Role of membranes in hydrodynamic interaction of small particles

The response of a fluid to a stationary force in the presence of membranes has been studied. Two different geometries of membrane systems are considered: two parallel flat membranes and a nearly spherical vesicle. In the case of a force acting between two parallel membranes, an induced velocity both between and behind the membranes is found. Between the membranes, at large distances from the application point, the induced velocity decays with the distance as 1/r, more slowly than between two solid walls where it decays as 1/r2, and similar to the decay in an unconfined liquid. Behind the membrane interface, the flow does not have a component normal to the membranes, and the normal component of the force does not affect the flow in this region. In the case of spherical symmetry, expressions for the flow both inside and outside the membrane vesicle are found in terms of spherical harmonics. We discuss the applications of our results to Brownian motion of particles in the system and the possibility of measuring the membrane internal viscosity.