Conservation-Dissipation Formalism for soft matter physics: II. Application to non-isothermal nematic liquid crystals

  • Liangrong Peng
  • Yucheng Hu
  • Liu HongEmail author
Regular Article


For most existing non-equilibrium theories, the modeling of non-isothermal processes is a hard task. Intrinsic difficulties involve the non-equilibrium temperature, the coexistence of conserved energy and dissipative entropy, etc. In this paper, by taking the non-isothermal flow of nematic liquid crystals as a typical example, we illustrate that thermodynamically consistent models in either vectorial or tensorial forms can be constructed within the framework of the Conservation-Dissipation Formalism (CDF). And the classical isothermal Ericksen-Leslie model and Qian-Sheng model are shown to be special cases of our new vectorial and tensorial models in the isothermal, incompressible and stationary limit. Most importantly, from the above examples, it is known that CDF can easily solve the issues relating with non-isothermal situations in a systematic way. The first and second laws of thermodynamics are satisfied simultaneously. The non-equilibrium temperature is defined self-consistently as a partial derivative of the entropy function. Relaxation-type constitutive relations are constructed, which give rise to classical linear constitutive relations, like Newton's law and Fourier's law, in stationary limits. Therefore, CDF is expected to have a broad scope of applications in soft matter physics, especially under complicated situations, such as non-isothermal, compressible and nanoscale systems.

Graphical abstract


Flowing Matter: Liquids and Complex Fluids 

Supplementary material

10189_2019_11839_MOESM1_ESM.pdf (221 kb)
Supplemental Material: A comprehensive derivation on the tensorial models for non-isothermal flows of nematic liquid crystals


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Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Zhou Pei-Yuan Center for Applied MathematicsTsinghua UniversityBeijingP. R. China
  2. 2.Department of MathematicsMinjiang UniversityFuzhouP. R. China

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