A numerical study on the electrophoresis of a liquid droplet embedded in a polyelectrolyte hydrogel medium is made by considering the full set of governing equations based on the conservation principle. The surface of the droplet is considered to be charged, and the liquid filling the droplet is non-conducting. The dielectric polarization of the non-conducting droplet is also addressed in the present study. The impact of the surface conduction, double layer polarization, and relaxation effects on the electrophoresis of the non-conducting polarizable uniformly charged droplet is elucidated for a wide range of the gel volume charge density, Debye length, and drop viscosity and size. The presence of the gel immobile charge and slip velocity at the droplet surface leads to a stronger surface conduction, which precludes consideration of a simplified model based on the thin-layer assumption. Our numerical solutions at a low ζ—potential corresponding to a droplet of large viscosity, for which surface conduction is negligible—agree well with the existing analytic solutions for a rigid colloid. The strong electroosmotic flow driven by the immobile charges of the gel medium creates a negatively charged drop in the hydrogel medium to translate along the direction of the applied field. Entrapment of the charged drop can be made by regulating the Debye length and volume charge density of the gel. The charged gel medium is found to be efficient in size-based sorting of the liquid drops.
Electrokinetic transport of an uncharged nonconducting microsized liquid droplet in a charged hydrogel medium is studied. Dielectric polarization of the liquid drop under the action of an externally imposed electric field induces a non‐homogeneous charge density at the droplet surface. The interactions of the induced surface charge of the droplet with the immobile charges of the hydrogel medium generates an electric force to the droplet, which actuates the drop through the charged hydrogel medium. A numerical study based on the first principle of electrokinetics is adopted. Dependence of the droplet velocity on its dielectric permittivity, bulk ionic concentration, and immobile charge density of the gel is analyzed. The surface conduction is significant in presence of charged gel, which creates a concentration polarization. The impact of the counterion saturation in the Debye layer due to the dielectric decrement of the medium is addressed. The modified Nernst–Planck equation for ion transport and the Poisson equation for the electric field is considered to take into account the dielectric polarization. A quadrupolar vortex around the uncharged droplet is observed when the gel medium is considered to be uncharged, which is similar to the induced charge electroosmosis around an uncharged dielectric colloid in free‐solution. We find that the induced charge electrokinetic mechanism creates a strong recirculation of liquid within the droplet and the translational velocity of the droplet strongly depends on its size for the dielectric droplet embedded in a charged gel medium.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.