Fluctuating viscoelasticity based on a finite number of dumbbells
Abstract
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.
Keywords
Cite
@article{arxiv.2011.02797,
title = {Fluctuating viscoelasticity based on a finite number of dumbbells},
author = {Markus Hütter and Peter D. Olmsted and Daniel J. Read},
journal= {arXiv preprint arXiv:2011.02797},
year = {2020}
}
Comments
14 pages, 1 figure