Electro-osmosis of nematic liquid crystals under weak anchoring and second-order surface effects

Advent of nematic liquid crystal flows has attracted renewed attention in view of microfluidic transport phenomena. Among various transport processes, electro-osmosis stands as one of the efficient flow actuation mechanisms through narrow confinements. In the present study, we explore the electrically actuated flow of an ordered nematic fluid with ionic inclusions, taking into account the influences from surface-induced elasticity and electrical double layer (EDL) phenomena. Toward this, we devise the coupled flow governing equations from fundamental free-energy analysis, considering the contributions from first- and second-order elastic, dielectric, flexoelectric, charged surface polarization, ionic and entropic energies. The present study focuses on the influence of surface charge and elasticity effects in the resulting linear electro-osmosis through a slit-type microchannel whose surfaces are chemically treated to display a homeotropic-type weak anchoring state. An optical periodic stripe configuration of the nematic director has been observed, especially for higher electric fields, wherein the Ericksen number for the dynamic study is restricted to the order of unity. Contrary to the isotropic electrolytes, the EDL potential in this case was found to be dependent on the external field strength. Through a systematic investigation, we brought out the fact that the wavelength of the oscillating patterns is dictated mainly by the external field, while the amplitude depends on most of the physical variables ranging from the anchoring strength and the flexoelectric coefficients to the surface charge density and electrical double layer thickness.