Diffusiophoresis of concentrated suspensions of spherical particles with identical ionic diffusion velocities

Diffusiophoresis of concentrated suspensions of spherical particles subject to a small electrolyte gradient is analyzed theoretically at arbitrary levels of zeta potential and double-layer thickness. The Kuwabara unit cell model is adopted to describe the system under consideration. The effect of double-layer polarization is taken into account. It is found that the diffusiophoretic mobility exhibits a local maximum as well as a local minimum with varying zeta potential or double-layer thickness, similar to the corresponding dilute dispersion. The direction of the particle movement may even change back and forth. The previous low-zeta-potential approach is found to significantly overestimate the diffusiophoretic mobility as the zeta potential goes high. The deviation may be several fold sometimes. The effect of the volume fraction ratio of colloids is also examined. The higher the ratio, the lower the mobility.     

Complex shear modulus of concentrated suspensions of solid spherical particles

Starting from the complex shear modulus equation for a dilute suspension system, three new equations are developed for the complex shear modulus of concentrated suspensions of solid spheres. The continuous phase (matrix) and the dispersed particles are treated as viscoelastic materials in the derivation. Complex shear modulus data on suspensions of spherical glass beads in polymeric liquid were obtained experimentally and compared with the predictions of the proposed equations. The proposed equations describe the experimental data reasonably well.     

Diffusiophoresis in suspensions of highly charged soft particles

Diffusiophoresis phenomenon of aoft particles suspended in binary electrolyte solutions is explored theoretically in this study based on the spherical cell model, focusing on the chemiphoresis component in absence of diffusion potential. Both the electrostatic and hydrodynamic aspects of the boundary confinement, or steric effect, due to the presence of neighboring particles are examined extensively under various electrokinetic conditions. Significant local extrema are found in mobility profiles expressed as functions of the Debye length in general, synchronized with the strength of the motion-inducing double layer polarization. Moreover, a seemingly peculiar phenomenon is observed that the soft particles may move faster in more concentrated suspensions. The competition between the simultaneous enhancement of the motion-inducing electric driving force and the motion-retarding hydrodynamic drag force from the boundary confinement effect of the neighboring particles is found to be responsible for it. The above findings are also demonstrated experimentally in a very recent study on the diffusiophoretic motion of soft particles through porous collagen hydrogels. The results presented here are useful in various practical applications of soft particles like drug delivery.     

Dynamic electrophoretic mobility of spherical colloidal particles in salt-free concentrated suspensions

In this contribution, the dynamic electrophoretic mobility of spherical colloidal particles in a salt-free concentrated suspension subjected to an oscillating electric field is studied theoretically using a cell model approach. Previous calculations focusing the analysis on cases of very low or very high particle surface charge are analyzed and extended to arbitrary conditions regarding particle surface charge, particle radius, volume fraction, counterion properties, and frequency of the applied electric field (sub-GHz range). Because no limit is imposed on the volume fractions of solids considered, the overlap of double layers of adjacent particles is accounted for. Our results display not only the so-called counterion condensation effect for high particle charge, previously described in the literature, but also its relative influence on the dynamic electrophoretic mobility throughout the whole frequency spectrum. Furthermore, we observe a competition between different relaxation processes related to the complex electric dipole moment induced on the particles by the field, as well as the influence of particle inertia at the high-frequency range. In addition, the influences of volume fraction, particle charge, particle radius, and ionic drag coefficient on the dynamic electrophoretic mobility as a function of frequency are extensively analyzed.     

Kinetics of supramolecular crystallization of concentrated suspensions of monodisperse spherical silica particles

The kinetics of supramolecular crystallization of concentrated suspensions is three-dimensional and follows the Avrami-Erofeev equation: A=1-exp[-(kt)^m], where m=4. The rate constant k is proportional to the probability of the appearance of a crystallization center in unit volume in unit time and the linear crystal growth rate, which is determined experimentally.     

Diffusiophoresis in a suspension of spherical particles with arbitrary double-layer thickness

The diffusiophoresis in a homogeneous suspension of identical dielectric spheres with an arbitrary thickness of the electric double layers in a solution of a symmetrically charged electrolyte with a constant imposed concentration gradient is analytically studied. The effects of particle interactions (or particle volume fraction) are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations that govern the ionic concentration distributions, the electrostatic potential profile, and the fluid flow field in the electrolyte solution surrounding the charged sphere in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. Analytical expressions for the diffusiophoretic velocity of the dielectric sphere in closed form correct to the second order of its surface charge density or zeta potential are obtained from a balance between its electrostatic and hydrodynamic forces. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made.     

Supramolecular crystal growth in concentrated suspensions of charged monodisperse spherical silica particles

Concentrated suspensions of charged monodisperse spherical silica particles (MSSP) stabilized by alkalis or ammonia are able to crystallize at a certain destabilization. Crystal structures with the particles fixed at certain distances from each other show an isotropic normal mechanism of continuous growth with a rough phase boundary. The crystallization is determined by three parameters,víz. the concentration of particles, temperature, the thickness of the ion atmosphere around the particles and the concentration of counterions. The crystallization of MSSP suspensions is considered as a model of the supramolecular crystallization in the field of synthesis of mesoporous structures.     

Mechanism of structural ordering of monodisperse spherical silica particles in concentrated alcohol suspensions

Structural ordering of monodispersed spherical silica particles (MSSP) occurs in ammonia stabilized concentrated suspensions obtained by tetraethoxysilane (TEOS) hydrolysis in alcohol-aqueous solutions in the ammonia concentration range from 0.0001 to 0.0008 mol/L. MSSP interaction follows the DLFO (Deryagin, Landau, Ferway, and Overbeck) mechanism when electrostatic repulsive forces between the particles predominate, and the structural ordering requires straightened conditions, which are provided by suspension concentrating through MSSP gravitational precipitation.     

dc Electrokinetics for spherical particles in salt-free concentrated suspensions including ion size effects

We study the electrophoretic mobility of spherical particles and the electrical conductivity in salt-free concentrated suspensions including finite ion size effects. An ideal salt-free suspension is composed of just charged colloidal particles and the added counterions that counterbalance their surface charge. In a very recent paper [Roa et al., Phys. Chem. Chem. Phys., 2011, 13, 3960-3968] we presented a model for the equilibrium electric double layer for this kind of suspensions considering the size of the counterions, and now we extend this work to analyze the response of the suspension under a static external electric field. The numerical results show the high importance of such corrections for moderate to high particle charges, especially when a region of closest approach of the counterions to the particle surface is considered. The present work sets the basis for further theoretical models with finite ion size corrections, concerning particularly the ac electrokinetics and rheology of such systems.     

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

The equilibrium electric double layer (EDL) that surrounds colloidal particles is essential for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed of charged colloidal particles and ionic countercharges released by the charging mechanism. Existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterion concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the high importance of such corrections for moderate to high particle charges at every particle volume fraction, especially when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions, particularly salt-free ones with small and highly charged particles.     

Sedimentation of concentrated spherical particles with a charge-regulated surface

The sedimentation of a concentrated colloidal dispersion is examined for the case of an arbitrary double-layer thickness. Here, a general mixed-type condition on particle surface is assumed, and the classic models, which assume constant surface properties, can be recovered as the special cases of the present analysis. In particular, the behavior of biological cells, which carry dissociable functional groups on their surfaces, and particles, which are capable of exchanging ions with the surrounding medium, can be simulated by the present model. The mixed-type boundary condition leads to several interesting results in both sedimentation velocity and sedimentation potential as double-layer thickness and the concentration of particles vary.     

The rheology of concentrated suspensions of deformable particles

The rheology of slightly deformable particles, in particular their dilatant behaviour, has been investigated using waxy maize starch as a ‘model’ suspension. Suspensions of such large particles present considerable experimental problems in rheological terms in that they exhibit phenomena such as wall slip and sedimentation. These are discussed in some detail, along with the methodologies developed to overcome them. Comparisons of the results with hard sphere data in the literature indicate that whilst the deformability of the starch granules does not play a significant role in the high shear limiting viscosity, the dilatant transition does appear to be strongly affected.     

Rotational and translational self-diffusion in concentrated suspensions of permeable particles

In our recent work on concentrated suspensions of uniformly porous colloidal spheres with excluded volume interactions, a variety of short-time dynamic properties were calculated, except for the rotational self-diffusion coefficient. This missing quantity is included in the present paper. Using a precise hydrodynamic force multipole simulation method, the rotational self-diffusion coefficient is evaluated for concentrated suspensions of permeable particles. Results are presented for particle volume fractions up to 45% and for a wide range of permeability values. From the simulation results and earlier results for the first-order virial coefficient, we find that the rotational self-diffusion coefficient of permeable spheres can be scaled to the corresponding coefficient of impermeable particles of the same size. We also show that a similar scaling applies to the translational self-diffusion coefficient considered earlier. From the scaling relations, accurate analytic approximations for the rotational and translational self-diffusion coefficients in concentrated systems are obtained, useful to the experimental analysis of permeable-particle diffusion. The simulation results for rotational diffusion of permeable particles are used to show that a generalized Stokes-Einstein-Debye relation between rotational self-diffusion coefficient and high-frequency viscosity is not satisfied.     

Electrokinetics of concentrated suspensions of spherical colloidal particles with surface conductance, arbitrary zeta potential, and double-layer thickness in static electric fields

In this paper the electrophoretic mobility and the electrical conductivity of concentrated suspensions of spherical colloidal particles have been numerically studied under arbitrary conditions including zeta potential, particle volume fraction, double-layer thickness (overlapping of double layers is allowed), surface conductance by a dynamic Stern layer model (DSL), and ionic properties of the solution. We present an extensive set of numerical data of both the electrophoretic mobility and the electrical conductivity versus zeta potential and particle volume fraction, for different electrolyte concentrations. The treatment is based on the use of a cell model to account for hydrodynamic and electrical interactions between particles. Other theoretical approaches have also been considered for comparison. Furthermore, the study includes the possibility of adsorption and lateral motion of ions in the inner region of the double layers (DSL model), according to the theory developed by C. S. Mangelsdorf and L. R. White (J. Chem. Soc. Faraday Trans.86, 2859 (1990)). The results show that the correct limiting cases of low zeta potentials and thin double layers for dilute suspensions are fulfilled by our conductivity formula. Moreover, the presence of a DSL causes very important changes, even dramatic, on the values of both the electrophoretic mobility and the electrical conductivity for a great range of volume fractions and zeta potentials, specially when double layers of adjacent cells overlap, in comparison with the standard case (no Stern layer present). It can be concluded that in general the presence of a dynamic Stern layer causes the electrophoretic mobility to decrease and the electrical conductivity to increase in comparison with the standard case for every volume fraction, zeta potential, and double-layer thickness.     

Frequency-dependent electrical conductivity of concentrated dispersions of spherical colloidal particles

This paper outlines the application of a self-consistent cell-model theory of electrokinetics to the problem of determining the electrical conductivity of a dense suspension of spherical colloidal particles. Numerical solutions of the standard electrokinetic equations, subject to self-consistent boundary conditions, are implemented in formulas for the electrical conductivity appropriate to the particle-averaged cell model of the suspension. Results of calculations as a function of frequency, zeta potential, volume fraction, and electrolyte composition, are presented and discussed.     

Effective static and high-frequency viscosities of concentrated suspensions of soft particles

We obtain an analytic expression that allows to determine the static η and high-frequency η(∞) viscosities as function of the volume fraction φ of a concentrated suspension of soft spherical particles in a liquid of viscosity η(0). The particles consist of a hard core of radius a covered by a porous layer of thickness d. Suspensions of hard spheres and homogeneous porous particles are limiting cases of the model. The proposed expression incorporates the results for the intrinsic viscosity obtained on the basis of a cell model [H. Ohshima, Langmuir 26, 6287 (2010)] into a recently obtained relation for the effective viscosity of concentrated colloidal suspensions [C. I. Mendoza and I. Santamari?a-Holek, J. Chem. Phys. 130, 044904 (2009); J. Colloid. Interface Sci. 346, 118 (2010)]. In this model, the correlations between the particles due to crowding effects are introduced through an effective volume fraction φ(eff) which is then used as integration variable in a differential effective medium procedure. The final expression is simple, accurate, and allows to collapse all the data in a universal master curve that is independent of the parameters characterizing the system. The only difference between the static and high-frequency cases is that in the later case φ(eff) also incorporates hydrodynamic interactions arising from the so-called relaxation term. We have tested the accuracy of our model comparing with experimental results for spherical polymeric brushes and simulations for the high-frequency viscosity of homogeneous porous particles. In all cases the agreement with the data is extremely good.     

Diffusiophoresis of a moderately charged spherical colloidal particle

An analytic expression is obtained for the diffusiophoretic mobility of a charged spherical colloidal particle in a symmetrical electrolyte solution. The obtained expression, which is expressed in terms of exponential integrals, is correct to the third order of the particle zeta potential so that it is applicable for colloidal particles with low and moderate zeta potentials at arbitrary values of the electrical double-layer thickness. This is an improvement of the mobility formula derived by Keh and Wei, which is correct to the second order of the particle zeta potential. This correction, which is related to the electrophoresis component of diffusiophoresis, becomes more significant as the difference between the ionic drag coefficients of electrolyte cations and anions becomes larger and vanishes in the limit of thin or thick double layer. A simpler approximate mobility expression is further obtained that does not involve exponential integrals.     

Diffusiophoresis and electrophoresis of elliptic cylindrical particles

An exact analysis is presented for the diffusiophoresis and electrophoresis of a rigid elliptic cylindrical particle in a uniform applied field oriented arbitrarily with respect to its axis. The range of the interaction between the solute species and the particle surface is assumed to be small relative to the minimum dimension of the particle, but the effect of polarization of the diffuse species in the thin particle-solute interaction layer is incorporated. To solve the conservative equations governing the system, a slip velocity of fluid and normal fluxes of solute species at the outer edge of the thin diffuse layer which balance convection and diffusion of the solute species along the particle surface are used as the boundary conditions for the fluid domain outside the diffuse layer. Expressions for the migration velocity of the particle are obtained in closed forms for the cases of diffusiophoresis in a nonionic solute concentration gradient, diffusiophoresis in a concentration gradient of symmetric electrolyte, and electrophoresis in an external electric field. An interesting feature is found that the diffusiophoretic or electrophoretic velocity of the particle decreases with the reduction of the maximum length of the particle in the direction of migration. Also, the average migration velocity for an ensemble of identical, noninteracting elliptic cylinders with random orientation distribution is obtained for each case considered.