relative contributions of electrophoresis and electro-osmosis, the mobilities of colloids on a negatively charged hydrophilic, a superhydrophobic (Cassie) and a partially hydrophilized superhydrophobic (Cassie composite) coating were measured. To vary the charge density as well as its sign with respect to those of the colloids the partially hydrophilized surfaces were coated with polyelectrolytes. We analyzed the electrokinetic mobilities of negatively charged polystyrene colloids dispersed in aqueous medium on porous hydrophilic and superhydrophobic surfaces by confocal laser scanning electron microscopy. In all cases, the external electric field was parallel to the surface. The total electrokinetic mobilities on the superhydrophobic (Cassie) and negatively charged partially hydrophilized (Cassie composite) surfaces were similar, showing that electro-osmosis is small compared to electrophoresis. The positively charged Cassie composite surfaces tend to 'trap' the colloids due to attracting electrostatic interactions and rough morphology, reducing the mobility. Thus, either the charge density of the coatings in the Cassie composite state or its slip length is too low to enhance electro-osmosis.

Primary charge effects on prolate spheroids with moderate aspect ratios

In this article, we investigate the behavior of charged spheroidal colloids with moderate aspect ratios in linear flow fields. We use direct numerical simulation with body-fitted grids for the solution of the Stokes-Poisson-Nernst-Planck system to include all non-linear effects. Therefore, we propose an efficient semi-implicit time discretization based on a splitting of the Stokes equation. We will study the effects of the electric double layer on the forces, torques and on the motion of spheroidal particles. For low Reynolds numbers, we find approximating linear expressions between the ambient fluid flow and the force and torque on the particle. The description of this linear behavior is based on the resistance functions, whose dependencies on the Debye length and the zeta potential are investigated. It is recovered that the resistance functions obey a quadratic dependence on the zeta potential in the small zeta potential regime. For low values of the zeta potential, approximate formulas for the resistance functions are given. The approximation properties are carefully studied by comparing the approximate results with direct numerical simulations. For the case of a shear flow, the approximate formulas can be used to avoid time-consuming direct numerical simulations.

Determination of the zeta potential for highly charged colloidal suspensions

We compute the electrostatic potential at the surface, or zeta potential ζ, of a charged particle embedded in a colloidal suspension using a hybrid mesoscopic model. We show that, for weakly perturbing electric fields, the value of ζ obtained at steady state during electrophoresis is statistically indistinguishable from ζ in thermodynamic equilibrium. We quantify the effect of counter-ion concentration on ζ. We also evaluate the relevance of the lattice resolution for the calculation of ζ and discuss how to identify the effective electrostatic radius.

Colloid electrophoresis for strong and weak ion diffusivity

We study the electrophoretic flow of suspensions of charged colloids with a mesoscopic method that allows us to model generic experimental conditions. We show that for highly charged colloids their electrophoretic mobility increases significantly and displays a mobility maximum on increasing the colloidal charge for all salt concentrations. The electrophoretic mobility of highly charged colloids is also enhanced significantly when ion advection is dominant, leading to a strong heterogeneity in the local electrophoretic response especially at low-salt concentration, when ion diffuse layers overlap.

Implementation of Lees-Edwards periodic boundary conditions for direct numerical simulations of particle dispersions under shear flow

A general methodology is presented to perform direct numerical simulations of particle dispersions in a shear flow with Lees-Edwards periodic boundary conditions. The Navier-Stokes equation is solved in oblique coordinates to resolve the incompatibility of the fluid motions with the sheared geometry, and the force coupling between colloidal particles and the host fluid is imposed by using a smoothed profile method. The validity of the method is carefully examined by comparing the present numerical results with experimental viscosity data for particle dispersions in a wide range of volume fractions and shear rates including nonlinear shear-thinning regimes.

A direct numerical simulation method for complex modulus of particle dispersions

We report an extension of the smoothed profile method (SPM) (Y. Nakayama, K. Kim, and R. Yamamoto, Eur. Phys. J. E 26, 361 (2008)), a direct numerical simulation method for calculating the complex modulus of the dispersion of particles, in which we introduce a temporally oscillatory external force into the system. The validity of the method was examined by evaluating the storage G'(ω) and loss G"(ω) moduli of a system composed of identical spherical particles dispersed in an incompressible Newtonian host fluid at volume fractions of Φ = 0 , 0.41, 0.46, and 0.51. The moduli were evaluated at several frequencies of shear flow; the shear flow used here has a zigzag profile, as is consistent with the usual periodic boundary conditions. The simulation results were compared with several experiments for colloidal dispersions of spherical particles.

Modeling Electrokinetic Flows by the Smoothed Profile Method

We propose an efficient modeling method for electrokinetic flows based on the Smoothed Profile Method (SPM) [1-4] and spectral element discretizations. The new method allows for arbitrary differences in the electrical conductivities between the charged surfaces and the the surrounding electrolyte solution. The electrokinetic forces are included into the flow equations so that the Poisson-Boltzmann and electric charge continuity equations are cast into forms suitable for SPM. The method is validated by benchmark problems of electroosmotic flow in straight channels and electrophoresis of charged cylinders. We also present simulation results of electrophoresis of charged microtubules, and show that the simulated electrophoretic mobility and anisotropy agree with the experimental values.

Electric-field-induced yielding of colloidal gels in microfluidic capillaries

We introduce a method to generate a purely internal rupture of colloidal particle gels by application of an electric field as they are confined in a microfluidic device. Characterization of the local, microstructural effect of yielding made possible by the device avoids the complication of shear banding that often occurs in attempts to generate yielding of colloidal gels. The gels are comprised of spherical sterically stabilized poly(methyl methacrylate) particles suspended in a density and refractive index matched organic solvent mixture. Because the particles are charged, application of an electric field imposes a force on the gel body that results in homogeneous internal rupture and yielding. After cessation of the electric field, the gel network rapidly reforms. The structure of the reformed gel differs significantly from the one present prior to the application of the electric field. The microstructural changes that accompany the yielding transition are quantified by comparing confocal microscopy image volumes acquired before and after rupture. We find that the local structure of the colloidal gel after recovery, as quantified by the contact number distribution, is negligibly affected by the yielding transition; however, the long-range structure of the gel, as quantified by spatial fluctuations in number density, is significantly impacted. The result highlights the effect of the small number of short-range bond-breaking events that induce the observed changes in collective, long-range structure.

Nonmonotonic density dependence of the diffusion of DNA fragments in low-salt suspensions

The high linear charge density of 20-base-pair oligomers of DNA is shown to lead to a striking nonmonotonic dependence of the long-time self-diffusion on the concentration of DNA in low-salt conditions. This generic nonmonotonic behavior results from the strong coupling between the electrostatic and solvent-mediated hydrodynamic interactions, from the renormalization of these electrostatic interactions at large separations, and specifically from the dominance of the far-field hydrodynamic interactions caused by the strong repulsion between the DNA fragments.

Simulating (electro)hydrodynamic effects in colloidal dispersions: smoothed profile method

Previously, we have proposed a direct simulation scheme for colloidal dispersions in a Newtonian solvent (Phys. Rev. E 71, 036707 (2005)). An improved formulation called the "Smoothed Profile (SP) method" is presented here in which simultaneous time-marching is used for the host fluid and colloids. The SP method is a direct numerical simulation of particulate flows and provides a coupling scheme between the continuum fluid dynamics and rigid-body dynamics through utilization of a smoothed profile for the colloidal particles. Moreover, the improved formulation includes an extension to incorporate multicomponent fluids, allowing systems such as charged colloids in electrolyte solutions to be studied. The dynamics of the colloidal dispersions are solved with the same computational cost as required for solving non-particulate flows. Numerical results which assess the hydrodynamic interactions of colloidal dispersions are presented to validate the SP method. The SP method is not restricted to particular constitutive models of the host fluids and can hence be applied to colloidal dispersions in complex fluids.

Influence of hydrodynamic interactions on lane formation in oppositely charged driven colloids

The influence of hydrodynamic interactions on lane formation of oppositely charged driven colloidal suspensions is investigated using Brownian dynamics computer simulations performed on the Rotne-Prager level of the mobility tensor. Two cases are considered, namely sedimentation and electrophoresis. In the latter case the Oseen contribution to the mobility tensor is screened due to the opposite motion of counterions. The simulation results are compared to that resulting from simple Brownian dynamics where hydrodynamic interactions are neglected. For sedimentation, we find that hydrodynamic interactions strongly disfavor laning. In the steady state of lanes, a macroscopic phase separation of lanes is observed. This is in marked contrast to the simple Brownian case where a finite size of lanes was obtained in the steady state. For strong Coulomb interactions between the colloidal particles a lateral square lattice of oppositely driven lanes is stable similar to the simple Brownian dynamics. In an electric field, on the other hand, the behavior is found in qualitative and quantitative accordance with the case of neglected hydrodynamics.

Interplay between hydrodynamic and Brownian fluctuations in sedimenting colloidal suspensions

We apply a hybrid molecular dynamics and mesoscopic simulation technique to study the steady-state sedimentation of hard sphere particles for Peclet number (Pe) ranging from 0.08 to 12. Hydrodynamic backflow causes a reduction of the average sedimentation velocity relative to the Stokes velocity. We find that this effect is independent of Pe number. Velocity fluctuations show the expected effects of thermal fluctuations at short correlation times. At longer times, nonequilibrium hydrodynamic fluctuations are visible, and their character appears to be independent of the thermal fluctuations. The hydrodynamic fluctuations dominate the diffusive behavior even for modest Pe number, while conversely the short-time fluctuations are dominated by thermal effects for surprisingly large Pe numbers. Inspired by recent experiments, we also study finite sedimentation in a horizontal planar slit. In our simulations distinct lateral patterns emerge, in agreement with observations in the experiments.

Electrophoresis of colloidal dispersions in the low-salt regime

We study the electrophoretic mobility of spherical charged colloids in a low-salt suspension as a function of the colloidal concentration. Using an effective particle charge and a reduced screening parameter, we map the data for systems with different particle charges and sizes, including numerical simulation data with full electrostatics and hydrodynamics and experimental data for latex dispersions, on a single master curve. We observe two different volume fraction-dependent regimes for the electrophoretic mobility that can be explained in terms of the static properties of the ionic double layer.

Transverse migration of a confined polymer driven by an external force

We demonstrate that a polymer confined to a narrow channel migrates towards the center when driven by an external force parallel to the channel walls. This migration results from asymmetric hydrodynamic interactions between polymer segments and the confining walls. A weak pressure-driven flow, applied in the same direction as the external force, enhances the migration. However, when the pressure gradient and the external force act in opposite directions the polymer can migrate towards the boundaries. Nevertheless, for sufficiently strong forces the polymer always migrates towards the center. A dumbbell kinetic theory explains these results qualitatively. A comparison of our results with experimental measurements on DNA suggests that hydrodynamic interactions in polyelectrolytes are only partially screened. We propose new experiments and analysis to investigate the extent of the screening in polyelectrolyte solutions.