Hydrodynamic Interactions and Collective Dynamics of Multiple Inclusions in Two-Dimensional Membranes

摘要

The hydrodynamics of multiple inclusions in two-dimensional, thin films of smectic liquid crystal material are studied. The self-mobilities of these inclusions are experimentally studied in highly crowded conditions by analyzing their Brownian motion. Saffman and Delbruck found the characteristic length, known as the Saffman length, beyond which momentum in a two-dimensional film has a negligible effect on an inclusion which is proportional to the thickness of the film. The effects of crowding are studied by varying the number of the nearest neighboring inclusions within one Saffman length. The self-mobilities of these inclusions are also experimentally studied for two islands of identical radii interacting within a couple of Saffman lengths experiencing an external force. This is achieved by the method of images. The interaction of two islands moving towards each other and along side each other is achieved by tilting the two-dimensional film. These two cases are thus experimentally studied by measuring the self-mobilities for islands moving perpendicular to the boundary and parallel to the boundary.