Translation drag coefficient of a self-similar assembly of spheres immersed in an incompressible fluid. |
| |
Authors: | C Y Tseng H K Tsao S B Chen |
| |
Affiliation: | Department of Chemical Engineering, National Central University, Chung-li, Taiwan 320, Republic of China. |
| |
Abstract: | On the basis of deterministic fractals and the Rotne-Prager hydrodynamic interaction tensor, we confirm the asymptotic as well as the finite size scaling of the friction coefficient lambda of a self-similar structure. The fractal assembly is made of N spheres with its dimension varying from D < 1 to D = 3. The number of spheres can be as high as N approximately O(10(4)). The asymptotic scaling behavior of the friction coefficient per sphere is lambda approximately N(1/D-1) for D > 1, lambda approximately (lnN)(-1) for D = 1, and lambda approximately N(0) for D < 1. The crossover behavior indicates that while in the regime of D > 1 the hydrodynamic screening effect grows with the size, for D<1 it is limited in a finite range, which decays with decreasing D. |
| |
Keywords: | |
|
|