The Phenomenon of Hydrodynamic Diffusion

It is now time to discuss yet another mechanism of particle motion in a suspension in view of influence of ambient particles. Up till now, slow motion of a test particle was usually considered with the proper account taken of interactions with the neighboring particles, but with the assumption of sufficiently small volume concentration of particles W. In spite of this restriction, the formula (8.150) can be used to And the velocity of constrained motion of a particle at rather high values of j, i.e. in highly concentrated suspensions. In such suspensions, particle motion (gravitational sedimentation or motion in a shear flow) has a random character, which is different, however, from the character of Brownian motion, because particles sizes are much greater. This type of motion is caused by hydro-dynamic interactions with the neighboring particles. 

Gradient diffusion appears as a drift of particles against the particle concentration gradient. [72] derives the following expression for the factor of cross diffusion Dj = 2aU. 

The phenomenon of hydrodynamic diffusion in a shear flow, and also its possible applications are discussed in [70]. 

1 Batchelor G. K., Developments in microhydrodynamics in theoretical and applied mechanics Ed. W. T. Koiter, North Holland, Amsterdam, 1976, p. 33-55. 

2 Happel J., Brenner H., Low Reynolds number hydrodynamics, Prentice-Hall, 1965. 

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