Stress fluctuations and Brownian motion in incompressible viscohyphen;elastic fluids

摘要

It is assumed that the viscohyphen;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 nonhyphen;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.