Calculation of translational friction and intrinsic viscosity. I. General formulation for arbitrarily shaped...

A general method for calculating translational friction and intrinsic viscosity is developed through exploiting relations between hydrodynamics and electrostatics. An approximate relation xi = 6 pi eta 0C between the translational friction coefficient xi of a particle (eta 0: solvent viscosity) and its capacitance C was derived previously. This involved orientationally preaveraging the Oseen tensor, but the result was found to be very accurate. Based on preaveraging, we find that the intrinsic viscosity [eta] of a particle can be estimated from its polarizability alpha through [eta] = 3/4 alpha + 1/4 Vp, where Vp is the volume of the particle. Both the capacitance and the polarizability can be obtained in a single calculation using the boundary-element technique. An efficient approach is thus found for estimating [eta], a quantity that is very useful in practice because of its sensitivity to particle shape but is notoriously difficult to calculate. Illustrative calculations on ellipsoids, cylinders, and dumbbells demonstrate both the accuracy of the approximate relations and the efficiency of the present method.