Stress fluctuations and Brownian motion in incompressible visco-elastic fluids

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Abstract
It is assumed that the visco‐elastic behavior is linear and can be described by integral relations between local stresses and strain rates. When stress fluctuations are added, the equations describe non‐Markovian random processes. To find the correlation functions for the fluctuating stresses, use is made of an analogy with the generalized Langevin equation. An application to the Brownian motion of a spherical particle in a Maxwell fluid shows that the random force on the particle has a memory which extends over times of the order of the relaxation time of the Maxwell model. The asymptotic behavior at large times is exactly the same as in a Newtonian liquid.

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