Electrophoresis of a polymeric Brinkman droplet in a cylindrical pore

Electrophoresis of a nondeforming polymeric Brinkman droplet with a constant surface potential in an uncharged cylindrical pore is investigated theoretically. The droplet is modeled as a polymer-containing fluid inclusion whose internal flow is resisted by a Debye–Büeche–Brinkman (DBB) hydrodynamic drag. An analytical relation converting the polymer-induced internal drag into an equivalent Newtonian viscosity is derived. A patched pseudo-spectral method based on Chebyshev polynomials is adopted to solve the coupled electrostatic, ionic-transport, and hydrodynamic equations. The results show that the boundary confinement effect is most profound in narrow pores. In addition to the extra hydrodynamic resistance, the nearby wall squeezes and deforms the electric double layer, thereby enhancing the motion-deterring double-layer polarization. Consequently, a droplet with a thick double layer may undergo mobility reversal and migrate against its usual electrophoretic direction. At low surface potential, increasing the DBB screening parameter suppresses internal circulation and shifts the mobility continuously from the Newtonian-droplet limit toward the rigid-sphere limit. At higher surface potentials, however, the ordering of the mobility curves for different DBB screening parameters reverses across a critical double-layer thickness. A hydrodynamic solidification point is observed where the mobility becomes nearly insensitive to internal hydrodynamic screening and the interior recirculating flow is strongly suppressed, while the translational mobility remains finite. These results provide physical insight into the electrophoretic transport of polymer-containing droplets through confined micro- and nanofluidic channels.