The general expression is derived for the diffusiophoretic velocity of a large spherical colloidal particle of radius a in a concentration gradient of general electrolytes of Debye-Huckel parameter κ. On the basis of this expression, simple approximate analytic expressions for the diffusiophoretic velocity correct to the order of (1/κa)0 are derived, which can be applied for large particles with κa ≥ 50 at arbitrary values of the particle zeta potential with negligible errors.

Diffusiophoretic velocity of a large spherical colloidal particle in a solution of general electrolytes

Diffusiophoresis of a charge regulated spherical polyelectrolyte nanogel (PE) due to an externally imposed ionic concentration gradient is considered The immobile charge density of the nanogel develops through the association/dissociation reactions of their inorganic functional groups The nanogel is ion and fluid permeable with dielectric permittivity different from that of the surrounding electrolyte medium This difference in dielectric permittivity creates an ion partitioning due to the difference in self energy of ions The Nernst–Planck equation for ion transport and the Poisson equation (PNP) for the electric field are modified to take into account the ion partitioning effects The diffusiophoresis mechanism is governed by the electrophoresis generated by the induced electric field and chemiphoresis develops due to the mitigation of counterions across the double layer of the nanogel In addition, the convection dominated double layer polarization and the counterion condensation as well as the electroosmotic flow created by the gel immobile charge play a role in the diffusiophoresis All these effects are incorporated through the modified PNP equations coupled with the Navier–Stokes equations The governing equations in their full form are solved numerically through a control volume approach Present computed solutions for the limiting cases are in good agreement with the existing solutions based on the first-order perturbation analysis In order to illustrate the diffusiophoresis mechanism we have measured the induced electric field and effective charge density of the PE and analyzed its dependence on several electrokinetic parameters The contribution due to chemiphoresis is low for PE compared to a rigid colloid For a highly permeable PE the diffusiophoretic velocity increases and approaches a saturation for higher range of the PE fixed charge density The ion partitioning effect depletes counterions in PE to manifests its diffusiophoretic velocity The diffusiophoretic velocity of PE for pH > IEP is higher than the case for which pH < IEP

Impact of ion partitioning and double layer polarization on diffusiophoresis of a pH-regulated nanogel

Diffusiophoretic velocity of a spherical soft particle

Ion size effect on the diffusiophoretic mobility of a large colloidal particle

Diffusiophoresis of a soft particle in electrolyte solutions normal to a conducting solid plane is investigated theoretically in this study, focusing on the highly charged particle in particular. A pseudo-spectral method based on Chebyshev polynomial is adopted to solve the resultant governing electrokinetic equations. It was found, among other things, that the closer the soft particle is to the plane, the faster it moves in general, provided only the chemiphoresis component of the diffusiophoresis is involved, i.e., no diffusion potential is present. The presence of the conducting plane is found to have three effects upon the particle motion nearby: the geometric boundary confinement effect, the electrostatic mirror-image force analog effect, and the hydrodynamic retarding effect. The enhancement of the double layer polarization by the first two effects leads to the seeming intriguing observation mentioned above. The particle always moves away from the plane in chemiphoresis. If a diffusion potential is present, however, then it is possible to drive the particle toward the plane. The results have potential applications in drug delivery.

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

Diffusiophoresis of a soft particle suspended in an infinite medium of symmetric binary electrolyte solution is investigated theoretically in this study, focusing on the chemiphoresis component when there is no global diffusion potential in the bulk solution. The general governing electrokinetic equations are solved with a pseudo-spectral method based on Chebyshev polynomials, and particle mobility, defined as the particle velocity per unit concentration gradient, is calculated. Parameters of electrokinetic interest are examined, in general, to explore their respective impact upon particle motion, such as the fixed charge density and permeability in the outer porous layer, the surface charge density and size of the inner rigid core, and the electrolyte strength in the solution. Nonlinear phenomena such as the motion-deterring double-layer polarization and the counterion condensation effects are scrutinized, in particular, for highly charged soft particles. Mobility reversal is observed in some range of electrolyte strength for highly charged particles. The generation of an axisymmetric counterclockwise vortex flow across the porous layer is found to be responsible for it. The onset of the mobility reversal is synchronized with the appearance or disappearance of this vortex flow. Mobility reversal may happen more than once, with particle moving toward or away from the region of higher solute concentration. The latter is undesirable in the application of drug delivery and thus should be avoided by delicate control of the electrokinetic environment. A local micro diffusion potential is discovered, which always speeds up the migration of coions and slows down that of counterions to guarantee that there is no net electric current across the double layer. Moreover, multilayer structure of the double-layer polarization is discovered when the electrolyte strength is high. The study presented here provides insight and crucial information for practical applications of soft particles, such as drug delivery.

Diffusiophoresis of a Highly Charged Soft Particle in Electrolyte Solutions.

Diffusiophoresis of a highly charged soft particle in electrolyte solutions induced by diffusion potential

Electrophoresis of a highly charged dielectric fluid droplet in electrolyte solutions.

A simple analytical formula is obtained for the diffusiophoresis of a dielectric fluid droplet in symmetric binary electrolyte solutions under Debye-Huckel approximation valid for weakly charged droplets. The chemiphoresis is found to yield negative mobilities most of the time for droplets of constant surface charge density, which implies that the droplets tend to move away from the source releasing ionic chemicals. This is undesirable in some practical applications like drug delivery with liposomes in terms of conveying the drug-carrying liposomes to the desired area in the human body releasing specific ionic chemicals utilizing the self-guiding nature of diffusiophoresis. The further involvement of the electrophoresis component, however, may change the scenario via the oriented electric field generated by the induced diffusion potential. The lesson here is that while the impact of the chemiphoresis component is determined by nature and uncontrollable, the electrophoresis component serves as an artificially adjustable factor via choosing droplets with the surface charge of appropriate sign in practical applications. The results here have potential use in practical applications such as drug delivery. The portable simple analytical formula is a powerful asset to experimental researchers and design engineers in colloid science and technology to facilitate their works.

Yvonne Wu

Papers

Diffusiophoresis of a Highly Charged Soft Particle in Electrolyte Solutions.

Diffusiophoresis of a highly charged soft particle in electrolyte solutions induced by diffusion potential

Electrophoresis of a highly charged dielectric fluid droplet in electrolyte solutions.

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

Analytical solution to dielectric droplet diffusiophoresis under Debye-Hückel approximation.