Classical Physics

Homogeneous Mixture Flow Field and Separated Flow Fields Dynamic Equations

Authors: Shisheng Wang
Comments: 18 Pages.

A multicomponent, multiphase fluid can be modelled as either a homogeneous mixture flow field or separated flow fields. The key concept is that fluid flows will be considered as continuum fields through suitable volumetric "average" procedures, so that the differential calculus tools can be used. For a homogeneous mixture flow field, the mixture is treated as a single system (single-phase flow). Starting from the mixture momentum density 1-form per unit volume, taking the exterior derivative of this 1-form yields a field strength tensor in a differential 2-form. The interior product (contraction) of this 2-form with the tangent velocity yields the dynamic equation of the homogeneous mixture flow, E u20d7+Ω u20d7×V u20d7=0 (or expressed as a differential 1-form of eq. (20)). It is equivalent to the Euler-Lagrange equation, but the gradient of kinetic energy doesn’t equal zero for continuum fields, in contrast to the classical Euler-Lagrange equation for a discrete isolated particle. For separated flow fields, different components travel at their own velocities; there exists a velocity difference between components, and each component is treated as an individual system to consider the interactions between different components. The homogeneous mixture dynamic equation turns into two equations for separated flow fields. The two equations become tightly entangled. This shows there are very complicated interaction forces between the two flows.
Category: Classical Physics