Sedimentation of a charged hydrophobic colloid with physisorbed surface charge and similarity with a charged droplet

The sedimentation of a charged hydrophobic rigid colloid by considering a surface charge-dependent slip condition is studied by numerical simulation alongside a simplified model. The primary aim is to elucidate the effect of the lateral mobility of ions adsorbed on the surface of the hydrophobic rigid colloid and establish an identity with the sedimentation of a charged liquid droplet. For the hydrophobic surface with mobile adsorbed charge, an additional electric force and a frictional force are produced by the physisorbed ions to create an alteration of the conventional slip boundary condition and the slip length. We have also considered separately the sedimentation of the liquid droplet by considering a stress balance condition at the charged interface, which includes a non-zero tangential component of the electric stress. The governing electrokinetic equations for the hydrophobic rigid particle as well as the droplet are solved numerically. We have also constructed a simplified model based on a first-order perturbation from equilibrium. The mobility of the physisorbed surface charge enhances the sedimentation velocity of the hydrophobic colloid by creating an enhanced slip velocity. The sedimentation velocity generally diminishes as the surface charge density increases. However, for a fully mobile surface charge, the velocity of the hydrophobic rigid colloid increases with the rise in surface charge density at an elevated value of the slip length. The numerical findings and the semi-analytical solution establish that the sedimentation of a hydrophobic particle with a fully mobile surface charge resembles that of a liquid droplet, wherein the viscosity of the droplet relates to the slip length of the hydrophobic particle.