A theoretical study of induced-charge dipolophoresis of ideally polarizable asymmetrically slipping Janus particles

We consider the non linear electrophoretic transport of uncharged, ideally polarizable hydrodynamic Janus spheres, the inhomogeneity of which is produced by a variable Navier slip condition at the particle surface. A general, three dimensional formulation enabling calculation of the electrophoretic mobility of any patchy particle, with an arbitrary tensorial slip boundary condition is provided. The solution avoids the common assumption of an infinitely thin electric double layer (λ) and Navier slip coefficient (b) and is thereby valid for finite values of these parameters, which is of particular importance at the nanoscale. The specific case of a Janus sphere, consisting of two equal hemispheres, each with a different but constant slip boundary condition is solved semi-analytically and numerically. In the instance where the slip coefficients at each hemisphere are equal, induced charge electro-osmotic flow is evident at an increased rate as compared to a homogeneous sphere with no slip. If the slip coefficients differ from each other, the particle is found to self-align with the electric field and travel with the slip surface facing forward. The increased pumping rates and mobility found in the cases of the homogeneous and Janus spheres respectively, occur as a function of the ratio b/bλλ and are most significant for the combination of a thin electric double layer (EDL) and large slip length. However, it is also illustrated that the size of the EDL independently dominates the effects of slip.