next up previous
Next: Mobility and diffusivity Up: Hydrodynamic Interactions Previous: The stokeslet approximation

Pair Diffusion

As a first application of the stokeslet approximation to colloidal hydrodynamics, we calculate two colloidal spheres' hydrodynamic coupling in an unbounded fluid. Each sphere moves in the flow field $ \ensuremath{\mathsf{G}}\xspace ^S$ due to its neighbor. The corresponding mobility tensor is

$\displaystyle \ensuremath{\mathsf{b}}\xspace _\ensuremath{{i \alpha, j \beta}}=...
...nsuremath{\mathsf{G}}\xspace ^S_\ensuremath{{\alpha\beta}}(\vec r_i - \vec r_j)$ (28)

with $ i,j = 1,2$. This result describes the spheres' hydrodynamic interactions at separations large compared with their diameters. It is not in the most convenient form for comparison with optical tweezer measurements, however. For those purposes, we relate spheres' mobility to their more easily measured diffusivity.


David G. Grier 2001-01-16