Drag of a Cottrell atmosphere by an edge dislocation in a smectic-A liquid crystal

In a recent letter (P. Oswald et al., EPL 103, 46004 (2013)), we have shown that a smectic-A phase hardens in compression normal to the layers when the liquid crystal is doped with gold nanoparticles. This is due to the formation of Cottrell clouds nearby the core of the edge dislocations and the appearance of an additional drag force that reduces their mobility. We theoretically calculate the shape of the Cottrell cloud and the associated drag force as a function of the climb velocity of the dislocations. The main result is that the drag force depends on velocity and vanishes when the temperature tends to the smectic-A-to-nematic transition temperature. The role of the diffusion anisotropy is also evaluated.