Author:
Hütter Markus,Olmsted Peter D.,Read Daniel J.
Abstract
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.Graphical abstract
Publisher
Springer Science and Business Media LLC
Subject
Surfaces and Interfaces,General Materials Science,General Chemistry,Biophysics,Biotechnology
Reference34 articles.
1. T.M. Squires, T.G. Mason, Annu. Rev. Fluid Mech. 42, 413 (2010)
2. G.E. Karniadakis, A. Beskok, N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation (Springer, New York, 2005)
3. B.J. Kirby, Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices (Cambridge University Press, Cambridge, 2010)
4. L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Course of Theoretical Physics, Vol. 6 (Pergamon Press, Oxford, 1959)
5. C. Hohenegger, S.A. McKinley, J. Comput. Phys. 340, 688 (2017)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献