Diffusiophoresis in Suspensions of Charged Soft Particles

Abstract

The diffusiophoresis in a suspension of charged soft particles in electrolyte solution is analyzed. Each soft particle is composed of a hard core of radius r0 and surface charge density σ and an adsorbed fluid-penetrable porous shell of thickness a−r0 and fixed charge density Q. The effect of particle interactions is considered by using a unit cell model. The ionic concentration, electric potential, and fluid velocity distributions in a unit cell are solved as power expansions in σ and Q, and an explicit formula for the diffusiophoretic velocity of the soft particle is derived from a balance between the hydrodynamic and electrostatic forces exerted on it. This formula is correct to the second orders of σ and Q and valid for arbitrary values of κa, λa, r0/a, and the particle volume fraction of the suspension, where κ is the Debye screening parameter and λ is the reciprocal of a length featuring the flow penetration into the porous shell. The effects of the physical characteristics and particle interactions on the diffusiophoresis (including electrophoresis and chemiphoresis) in a suspension of charged soft particles, which become those of hard particles and porous particles in the limits r0=a and r0=0, respectively, are significant and complicated.

Electroosmosis and Electric Conduction of Electrolyte Solutions in Charge-Regulating Fibrous Media

“…By substituting Equations (14) and (15) into the Gauss condition, one obtains the following formula relating the zeta potential and surface charge density of the cylinder at equilibrium:…”

“…, and F ρ (ρ) for the perturbed ionic electrochemical potential energy δµ m and the fluid flow, but it does contribute to the perturbed pressure δp via Equation (19c) and influence the force balance on the unit cell. The electric potential distribution along the cylinder surface ψ s may be determined from Equations (1), (14), (15), (17), and (21) by taking ρ = a, and then the surface charge density distribution σ is obtained from Equation (A3).…”

“…To avoid the difficulty of multiple-entity boundary value problems, the unit cell model was frequently used to predict the effects of interactions among the small solid entities constructing the porous medium on the electroosmotic velocity and effective electric conductivity. Although different shapes of the cell may be employed, a spherical [6][7][8][9][10][11][12][13][14] or circular cylindrical [15][16][17][18][19][20] one for the fictitious envelope of fluid surrounding each spherical or circular cylindrical entity is most convenient.…”

Diffusiophoresis of a highly charged soft particle normal to a conducting plane

“…Motivated by this application in particular, Lee and his coworkers [21,22] investigated the diffusiophoresis of a soft particle in electrolyte solutions recently, focusing on the unique behaviors of highly charged ones, as they are most often encountered in practice. Suspensions of soft particles were explored by other groups as well [23,24]. However, the drug-carrying soft particles have to reach their target location somehow eventually: approaching the tissue needing therapy, which can be treated as a planar solid boundary as the particles are so small compared to their size.…”

Electrophoretic Mobility and Electric Conductivity of Salt-Free Suspensions of Charged Soft Particles

“…As a result, the disperse fluid is dragged to flow, and the electric current in the suspension is different from that in a bulk solution. Numerous formulas for the electrophoretic mobility and electric conductivity in suspensions of charged particles have been obtained in the past [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”