Electrokinetic droplet transport from electroosmosis to electrophoresis

Droplet transport in microfluidic channels by electrically induced flows often entails the simultaneous presence of electroosmosis and electrophoresis. Here we make use of coupled lattice-Boltzmann/molecular dynamics simulations to compute the mobility of a droplet in a microchannel under the effect of an external electric field. By varying the droplet solvation free energy of the counterions released at the channel walls, we observe the continuous transition between the electroosmotic and electrophoretic regime. We show that it is possible to describe the mobility of a droplet in a unified, consistent way, by combining the theoretical description of the electroosmotic flow with, in this case, the Hückel limit of electrophoresis, modified in order to take into account the Hadamard–Rybczynski droplet drag.