Electric-field induced micromixing within a droplet embedded in a polyelectrolyte hydrogel

The electric field induced response of a droplet embedded in a quenched polyelectrolyte gel is calculated theoretically. The polyelectrolyte hydrogel is modeled as a soft, charged porous solid saturated with a salted Newtonian fluid. The droplet is considered an incompressible Newtonian fluid with no free charge. An exact analytical solution, in the context of linear superposition, is obtained for the steady response to a DC electricfield. Interestingly, the fluid within the droplet is driven owing to hydrodynamic coupling with electroosmotic flow. The fluid velocity within the droplet is proportional to the electroosmotic flow, and depends on thepolymer boundary condition at the droplet-gel interface. As the polymer stick to the droplet interface increases, the flow within the droplet decreases, and at no-slip boundary condition, the droplet behaves like a rigid spherical particle with no internal flow