Lehmann force acting on a micro-particle in smectic C* free-standing films subjected to methanol vapor transport

Gas permeation through smectic C* free-standing films causes a unidirectional director rotation, occasionally accompanied by a unidirectional vortex-like hydrodynamic flow. In this study, by placing ZrO₂ micro-particles on the film subjected to methanol vapor transport, we observed the particle motions and measured a drag force acting on them. The particles underwent a unidirectional quasi-circular motion with the velocity linear to the methanol transfer rate with the magnitude of the drag force being on the order of several pN that increased approximately linearly with the velocity of the flow. A simple analysis shows that the conversion efficiency from the transmembrane methanol current to the drag force on the particles is ∼1.4 × 10^-10 N·s·m²/mol in our system. The present hydrodynamic experiment is complementally to the previous observations of linear director rotation in the Lehmann effect, which well supports Leslie's phenomenological theory.