Eur. Phys. J. E (2019) 42: 73
https://doi.org/10.1140/epje/i2019-11847-2

Regular Article

Conservation-Dissipation Formalism for soft matter physics: I. Augmentation to Doi's variational approach

¹ Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, 100084, Beijing, P. R. China
² Department of Mathematics, Minjiang University, 350121, Fuzhou, P. R. China

^* e-mail: zcamhl@tsinghua.edu.cn

Received: 4 December 2018
Accepted: 20 May 2019
Published online: 13 June 2019

Abstract

In the first paper of this series, we prove that by choosing the proper variational function and variables, the variational approach proposed by Doi in soft matter physics is equivalent to the Conservation-Dissipation Formalism. To illustrate the correspondence between these two theories, several novel examples in soft matter physics, including the particle diffusion in dilute solutions, polymer phase separation dynamics and nematic liquid crystal flows, are carefully examined. Based on our work, a deep connection among the generalized Gibbs relation, the second law of thermodynamics and the variational principle in non-equilibrium thermodynamics is revealed.