Chin. Phys. B, 2020, Vol. 29(12): 124701    DOI: 10.1088/1674-1056/abb3e5
 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next

# Alternative constitutive relation for momentum transport of extended Navier-Stokes equations

Guo-Feng Han(韩国锋)1, Xiao-Li Liu(刘晓丽)2,†, Jin Huang(黄进)2, Kumar Nawnit2, and Liang Sun(孙亮)3
1 Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China; 2 State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China; 3 PetroChina Research Institute of Petroleum Exploration & Development, Beijing 100083, China
Abstract  The classical Navier-Stokes equation (NSE) is the fundamental partial differential equation that describes the flow of fluids, but in certain cases, like high local density and temperature gradient, it is inconsistent with the experimental results. Some extended Navier-Stokes equations with diffusion terms taken into consideration have been proposed. However, a consensus conclusion on the specific expression of the additional diffusion term has not been reached in the academic circle. The models adopt the form of the generalized Newtonian constitutive relation by substituting the convection velocity with a new term, or by using some analogy. In this study, a new constitutive relation for momentum transport and a momentum balance equation are obtained based on the molecular kinetic theory. The new constitutive relation preserves the symmetry of the deviation stress, and the momentum balance equation satisfies Galilean invariance. The results show that for Poiseuille flow in a circular micro-tube, self-diffusion in micro-flow needs considering even if the local density gradient is very low.
Keywords:  extended Navier-Stokes equation      constitutive relation      momentum transport      mass diffusion
Received:  01 May 2020      Revised:  28 June 2020      Accepted manuscript online:  01 September 2020
 PACS: 47.10.ad (Navier-Stokes equations) 47.10.ab (Conservation laws and constitutive relations) 91.65.My (Fluid flow)
Fund: Project supported by the National Natural Science Foundation of China-Outstanding Youth Foundation (Grant No. 51522903), the National Natural Science Foundation of China (Grant Nos. 11602276 and 51479094), and the Fund from the Key Laboratory for Mechanics in Fluid Solid Coupling Systems of the Chinese Academy of Sciences.
Corresponding Authors:  Corresponding author. E-mail: xiaoli.liu@tsinghua.edu.cn