Hydrodynamic friction and the capacitance of arbitrarily shaped objects.

Abstract

The translational friction coefficient and the capacitance of a variety of objects are calculated with a probabilistic method involving hitting the ``probed'' objects with random walks launched from an enclosing spherical surface. This method is applied to exactly solvable examples to test the program accuracy and to physically important and analytically intractable examples (cube, chain of spheres at the vertices of self-avoiding and random walks, etc.). Large fluctuations in the friction of polymer chains with a random coil structure are found to give large deviations from the mean-field Kirkwood-Riseman theory and ``hydrodynamic fluctuation'' effects are found to diminish with the chain swelling accompanying excluded volume interaction. Capacity applications are reviewed and our probabilistic estimates of polymer friction are compared with previous calculations using alternative methods. Transients to the capacity and related properties are expressed in terms of fluctuations in the ``Wiener sausage'' volume (volume swept out by a Brownian particle where a repeated visit to a spatial region does not contribute to the volume increase in time).