Electric-field-induced displacement of a charged spherical colloid embedded in an elastic Brinkman medium

Gel Electrophoresis of a Hydrophobic Liquid Droplet with an Equipotential Slip Surface

A theoretical study has been carried out on the electrophoresis of charged dielectric liquid droplets with an equipotential and hydrodynamically slipping surface moving in a quenched polymeric charged hydrogel medium. The liquid inside the droplet is electrically neutral. The Brinkman-Debye-Bueche model is employed to study the gel electrophoresis of such a hydrophobic and equipotential liquid droplet considering the long-range hydrodynamic interaction between a migrating droplet and the gel skeleton. Within the weak field and Debye-Hückel electrostatic framework, we derive an original closed-form expression for electrophoretic mobility, which further recovers the existing mobility expressions derived under several limiting conditions. The derived expressions for electrophoretic mobility explicitly involve exponential integrals, which are not so convenient for practical applications. Thus, the exact forms of the electrophoretic mobility under various electrohydrodynamic conditions are further approximated to make them free from exponential integrals. The approximate forms are found to be in excellent agreement with the exact results with maximum relative errors of about 1.5%.

Gel electrophoresis of a soft particle

A review is given on the theory of the gel electrophoresis of a spherical soft particle, i.e., the electrophoresis of a spherical hard particle covered with an ion-penetrable surface layer of polyelectrolytes moving in a polymer gel medium, which may either be charged or uncharged. A detailed study is made on the fundamental electrokinetic equations describing the soft-particle gel electrophoresis due to the long-range hydrodynamic particle-gel interaction on the basis of the Brinkman-Debye-Bueche model. A general expression and several approximate analytic expressions are given for the electrophoretic mobility of a soft particle in a polymer gel medium.

Hydrogel charge regulation and electrolyte ion-concentration perturbations in nanoparticle gel electrophoresis

Gel electrophoresis of spherical nanoparticles (NPs) is studied using an electrokinetic model that couples the ion conservation equations to the Poisson and fluid momentum equations, thus including the so-called polarization and relaxation processes. This model is therefore the charged gel electrophoresis analogue of the well-known O’Brien and White solution of the standard electrokinetic model for free-solution electrophoresis. Results are provided for the small NPs (size around 10 nm) to which gel electrophoresis is relevant, because particles must be small enough to permeate the gel: these include the particle drag coefficient (or Brownian diffusivity), which is subject to hydrodynamic screening and electroviscous effects, and the electrophoretic mobility, which is subject to nonlinear electrostatic and charge polarization influences. Also addressed are the influences of charge-regulating gels and the accompanying particle-induced immobile charge-density perturbations. Ion-concentration perturbations attenuate the electrophoretic mobility and enhance the drag coefficient according to the particle charge and the mobility of the most abundant counterion. However, dynamic regulation of the hydrogel charge—termed the secondary immobile charge-density perturbation—has a negligible influence on the particle mobility, and may therefore be neglected for most practical purposes.

Steady electrical and micro-rheological response functions for uncharged colloidal inclusions in polyelectrolyte hydrogels

The electric-field-induced response of an uncharged colloidal sphere embedded in a quenched polyelectrolyte hydrogel is calculated from a model where the polymer network is treated as an elastic, porous skeleton saturated with an aqueous electrolyte. We present exact analytical solutions for the steady response to a uniform electric field, as well as the steady susceptibility, defined as the ratio of the particle displacement to the strength of an optical or magnetic force. Even though the particle is uncharged, it attains a finite electric-field-induced displacement owing to hydrodynamic coupling with electroosmotic flow. The steady susceptibility decreases with increasing charge and decreasing electrolyte concentration; in general, charge imparts a small correction to the classical theory for an uncharged linearly elastic continuum.