2014/03/31 by Ilya Peshkov, Peshkov, Ilya, Evgeniy Romenski +1 · 5 citations
Chemical Engineering · Engineering · Mathematics · Physics and Astronomy · #Classical mechanics #Compressibility #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Generalized Newtonian fluid #Lattice Boltzmann Simulation Studies #Mathematics #Mechanics #Newtonian fluid #Non-Newtonian fluid #Physics #Rheology and Fluid Dynamics Studies #Shear rate #Shear stress #Shear thinning #Simple shear #Thermodynamics #Viscosity #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1403.8068
published in arXiv (Cornell University) (Cornell University) · 27 pages, 3 figures, 1 table
openalex publication_date 2014/03/31 · arxiv created 2014/11/27 · arxiv updated 2014/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We discuss a pure hyperbolic alternative to the Navier-Stokes equations, which are of parabolic type. As a result of the substitution of the concept of the viscosity coefficient by a microphysics-based temporal characteristic, particle settled life (PSL) time, it becomes possible to formulate a model for viscous fluids in a form of first order hyperbolic partial differential equations. Moreover, the concept of PSL time allows the use of the same model for flows of viscous fluids (Newtonian or non-Newtonian) as well as irreversible deformation of solids. In the theory presented, a continuum is interpreted as a system of material particles connected by bonds; the internal resistance to flow is interpreted as elastic stretching of the particle bonds; and a flow is a result of bond destructions and rearrangements of particles. Finally, we examine the model for simple shear flows, arbitrary incompressible and compressible flows of Newtonian fluids and demonstrate that Newton's viscous law can be obtained in the framework of the developed hyperbolic theory as a steady-state limit. A basic relation between the viscosity coefficient, PSL time, and the shear sound velocity is also obtained.