Fluctuating viscoelasticity based on a finite number of dumbbells

Markus Hütter (Corresponding author), Peter D. Olmsted, Daniel J. Read

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Two alternative routes are taken to derive, on the basis of the dynamics of a finite number of dumbbells, viscoelasticity in terms of a conformation tensor with fluctuations. The first route is a direct approach using stochastic calculus only, and it serves as a benchmark for the second route, which is guided by thermodynamic principles. In the latter, the Helmholtz free energy and a generalized relaxation tensor play a key role. It is shown that the results of the two routes agree only if a finite-size contribution to the Helmholtz free energy of the conformation tensor is taken into account. Using statistical mechanics, this finite-size contribution is derived explicitly in this paper for a large class of models; this contribution is non-zero whenever the number of dumbbells in the volume of observation is finite. It is noted that the generalized relaxation tensor for the conformation tensor does not need any finite-size correction.
Original languageEnglish
Article number71
Number of pages14
JournalEuropean Physical Journal E
Issue number11
Publication statusPublished - 20 Nov 2020


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