Drift in supported membranes

An object moving in a fluid transports the fluid along the direction of its motion. Using the concept of drift, i.e., the net motion of a small volume of fluid or a tracer particle due to a moving body, we quantify this entrainment for an inclusion in a supported lipid bilayer membrane. Our analysis demonstrates that a moving object in a supported membrane transports a small volume of fluid by a significant distance only when the initial position of the fluid volume in question is within a distance ξ from the line of motion, where ξ is the screening length of the membrane. The total area swept out by a line of such fluid volume elements, initially at rest and oriented perpendicular to the direction of motion, is the drift area. We show that the drift area is related quadratically to the screening length. These calculations suggest that dynamic domains of entrained lipids of size ξ form spontaneously around moving objects in supported membranes due to hydrodynamic interactions. This effect is potentially important for transport processes in biological and artificial membranes.