Translation drag coefficient of a self-similar assembly of spheres immersed in an incompressible fluid

On the basis of deterministic fractals and the Rotne-Prager hydrodynamic in teraction tensor, we confirm the asymptotic as well as the finite size scal ing of the friction coefficient A 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 similar to O(10(4)). The asymp totic scaling behavior of the friction coefficient per sphere is lambda sim ilar to N1/D-1 for D > 1, lambda similar to (InN)(-1) for D = 1, and lambda similar to N-0 fur D < 1. The crossover behavior indicates that while in t he regime of D > 1 the hydrodynamic screening effect grows with tile size, for D < 1 it is limited in a finite range, which decays with decreasing D.