TY - JOUR
T1 - Fluctuating viscoelasticity based on a finite number of dumbbells
AU - Hütter, Markus
AU - Olmsted, Peter D.
AU - Read, Daniel J.
PY - 2020/11/20
Y1 - 2020/11/20
N2 - 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.
AB - 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.
KW - Flowing Matter: Liquids and Complex Fluids
UR - http://www.scopus.com/inward/record.url?scp=85096506542&partnerID=8YFLogxK
U2 - 10.1140/epje/i2020-11999-x
DO - 10.1140/epje/i2020-11999-x
M3 - Article
C2 - 33226463
SN - 1292-8941
VL - 43
JO - European Physical Journal E
JF - European Physical Journal E
IS - 11
M1 - 71
ER -