Suspensions Of Charged Particles Research Articles

Electrophoresis and electric conduction in a salt-free suspension of charged particles.

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.

Transient electrophoresis in a suspension of charged particles with arbitrary electric double layers.

The startup of electrophoretic motion in a suspension of spherical colloidal particles, which may be charged with constant zeta potential or constant surface charge density, due to the sudden application of an electric field is analytically examined. The unsteady modified Stokes equation governing the fluid velocity field is solved with unit cell models. Explicit formulas for the transient electrophoretic velocity of the particle in a cell in the Laplace transforms are obtained as functions of relevant parameters. The transient electrophoretic mobility is a monotonic decreasing function of the particle-to-fluid density ratio and in general a decreasing function of the particle volume fraction, but it increases and decreases with a raise in the ratio of the particle radius to the Debye length for the particles with constant zeta potential and constant surface charge density, respectively. On the other hand, the relaxation time in the growth of the electrophoretic mobility increases substantially with an increase in the particle-to-fluid density ratio and with a decrease in the particle volume fraction but is not a sensitive function of the ratio of the particle radius to the Debye length. For specified values of the particle volume fraction and particle-to-fluid density ratio in a suspension, the relaxation times in the growth of the particle mobility in transient electrophoresis and transient sedimentation are equivalent.

Discrete and Continuum Models for the Salt in Crowded Environments of Suspended Charged Particles.

Electrostatic forces greatly affect the overall dynamics and diffusional activities of suspended charged particles in crowded environments. Accordingly, the concentration of counter- or co-ions in a fluid-''the salt"-determines the range, strength, and order of electrostatic interactions between particles. This environment fosters engineering routes for controlling directed assembly of particles at both the micro- and nanoscale. Here, we analyzed two computational modeling schemes that considered salt within suspensions of charged particles, or polyelectrolytes: discrete and continuum. Electrostatic interactions were included through a Green's function formalism, where the confined fundamental solution for Poisson's equation is resolved by the general geometry Ewald-like method. For the discrete model, the salt was considered as regularized point-charges with a specific valence and size, while concentration fields were defined for each ionic species for the continuum model. These considerations were evolved using Brownian dynamics of the suspended charged particles and the discrete salt ions, while a convection-diffusion transport equation, including the Nernst-Planck diffusion mechanism, accounted for the dynamics of the concentration fields. The salt/particle models were considered as suspensions under slit-confinement conditions for creating crowded "macro-ions", where density distributions and radial distribution functions were used to compare and differentiate computational models. Importantly, our analysis shows that disparate length scales or increased system size presented by the salt and suspended particles are best dealt with using concentration fields to model the ions. These findings were then validated by novel simulations of a semipermeable polyelectrolyte membrane, at the mesoscale, from which ionic channels emerged and enable ion conduction.

Rotational self-diffusion in suspensions of charged particles: simulations and revised Beenakker-Mazur and pairwise additivity methods.

We present a comprehensive joint theory-simulation study of rotational self-diffusion in suspensions of charged particles whose interactions are modeled by the generic hard-sphere plus repulsive Yukawa (HSY) pair potential. Elaborate, high-precision simulation results for the short-time rotational self-diffusion coefficient, D(r), are discussed covering a broad range of fluid-phase state points in the HSY model phase diagram. The salient trends in the behavior of D(r) as a function of reduced potential strength and range, and particle concentration, are systematically explored and physically explained. The simulation results are further used to assess the performance of two semi-analytic theoretical methods for calculating D(r). The first theoretical method is a revised version of the classical Beenakker-Mazur method (BM) adapted to rotational diffusion which includes a highly improved treatment of the salient many-particle hydrodynamic interactions. The second method is an easy-to-implement pairwise additivity (PA) method in which the hydrodynamic interactions are treated on a full two-body level with lubrication corrections included. The static pair correlation functions required as the only input to both theoretical methods are calculated using the accurate Rogers-Young integral equation scheme. While the revised BM method reproduces the general trends of the simulation results, it significantly underestimates D(r). In contrast, the PA method agrees well with the simulation results for D(r) even for intermediately concentrated systems. A simple improvement of the PA method is presented which is applicable for large concentrations.

The metastable states of foam films containing electrically charged micelles or particles: Experiment and quantitative interpretation

The stepwise thinning (stratification) of liquid films containing electrically charged colloidal particles (in our case — surfactant micelles) is investigated. Most of the results are applicable also to films from nanoparticle suspensions. The aim is to achieve agreement between theory and experiment, and to better understand the physical reasons for this phenomenon. To test different theoretical approaches, we obtained experimental data for free foam films from micellar solutions of three ionic surfactants. The theoretical problem is reduced to the interpretation of the experimental concentration dependencies of the step height and of the final film thickness. The surface charges of films and micelles are calculated by means of the charge-regulation model, with a counterion-binding (Stern) constant determined from the fit of surface tension isotherms. The applicability of three models was tested: the Poisson–Boltzmann (PB) model; the jellium-approximation (JA), and the cell model (CM). The best agreement theory/experiment was obtained with the JA model without using any adjustable parameters. Two theoretical approaches are considered. First, in the energy approach the step height is identified with the effective diameter of the charged micelles, which represents an integral of the electrostatic-repulsion energy calculated by the JA model. Second, in the osmotic approach the step height is equal to the inverse cubic root of micelle number density in the bulk of solution. Both approaches are in good agreement with the experiment if the suspension of charged particles (micelles) represents a jellium, i.e. if the particle concentration is uniform despite the field of the electric double layers. The results lead to a convenient method for determining the aggregation number of ionic surfactant micelles from the experimental heights of the steps.

Dynamic surfing and trapping of charged colloids in a traveling-wave electrophoretic ratchet

The author theoretically demonstrates a gel-free electrophoretic ratchet under a nearly unidirectional traveling electric field whose wavelength is much longer than the transverse dimension. Because of length scale separation, a charged particle can migrate synchronously or asynchronously with the field as if it was surfing on the wave. The author shows, with a dynamical phase portrait, that if the wave speed is slower than the characteristic electrophoretic velocity, a suspension of charged particles can be trapped into distinct particle bands synchronizing with the field. A tunable sieving capability of this ratchet provides the potential for continuous fractionation and characterization of colloidal suspensions.

Colloidal Interactions in Partially Quenched Suspensions of Charged Particles

Colloidal Interactions in Partially Quenched Suspensions of Charged Particles

Electrical conductivity of a suspension of charged spherical particles in electrolyte solution

We investigate the influence of interaction between dispersed particles to ac conductivity of suspension of charged particles immersed in electrolyte solution. Using the Rayleigh technique, we establish an identity for charged suspensions, and derive a formula for effective complex conductivity of the systems. A useful scheme for computation of effective constants of composite media is proposed.

A note on the deposition of aerosol particles in a channel due to diffusion and electric charge

Abstract Flow suspensions of charged particles near the entrance to a parallel plate channel has been solved using a boundary layer analysis. Results for plug flow and Poiseuille flow are given.

Electrophoretic light scattering

Electrophoresis in its various forms has had an enormous impact on biochemistry. The primary use has been the quantitative determination of electrophoretically distinct species in a mixture. A second, less common, type of application is the interpretation of the elctrophoretic mobility in terms of the surface charge of the species. The latter application has been hindered both by experimental difficulties of measuring the electrophoretic mobility and by the theoretical difficulties of relating the electrophoretic mobility to the number of electronic charges on the surface of the particle. Classical electrophoresis techniques measure the distance travelled per unit time by a charged particle in an electric field. Since electrophoretic velocities are small, the time required for transit of a measurable distance can be inconveniently long. However, if the velocity could be measured directly, then the electrophoresis experiment could be accomplished without waiting for macroscopic migration, and electrophoretically distinct species could be determined without requiring theirphysicalseparation.Velocitymeasurements of macroscopic objects are commonplace. Everyone is familiar with the use of radar for determining the velocity of an object by measuring the Doppler shift of the microwave radiation reflected from the object. The development of the optical laser has made it possible to use the Doppler principle to determine the velocities of particles of all sizes by measuring the frequency shift of the laser light which has been scattered from them. This new technique, usually called laser Doppler velocimetry, has already been applied to several interesting problems in biology and medicine [ 11. Determination ofelectrophoretic velocities by laser Doppler velocimetry is known as electrophoretic light scattering. The theory of electrophoretic light scattering and the first successful experiments were reported in 197 1 by Ware and Flygare [2]. Since that time the technique has been refined and adapted by several groups, and over thirty publications have appeared, including applications to proteins, nucleic acids, viruses, bacteria, blood cells and synthetic polyelectrolytes. The information obtained in these experiments always includes the electrophoretic mobility of the species being studied. In heterogeneous samples, the mobility of several species can be measured simultaneously, since each contributes a spectral peak corresponding to the Doppler shift of its characteristic velocity. In many cases the width of the peak in the electrophoretic light scattering spectrum is attributable solely to diffusion and can be used to determine the diffusion coefficient of that particular species. The linewidth can therefore be used as an indicator of macromolecular conformation or the state of aggregation or fusion of the observed species. In rhe case of very large particles such as blood cells, the diffusion broadening is negligible, and the electrophoretic light scattering spectrum is a simple histogram representing the electrophoretic distribution of the sample. spectrum analyzer or a Fourier transform minicomputer, and miscellaneous optical and electronic components. In addition, a special electrophoretic light-scattering chamber must be fabricated. Once a satisfactory apparatus has been assembled, experiments can be performed rapidly and efficiently. The complete electrophoretic spectrum of a sample can be measured in as little time as a few seconds and rarely takes longer than a few minutes. Signal-to-noise ratios of 100 or greater are common, and the precision of an electrophoretic mobility determination is typically between 1% and 5%. The technique is ideal for repeated analysis of a sample which is changing in time or for routine analysis of a large number of samples. Adaptation for on-line repeated analyses would be a straightforward modification of existing equipment. Electrophoreticlight scatteringmeasurements are performed on solutions or suspensions of charged particles. Attempts to utilize this technique to detect electrophoretic motion on supporting media such as paper or gels have not been successful Therefore, the high resolution among species obtainable by electrophoresis on supporting media is not matched by electrophoretic light scattering. For proteins and other macromolecules of molecular weight less than one million, the principal uses of this new technique will probably be the measurement of solution electrophoretic mobilities and the study of interacting systems.

Electrophoretic light scattering

Electrophoresis in its various forms has had an enormous impact on biochemistry. The primary use has been the quantitative determination of electrophoretically distinct species in a mixture. A second, less common, type of application is the interpretation of the elctrophoretic mobility in terms of the surface charge of the species. The latter application has been hindered both by experimental difficulties of measuring the electrophoretic mobility and by the theoretical difficulties of relating the electrophoretic mobility to the number of electronic charges on the surface of the particle. Classical electrophoresis techniques measure the distance travelled per unit time by a charged particle in an electric field. Since electrophoretic velocities are small, the time required for transit of a measurable distance can be inconveniently long. However, if the velocity could be measured directly, then the electrophoresis experiment could be accomplished without waiting for macroscopic migration, and electrophoretically distinct species could be determined without requiring theirphysicalseparation.Velocitymeasurements of macroscopic objects are commonplace. Everyone is familiar with the use of radar for determining the velocity of an object by measuring the Doppler shift of the microwave radiation reflected from the object. The development of the optical laser has made it possible to use the Doppler principle to determine the velocities of particles of all sizes by measuring the frequency shift of the laser light which has been scattered from them. This new technique, usually called laser Doppler velocimetry, has already been applied to several interesting problems in biology and medicine [ 11. Determination ofelectrophoretic velocities by laser Doppler velocimetry is known as electrophoretic light scattering. The theory of electrophoretic light scattering and the first successful experiments were reported in 197 1 by Ware and Flygare [2]. Since that time the technique has been refined and adapted by several groups, and over thirty publications have appeared, including applications to proteins, nucleic acids, viruses, bacteria, blood cells and synthetic polyelectrolytes. The information obtained in these experiments always includes the electrophoretic mobility of the species being studied. In heterogeneous samples, the mobility of several species can be measured simultaneously, since each contributes a spectral peak corresponding to the Doppler shift of its characteristic velocity. In many cases the width of the peak in the electrophoretic light scattering spectrum is attributable solely to diffusion and can be used to determine the diffusion coefficient of that particular species. The linewidth can therefore be used as an indicator of macromolecular conformation or the state of aggregation or fusion of the observed species. In rhe case of very large particles such as blood cells, the diffusion broadening is negligible, and the electrophoretic light scattering spectrum is a simple histogram representing the electrophoretic distribution of the sample. spectrum analyzer or a Fourier transform minicomputer, and miscellaneous optical and electronic components. In addition, a special electrophoretic light-scattering chamber must be fabricated. Once a satisfactory apparatus has been assembled, experiments can be performed rapidly and efficiently. The complete electrophoretic spectrum of a sample can be measured in as little time as a few seconds and rarely takes longer than a few minutes. Signal-to-noise ratios of 100 or greater are common, and the precision of an electrophoretic mobility determination is typically between 1% and 5%. The technique is ideal for repeated analysis of a sample which is changing in time or for routine analysis of a large number of samples. Adaptation for on-line repeated analyses would be a straightforward modification of existing equipment. Electrophoreticlight scatteringmeasurements are performed on solutions or suspensions of charged particles. Attempts to utilize this technique to detect electrophoretic motion on supporting media such as paper or gels have not been successful Therefore, the high resolution among species obtainable by electrophoresis on supporting media is not matched by electrophoretic light scattering. For proteins and other macromolecules of molecular weight less than one million, the principal uses of this new technique will probably be the measurement of solution electrophoretic mobilities and the study of interacting systems.