Taylor's swimming sheet in a smectic-A liquid crystal

We calculate the swimming speed of a Taylor sheet in a smectic-A liquid crystal. Assuming that the amplitude of the wave propagating on the sheet is much smaller than the wave number, we solve the governing equations using the method of series expansion up to the second order in amplitude. We find that the sheet can swim much faster in smectic-A liquid crystals than in Newtonian fluids. The elasticity associated with the layer compressibility is responsible for the enhanced speed. We also calculate the power dissipated in the fluid and the flux of the fluid. The fluid is pumped opposite to the direction of the wave propagation.