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.     

An application of the modified Poisson- Boltzmann equation in studies of osmotic properties of micellar solutions

The spherical cell model of colloidal solutions is applied in calculations of the osmotic pressure of micellar systems. The predictions of the nonlinear Poisson-Boltzmann equation (MPB) and of the Modified Poisson-Boltzmann equation (MPB) containing the leading terms of the fluctuation potential and the exclusion volume corrections to the mean potential acting on simple ions are compared with the results of recent computer simulations. Both PB and MPB seem satisfactory for solutions with monovalent counterions while the MPB is preferable for studies of the solutions containing divalent countenons.On leave from the University of Ljubljana, Ljubljana, Yugoslavia     

Osmotic stress tensor in charge stabilized colloidal crystals

Osmotic stress tensor is introduced to describe the osmotic pressure in colloidal crystals within the framework of the theory of the Poisson-Boltzmann equation. The osmotic stress tensor is related to the fundamental stress tensor, which is associated with the Poisson-Boltzmann equation. It is shown that the osmotic stress tensor can be determined for colloidal crystals with arbitrary structures, as well as for media that are described by cell models. The general results are exemplified by spherical and cylindrical cell models.     

Contribution of the surface dipole moment and the contact potential-induced disjoining pressure to the stress balance at a three-phase contact

The contact between three insulators results in a set up of contact potentials related to the adsorbed dipole moment at each surface. The produced electric field applies force (disjoining pressure) on each interface. This disjoining pressure is a long-ranged force (1/distance²) which is proportional to the difference between the dielectric permittivities of the phases on the two sides of the interface and, for small angles, to the square of the contact angle. The contact potential leads to a logarithmic perturbation of the profile of the three-phase contact zone.     

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.     

The efficiency of electrokinetic pumping at a condition of maximum work

Numerical methods are employed to examine the work, electric power input, and efficiency of electrokinetic pumps at a condition corresponding to maximum pump work. These analyses employ the full Poisson-Boltzmann equations and account for both convective and conductive electric currents, including surface conductance. We find that efficiencies at this condition of maximum work depend on three dimensionless parameters, the normalized zeta potential, normalized Debye layer thickness, and a fluid property termed the Levine number indicating the nominal ratio of convective to conductive electric currents. Efficiencies at maximum work exhibit a maximum for an optimum Debye layer thickness when the zeta potential and Levine number are fixed. This maximum efficiency increases with the square of the zeta potential when the zeta potential is small, but reaches a plateau as the zeta potential becomes large. The maximum efficiency in this latter regime is thus independent of the zeta potential and depends only on the Levine number. Simple analytical expressions describing this maximum efficiency in terms of the Levine number are provided. Geometries of a circular tube and planar channel are examined.     

Transport properties of long straight nano-channels in electrolyte solutions: a systematic approach

The principle of local thermodynamic equilibrium is systematically employed for obtaining various transport properties of long straight nano-channels. The concept of virtual solution is used to describe situations of non-negligible overlap of diffuse parts of electric double layers (EDLs) in nano-channels. Generic expressions for a variety of transport properties of long straight nano-channels are obtained in terms of quasi-equilibrium distribution coefficients of ions and functionals of quasi-equilibrium distribution of electrostatic potential. Further, the Poisson-Boltzmann approach is used to specify these expressions for long straight slit-like nano-channels. In the approximation of non-overlapped diffuse parts of double electric layers in nano-channels, simple analytical expressions are obtained for the apparent electrophoretic mobilities of (trace) analytes of arbitrary charge as well as for the salt reflection coefficient (osmotic pressure), salt diffusion permeability and electro-viscosity (electrokinetic energy conversion). The approximate solutions are compared with the results of rigorous solution of non-linearized Poisson-Boltzmann equation, and the accuracy of approximation is shown to be typically excellent when the nano-channel half-height exceeds ca.3 Debye screening lengths. Due to non-negligible electrostatic adsorption of ions by nano-channels, the apparent electrophoretic mobilities of counter-ionic analytes in nano-channels are smaller than in micro-channels whereas those of co-ionic analytes are larger. This dependence on the charge is useful for the separation of analytes of close electrophoretic mobilities. The osmotic pressure is shown to be positive, negative or pass through maxima as a function of applied salt-concentration difference within a fairly narrow range of ratios of nano-channel height to the Debye screening length. The diffusion permeability of charged nano-channels to single salts is demonstrated (for the first time) to be typically larger than that of neutral nano-channels of the same dimensions due to electrical facilitation of salt diffusion.     

Electrostatic interaction of neutral semi-permeable membranes

We consider an osmotic equilibrium between bulk solutions of polyelectrolyte bounded by semi-permeable membranes and separated by a thin film of salt-free liquid. Although the membranes are neutral, the counter-ions of the polyelectrolyte molecules permeate into the gap and lead to a steric charge separation. This gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure. From the solution of the nonlinear Poisson-Boltzmann equation, we obtain the distribution of the potential and of ions. We then derive an explicit formula for the pressure exerted on the membranes and show that it deviates from the classical van't Hoff expression for the osmotic pressure. This difference is interpreted in terms of a repulsive electrostatic disjoining pressure originating from the overlap of counterion clouds inside the gap. We also develop a simplified theory based on a linearized Poisson-Boltzmann approach. A comparison with simulation of a primitive model for the electrolyte is provided and does confirm the validity of the theoretical predictions. Beyond the fundamental result that the neutral surfaces can repel, this mechanism not only helps to control the adhesion and long-range interactions of living cells, bacteria, and vesicles, but also allows us to argue that electrostatic interactions should play enormous role in determining behavior and functions of systems bounded by semi-permeable membranes.     

Osmotic pressure measurements on strongly interacting polymer colloid dispersions

Equipment has been developed for the determination of the osmotic pressure of small-sized particulate dispersions of polystyrene at low volume fractions. The specific conductance of the dispersion and that of a reservoir of salt, in equilibrium with the dispersion separated by a membrane, was measured simultaneously with osmotic pressure. The results are analysed in terms of a low volume fraction theory of osmotic pressure equilibrium between a colloid compartment and salt solution compartment separated by a membrane.     

Density functional study on the structural and thermodynamic properties of aqueous DNA-electrolyte solution in the framework of cell model

A density functional theory (DFT) in the framework of cell model is proposed to calculate the structural and thermodynamic properties of aqueous DNA-electrolyte solution with finite DNA concentrations. The hard-sphere contribution to the excess Helmholtz energy functional is derived from the modified fundamental measure theory, and the electrostatic interaction is evaluated through a quadratic functional Taylor expansion around a uniform fluid. The electroneutrality in the cell leads to a variational equation with a constraint. Since the reference fluid is selected to be a bulk phase, the Lagrange multiplier proves to be the potential drop across the cell boundary (Donnan potential). The ion profiles and electrostatic potential profiles in the cell are calculated from the present DFT-cell model. Our DFT-cell model gives better prediction of ion profiles than the Poisson-Boltzmann (PB)- or modified PB-cell models when compared to the molecular simulation data. The effects of polyelectrolyte concentration, ion size, and added-salt concentration on the electrostatic potential difference between the DNA surface and the cell boundary are investigated. The expression of osmotic coefficient is derived from the general formula of grand potential. The osmotic coefficients predicted by the DFT are lower than the PB results and are closer to the simulation results and experimental data.     

Dynamic electrophoresis of droplet dispersions at low surface potentials

The dynamic electrophoresis of a dispersion of spherical droplets under conditions of low surface potential and arbitrary double-layer thickness and droplet volume fraction is analyzed. A cell model with the Shilov-Zharkikh boundary condition for the electric potential is adopted to simulate a dispersion, and the governing equations and the associated boundary conditions are solved by a pseudo-spectral method based on Chebyshev polynomials. The influence of the frequency of the applied electric field, the volume fraction of the droplets, the thickness of the double layer, and the relative magnitude of the viscosity of the droplet fluid on the electrophoretic behavior of a dispersion is discussed.     

Thermodynamics of exogenous nanophases in metal melts

The conditions of the stability of heterophase disperse systems obtained by the exogenous introduction of nanosized solid phases in metal melts were considered by assuming the formation of thick and thin elastic films and disjoining pressure at the contact boundary of particles of disperse phase. The introduced criteria are expressed in the measured interface characteristics, i.e., surface tension and contact angles. The prospects for using a series of compounds of the Periodic system??s IV?CVI group metals as exogenous modifiers of nickel-based alloys are assessed on the basis of our experimental data.     

Osmotic coefficient of a polyelectrolyte solution with a mixture of monovalent counterions

An analytical solution of the Poisson-Boltzmann equation is presented for the cell model of a polyelectrolyte solution with two species of monovalent counterions of different size. On this basis the osmotic coefficient is calculated as a function of the mole fraction of counterions and their radii. It is shown that the degree of binding of the smaller ion species increases as its mole fraction decreases.     

Quantification of solid pressure in the concentration polarization (CP) layer of colloidal particles and its impact on ultrafiltration

Here we describe the nature and implications of the "concentration polarization" (CP) layer that is formed during ultrafiltration of colloidal particles using a new approach in which the solid pressure, which arises from inter-particle interactions, and the inherent osmotic pressure are separately considered. The approach makes use of the particle transport mass balance between the convective and diffusive fluxes. The particle convection rate is hindered when inter-particle interactions take effect by reducing the particle velocities while the particle diffusion is solely controlled by the Brownian motion. An increase in solid pressure accounts for the reduction of the water potential caused by the relative motions of the particles and the surrounding water. A cell model is adopted to relate the local solid pressure with the local solid fraction and inter-particle interactions. The inter-particle interactions critically determine the form of particle accumulation (i.e. CP or gel/cake) on the membrane. The Shirato-Darcy equation is employed to relate the rate of increase in solid pressure, the relative liquid velocity and the solid fraction. Numerical integration approaches are employed to quantify the properties of the CP layer during both the development as well as the steady state phases (with steady state normally being achieved in a few minutes). The solid fractions are always no higher than those obtained when the inter-particle interactions are not considered. The decrease of the water potential caused by CP formation leads to the increase of both the solid pressure and the osmotic pressure. The dependence of the solid pressure on the solid fraction is usually stronger than that of the osmotic pressure. It is thus apparent that the solid pressure would be expected to dominate water potential reduction for solid fractions above a certain value though the solid pressure will be negligible when the solid fraction is relatively low.     

Electrophoresis of a colloidal sphere in a spherical cavity with arbitrary zeta potential distributions and arbitrary double-layer thickness

The electrophoretic motion of a dielectric sphere situated at the center of a spherical cavity with an arbitrary thickness of the electric double layers adjacent to the particle and cavity surfaces is analyzed at the quasisteady state when the zeta potentials associated with the solid surfaces are arbitrarily nonuniform. Through the use of the multipole expansions of the zeta potentials and the linearized Poisson-Boltzmann equation, the equilibrium double-layer potential distribution and its perturbation caused by the applied electric field are separately solved. The modified Stokes equations governing the fluid velocity field are dealt with using a generalized reciprocal theorem, and explicit formulas for the electrophoretic and angular velocities of the particle valid for all values of the particle-to-cavity size ratio are obtained. To apply these formulas, one only has to calculate the monopole, dipole, and quadrupole moments of the zeta potential distributions at the particle and cavity surfaces. In some limiting cases, our result reduces to the analytical solutions available in the literature. In general, the boundary effect on the electrophoretic motion of the particle is a qualitatively and quantitatively sensible function of the thickness of the electric double layers relative to the radius of the cavity.     

Gravitational effects on transmembrane flux: the rayleigh—taylor convective instability

Using a cell with horizontally mounted membranes, volume flux was measured as a function of gravitational geometry. Water was placed on one side of the membrane. The opposite side of the membrane was exposed to either aqueous glucose solutions, with densities greater than water; or aqueous ethanol, less dense than water; or ethanol—glucose—water solutions. In all cases, the osmotic pressure gradient generated volume flux from water to the solution. No mechanical stirring was used.Experiments were performed first with water above the membrane and the solution below it. They were then repeated with water below and the solution above the membrane. In all cases, volume flux was significantly larger when the denser liquid was above the membrane.Mach—Zehnder interferograms were obtained for the interface region of the water—membrane—0.1 M glucose system, Results show directly that boundary layers are substantially larger and more uniform with the lower-density liquid above the membrane than with the opposite geometry.These experimental findings are interpreted in terms of a convective gravitational instability that reduces boundary layer dimensions and increases volume flux. Following Rayleigh—Tavlor analysis of fluid gravitational stability, a concentration-gradient Rayleigh Number is developed and used in a mathematical model for gravitationally sensitive volume flux.     

Interfacial tension between microemulsion and excess dispersed phases

Two-phase systems consisting of water-in-oil (W/O) microemulsions in equilibrium with excess water and oil-in-water (O/W) microemulsions in equilibrium with excess oil have been prepared using the surfactant sodium bis (2-ethylhexyl)sulphosuccinate (AOT) without cosurfactant. The interfacial tension of the planar interface separating the phases for the W/O case is only weakly dependent upon the volume fraction of droplets in the microemulsion phase whereas for the O/W case, the microemulsion droplet size increases and the tension drops as the dispersed volume fraction is increased.     

Optimal linearized Poisson-Boltzmann theory applied to the simulation of flexible polyelectrolytes in solution

Optimal linearized Poisson-Boltzmann (OLPB) theory is applied to the simulation of flexible polyelectrolytes in solution. As previously demonstrated in the contexts of the cell model [H. H. von Grunberg, R. van Roij, and G. Klein, Europhys. Lett. 55, 580 (2001)] and a particle-based model [B. Beresfordsmith, D. Y. C. Chan, and D. J. Mitchell, J. Colloid Interface Sci. 105, 216 (1985)] of charged colloids, OLPB theory is applicable to thermodynamic states at which conventional, Debye-Huckel (DH) linearization of the Poisson-Boltzmann equation is rendered invalid by violation of the condition that the electrostatic coupling energy of a mobile ion be much smaller than its thermal energy throughout space, |nu(alpha)e psi(r)|相似文献   

Unsteady electroosmosis in a microchannel with Poisson-Boltzmann charge distribution

The present study is concerned with unsteady electroosmotic flow (EOF) in a microchannel with the electric charge distribution described by the Poisson-Boltzmann (PB) equation. The nonlinear PB equation is solved by a systematic perturbation with respect to the parameter λ which measures the strength of the wall zeta potential relative to the thermal potential. In the small λ limits (λ<1), we recover the linearized PB equation - the Debye-Hückel approximation. The solutions obtained by using only three terms in the perturbation series are shown to be accurate with errors <1% for λ up to 2. The accurate solution to the PB equation is then used to solve the electrokinetic fluid transport equation for two types of unsteady flow: transient flow driven by a suddenly applied voltage and oscillatory flow driven by a time-harmonic voltage. The solution for the transient flow has important implications on EOF as an effective means for transporting electrolytes in microchannels with various electrokinetic widths. On the other hand, the solution for the oscillatory flow is shown to have important physical implications on EOF in mixing electrolytes in terms of the amplitude and phase of the resulting time-harmonic EOF rate, which depends on the applied frequency and the electrokinetic width of the microchannel as well as on the parameter λ.