Anisotropy of Particle Mobility

The quantities (7.5) can be determined in some simple cases. In the simplest case, when no hydrodynamic interaction is assumed, one uses equation (3.8) with matrix (3.10) and, omitting the diffusive normal mode with the label 0, has 

A more complicated cases take into account global and local anisotropy. Global Anisotropy 

The system of entangled macromolecules becomes anisotropic when velocity gradients are applied, and one can assume that each Brownian particle of the chain moves in the anisotropic medium. The expressions for the discussed quantities (7.5) for case, when one can neglect the hydrodynamic interaction 

The linear approximation (7.9) is insufficient to describe the variation of the friction coefficient at large velocity gradients. In this case, approximation (7.9) can be generalised (Pokrovskii and Pyshnograi 1990, 1991) to become 

With accuracy up to the first-order terms in respect of the tensor of anisotropy, expressions (7.9) and (7.10) coincide. Of course, one can use any other approximation that is consistent with (7.9). 

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