Suspensions Of Soft Particles Research Articles

Migration and fractionation of deformable particles in microchannel

The complexity of the coupling between soft particle deformation and fluid perturbation has limited studies of soft particle hydrodynamics to dilute suspensions. A hybrid Brownian dynamics-lattice Boltzmann method is presented that models nondilute soft spherical deformable particle (DP) suspensions in flow. Dependences on particle size and density are investigated for suspensions with over 100 DP. Multi-DP interactions lead to complex dependence of particle distributions on concentration and flow rate. Flow-induced DP migration toward channel center for DP in narrow channels is found. In wide channels, off-center peaks in the center of mass distribution for DP are found. The migration of DP leads to faster average speed of DP than the flow, which can be exploited for fractionating DPs of different sizes.

Shaking-induced motility in suspensions of soft active particles

We investigate theoretically the collective dynamics of soft active particles living in a viscous fluid. We focus on a minimal model for active but nonmotile particles consisting of N>1 elastic dimers deformed by active stresses and interacting hydrodynamically. We first derive a set of effective equations of motion for the positions of the particles. We then exploit these equations in two experimentally relevant cases: uncorrelated random internal stresses, and uniform monochromatic external shaking. In both cases, we show that small groups of intrinsically nonmotile particles can display nontrivial modes of locomotion resulting from the hydrodynamic correlations between the particle-conformation fluctuations. In addition, we demonstrate that a coherent shaking yields spatial ordering in suspension of soft particles interacting solely through the fluid.

Aging in dense suspensions of soft thermosensitive microgel particles studied with particle-tracking microrheology

Using particle tracking microrheology, we studied the glass transition in dense suspensions of thermosensitive microgel particles. These suspensions can be tuned reversibly between the glass state at low temperature and the liquid state at high temperature. In the glass state, the ensemble averaged mean squared displacements (MSDs) of added fluorescent tracer particles depend on the age of the suspension. We also determine the local viscoelastic moduli, G' and G", from the MSDs using the Generalized Stokes-Einstein Relation and compare them to the bulk moduli, measured using conventional rheometry. With particle tracking, one probes the viscoelastic moduli in a lower frequency range than with macrorheology, which makes it possible to determine the mean relaxation time that is inaccessible with macrorheology. In the glass state, the mean relaxation time increases linearly with the age of the sample and the short time particle displacement distributions are non-Gaussian, indicating inhomogeneity of the system. The observed difference between conventional and microrheology is explained quantitatively assuming that the tracer particles are surrounded by a viscoelastic liquid shell, different from the bulk.

Effective Viscosity of a Concentrated Suspension of Uncharged Spherical Soft Particles

We present a theory of the effective viscosity eta(s) of a concentrated suspension of uncharged polymer-coated spherical particles, which are termed uncharged spherical soft particles, in a liquid of viscosity eta on the basis of a cell model. These particles consist of the uncharged particle core of radius a covered with an uncharged polymer layer of thickness d (a polymer-coated particle thus has an inner radius a and an outer radius b = a + d). We assume that polymer segments are regarded as resistance centers, exerting frictional forces--gamma u on the liquid flowing in the polymer layer, where u is the liquid velocity and gamma is the frictional coefficient. We derive an analytic expression for the effective viscosity eta(s) of the suspension, which depends on the radii a and b, and volume fraction phi of the spheres and a parameter lambda = (gamma/eta)(1/2). The obtained expression for eta(s) exhibits the correct limiting behaviors. That is, as phi --> 0, the obtained expression for eta(s) becomes that for a dilute suspension of uncharged soft spheres (Ohshima, Langmuir 2008, 24, 6453). As a --> 0, the obtained viscosity expression becomes that for the case of a concentrated suspension of uncharged porous spheres (Ohshima, Colloids Surf. A: Physicochem. Eng. Aspects 2009, 347, 33). In the further limit of a --> 0 and phi --> 0, the obtained viscosity expression becomes the viscosity expression derived for the case of a dilute suspension of uncharged porous spheres by Natraj and Chen (J. Colloid Interface Sci. 2002, 251, 200). As lambda --> infinity or a --> b, the obtained viscosity expression tends to Simha's result (J. Appl. Phys. 1952, 23, 1020) for a concentrated suspension of uncharged rigid spheres of radius b, while as lambda --> 0, it becomes that for uncharged rigid spheres of radius a.

Vesicles and red blood cells in flow: From individual dynamics to rheology

Abstract The rheology of suspensions of soft particles, such as red blood cells, is a long-standing problem in science and engineering due to the complex interplay between deformable microstructure and the macroscale flow. The major challenge stems from the free-boundary nature of the particle interface. Lipid bilayer membranes that envelop cells and vesicles are particularly complex interfaces because of their unusual mechanics: the molecularly thin membrane is a highly-flexible incompressible fluid sheet. As a result, particles made of closed lipid bilayers (red cells and vesicles) can exhibit richer dynamics than would capsules and drops. We overview the key experimental observations and recent advances in the theoretical modeling of the vesicles and red blood cells in flow. To cite this article: P.M. Vlahovska et al., C. R. Physique 10 (2009).

AC Electrokinetics of Concentrated Suspensions of Soft Particles

In this work, we show how the cell model traditionally used for the evaluation of the electrokinetic properties of concentrated suspensions can be modified to include the case of soft particles, that is, particles consisting of a rigid core and a polyelectrolyte membrane. The Navier-Stokes and Poisson's equations have been modified to account for the presence of extra friction and a volume-distributed charge in the membrane. In addition to the boundary conditions on the particle and the cell boundary, it is necessary to define conditions on the polymer-electrolyte solution interface. The frequency dependence of the dynamic mobility and electric permittivity of suspensions of soft particles with arbitrary solids concentration is computed. It is shown that the dynamic mobility of these systems is larger than that corresponding to hard particles with the same charge. For the permittivity, the same trends are observed: the R-relaxation amplitude increases upon coating. It is found that friction plays an important role in determining the mobility, while the permittivity is more affected by the concentration of solids. The model also predicts that the charges on the core and in the membrane are very important parameters, although their effects differ on the mobility and the permittivity. While the former depends mainly on the membrane charge, the latter is responsive to both charges at comparable extents.

Influence of short-range forces on wall-slip in microgel pastes

Concentrated suspensions of soft deformable particles, e.g., polymer microgel pastes and compressed emulsions, display a generic slip behavior [Meeker et al., J. Rheol. 92, 18302 (2004a); Meeker et al., J. Rheol. 48, 1295–1320 (2004b)]. When sheared with smooth surfaces, they exhibit apparent motion due to slip at the wall. Wall-slip stops at a sliding yield stress the value of which is much lower than the bulk yield stress. The physical mechanism of slip at low stresses and the origin of the sliding yield stress have so far been unresolved issues. We propose that the paste-wall interactions control the wall-slip behavior and determine the occurrence of the sliding yield point. We present experiments performed with different shearing surfaces. Two distinct slip behaviors are identified: depending on whether the interaction between the microgel particles and the wall is attractive or repulsive, wall-slip can be either suppressed or promoted. We provide an extension to the elastohydrodynamic slip model of Meeker and co-workers by incorporating attractive or repulsive interactions between the slipping paste particle and the wall. The interplay of various short range forces due to van der Waals, hydrophobic/hydrophilic, and/or electrostatic interactions and elastohydrodynamics is used to explain the influence of the shearing surface on wall-slip. The model encompasses the different slip regimes observed in our experiments and can predict the slip behavior accurately for well characterized surfaces.

Metal Speciation Dynamics in Monodisperse Soft Colloidal Ligand Suspensions

A comprehensive theory is presented for the dynamics of metal speciation in monodisperse suspensions of soft spherical particles characterized by a hard core and an ion-permeable shell layer where ligands L are localized. The heterogeneity in the binding site distribution leads to complex formation/dissociation rate constants (denoted as k a (*) and k d (*), respectively) that may substantially differ from their homogeneous solution counterparts (k a and k d). The peculiarities of metal speciation dynamics in soft colloidal ligand dispersions result from the coupling between diffusive transport of free-metal ions M within and around the soft surface layer and the kinetics of ML complex formation/dissociation within the shell component of the particle. The relationship between k a,d (*) and k a,d is derived from the numerical evaluation of the spatial, time-dependent distributions of free and bound metal. For that purpose, the corresponding diffusion equations corrected by the appropriate chemical source term are solved in spherical geometry using a Kuwabara-cell-type representation where the intercellular distance is determined by the volume fraction of soft particles. The numerical study is supported by analytical approaches valid in the short time domain. For dilute dispersions of soft ligand particles, it is shown that the balance between free-metal diffusion within and outside of the shell and the kinetic conversion of M into ML within the particular soft surface layer rapidly establishes a quasi-steady-state regime. For sufficiently long time, chemical equilibrium between the free and bound metal is reached within the reactive particle layer, which corresponds to the true steady-state regime for the system investigated. The analysis reported covers the limiting cases of rigid particles where binding sites are located at the very surface of the particle core (e.g., functionalized latex colloids) and polymeric particles that are devoid of a hard core (e.g., polysaccharide macromolecules, gel particles). For both the transient and quasi-steady-state regimes, the dependence of k a,d (*) on the thickness of the soft surface layer, the radius of the hard core of the particle, and the kinetic rate constants k a,d for homogeneous ligand solutions is thoroughly discussed within the context of dynamic features for colloidal complex systems.

Primary Electroviscous Effect in a Dilute Suspension of Soft Particles

A theory for the primary electroviscous effect in a dilute suspension of soft particles (i.e., particles coated with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution is presented. The general expression for the effective viscosity eta s of the suspension and the primary electroviscous coefficient p, which is further expressed in terms of a function L, is given. On the basis of the general expressions, we derive approximate analytic expressions for eta s and p, which are applicable when the density of the fixed charges distributed within the surface layer is low. Further we obtain a simple approximate analytic expression (without involving numerical integrations) for p applicable for most practical cases. It is found that the function L exhibits a minimum when plotted as a function of kappa a (kappa is the Debye-Hückel parameter and a is the particle core radius), unlike the case of a suspension of hard particles, in which case L decreases as kappa a increases, exhibiting no minimum. The presence of a minimum for the case of a suspension of soft particles is due to the fact that L is proportional to 1/kappa 2 at small kappa a and to kappa 2 at large kappa a. Because of the presence of this minimum, the difference in L between soft and hard particles becomes very large for large kappa a.

柔らかい粒子と環境科学

Interfacial electric phenomena in a suspension of soft particles (i.e., particles covered with an ion-penetrable polyelectrolyte layer) are discussed with special emphasis on soft particles in environmental science. Fundamental equations are given which describe the oscillatory motion of soft particles in an applied electric field and in an applied pressure gradient field. Soft particles are shown to serve as a model for humic substances. It is shown that colloid vibration potential will be a key quantity providing information on the electric properties of soft particles.

Colloid vibration potential in a suspension of soft particles

We develop a theory of the vibration potential produced in a dilute suspension of soft particles (i.e., hard particles covered with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution when a sound wave (i.e., an oscillating pressure gradient field) is applied to the suspension. The total vibration potential (TVP) consists of two components. One is the colloid vibration potential (CVP) and the other is the ion vibration potential (IVP). The obtained CVP expression covers two extreme cases, that is, the CVP in a suspension of hard particles (in the absence of the polyelectrolyte layer) and that in a suspension of spherical polyelectrolytes (in the absence of the particle core). A simple analytic expression for CVP, which is proportional to the dynamic electrophoretic mobility of a soft particle, is given. It is shown that the CVP of a suspension of a soft particle depends on the density of the volume charge distributed in the polyelectrolyte layer, on the frictional coefficient characterizing the frictional forces exerted by the polymer segments on the liquid flow in the polyelectrolyte layer, on the particle size, on the thickness of the polyelectrolyte layer, and on the frequency of the applied oscillating pressure gradient field.

Numerical calculation of the electrophoretic mobility of concentrated suspensions of soft particles

The electrophoretic mobility of spherical soft particles in concentrated colloidal suspensions is numerically calculated. The particle is modeled as a hard core coated with an ion-penetrable membrane bearing a uniform distribution of fixed charges, while the high particle concentration is taken into account by means of a cell model. The network simulation method used makes it possible to solve the problem without any restrictions on the values of the parameters such as particle concentration, membrane thickness, fixed charge density in the membrane, viscous drag in the membrane, number and valence of ionic species, electrolyte concentration, etc. The theoretical model used is similar to the one presented by Ohshima [H. Ohshima, J. Colloid Interface Sci. 225 (2000) 233], except for the use of the Shilov–Zharkikh, rather than the Levine–Neale, boundary condition for the electric potential, and the inclusion in the force balance equation of an additional term corresponding to the force exerted by the liquid on the core of the moving particle [J.J. López-García, C. Grosse, J. Horno, J. Colloid Interface Sci. 265 (2003) 327]. The obtained results only coincide with existing analytical expressions for low particle concentrations, low particle charge, and when the electrolyte concentration is high, the membrane is thick, and its resistance to the fluid flow is high. This suggests that most interpretations of the electrophoretic mobility of soft particles in concentrated suspensions require numerical calculations.

Analysis of the response of suspended colloidal soft particles to a constant electric field

A network model, originally designed for an electrokinetic study of soft particle suspensions, has been used for an in-depth analysis of the physical behavior of these systems under the action of an externally applied DC electric field. The versatility of the network simulation method used makes it possible to obtain information readily not only about the electrophoretic mobility, but also about any physical variable of interest at all points around the suspended particle: electric potential, ion concentrations, fluid velocity. The field-induced polarization of the double layer is described in terms of the dependence of these and other derived variables (volume charge density, electric field components, ion flux components) on the distance to the membrane–solution interface. In contrast to colloidal suspensions of hard particles, which basically depend on just two parameters (the reciprocal Debye length multiplied by the particle radius, κa, and the zeta potential, ζ), soft particle suspensions require a wider parameter set. First, there are two characteristic diffusion lengths in the system (one inside the membrane and the other in the solution) and two geometrical lengths (the core radius a and the membrane thickness ( b − a )). Furthermore, there is the fixed charge density inside the membrane (and possibly a surface charge density over the core) that cannot be represented by a ζ potential. Finally, the parameter that characterizes the interaction between the fluid and the permeable membrane, γ, strongly influences the behavior of the system. Dependences on all these parameters (except the geometrical ones) are included in this study.

Numerical study of colloidal suspensions of soft spherical particles using the network method: 2. AC electrokinetic and dielectric properties

The network simulation method is used to solve numerically the equation system that determines the dynamic electrophoretic mobility and the dielectric response of dilute suspensions of soft particles. This system was extensively studied theoretically by Ohshima (H. Ohshima, J. Colloid Interface Sci. 233 (2001) 142–152), who obtained analytical expressions for the static and dynamic electrophoretic mobility. However, the validity of his analytical result is restricted to relatively thick membranes with high drag coefficient and to relatively high electrolyte concentrations. As for the dielectric properties, there are only a few works dealing with particles without a core (ion exchange resins) and, to our knowledge, no numerical studies. Our theoretical model is basically similar to Ohshima's, except that we take into account the mechanical force acting on the surface of the core, which he neglects. The inclusion of this term is crucial when the general problem including arbitrary values of the parameters is analyzed. However, it has little bearing when the membrane is thick and the drag coefficient is high, so that our results for the electrophoretic mobility generally confirm Ohshima's equation when all the required conditions are met.

Numerical study of colloidal suspensions of soft spherical particles using the network method: 1. DC electrophoretic mobility

The electrophoretic mobility of a spherical particle coated with a uniformly charged permeable membrane and suspended in a general electrolyte solution is calculated numerically. The network simulation method used makes it possible to solve the problem without any restrictions on the values of the parameters such as the membrane thickness, fixed charge density in the membrane, viscous drag in the membrane, number and valence of the ionic species, and electrolyte concentration. The theoretical model used is similar to the one presented by Ohshima (H. Ohshima, J. Colloid Interface Sci. 228 (2000) 190), except for the inclusion in the force balance equation of an additional term corresponding to the force exerted by the liquid on the core of the moving particle. This inclusion is theoretically proven in the limiting case of a nonconducting suspending medium, in which the equation system can be analytically solved. The results obtained coincide with existing analytical expressions when the electrolyte concentration is high, the membrane is thick, and its resistance to the fluid flow is high.

Electrokinetic phenomena in a concentrated suspension of soft particles

A theory of electrokinetics in concentrated suspensions of soft particles (i.e. polyelectrolyte-coated particles) is reviewed with particular emphasis on an Onsager relation between sedimentation potential and electrophoretic mobility. A more general Onsager relation is derived on the basis of the thermodynamics of irreversible processes, which is an extension to high potentials. Expressions for colloid vibration potential (CVP) and electrokinetic sonic amplitude (ESA) are also derived.

Rheological characterization of aging in a concentrated colloidal suspension

Suspensions of soft particles display a rheological transition when their concentration is increased: above a critical concentration, they become pasty and display a yield-stress. We report experiments on silica suspensions in the pasty phase that show how the response of the system to the application of mechanical perturbations depends on its history. Stress relaxation experiments performed after different waiting times clearly show aging taking place in the pasty phase, characterized by an aging exponent of order μ∼0.5–0.7.

Sedimentation Potential and Velocity in a Concentrated Suspension of Soft Particles

A theory of sedimentation in a concentrated suspension of spherical soft particles (i.e., polyelectrolyte-coated particles) is developed to obtain general expressions for sedimentation velocity of soft particles and sedimentation potential in the suspension. An Onsager relation between sedimentation potential and electrophoretic mobility of spherical soft particles in concentrated suspensions is derived for the case of low potentials and nonoverlapping electrical double layers of adjacent particles.

Electrical Conductivity of a Concentrated Suspension of Soft Particles

A general expression for the electrical conductivity of a concentrated suspension of spherical soft particles (polyelectrolyte-coated particles) is obtained for the case where the overlapping of the electrical double layers of adjacent particles is negligible by using Kuwabara's cell model. It is shown that in the limit of very low potentials the obtained conductivity expression reduces to Maxwell's relation with respect to the volume fraction of the particle core and the contribution from the polyelectrolyte layer becomes negligible. An approximate conductivity expression is derived for the case of low potentials.

Mechanics near a jamming transition: a minimalist model

Concentrated suspensions of soft particles exhibit a pasty-like mechanical behaviour due to the jamming of the particles. In particular these solutions display a yield stress and typically exhibit very non-linear mechanical responses. Here, we introduce a very naive mode-coupling model that describes in a mean-field way the mechanics of such systems close to the jamming transition. Despite its simplicity this model correctly reproduces many features characteristic of real systems, in particular, non-linear features of the apparent viscoelastic modulus. It is also shown that, as linear response theory can not be applied, different mechanical tests provide different information. Moreover our model is a helpful tool to understand, in terms of trajectories in phase space, the origin of the observed non-linearities, which are essentially of two types.