To derive the mass balance equation we start from the law of mass conservation. This will be further explained in the Mass Transport with Chemical Reaction section. The term denotes a mass production or consumption rate of chemical species, typically due to a chemical reaction. If the simulation medium is a solid then this term is zero, regardless of which formulation is made use of.Ĭontrary to the convective term, the diffusive term may be present if the medium is solid or fluidic.
In either case, this term is only present if mass transport occurs in a fluid medium with a fluid flow velocity. The difference between the conservative and the non-conservative form are explained in the section Mass Balance Equation Derivation. In the non-conservative formulation the convective term is. In the conservative formulation the convective term is. The second component is a convective term.
The details of variable diffusion coefficients will be discussed later in the section: Variable Mass Diffusion Coefficient. In some cases the diffusion coefficient may depend on other properties such as a temperature and the concentration itself making the equation nonlinear. First and foremost there is a diffusive term: with a diffusion coefficient, which is also known as the species diffusivity. The derivation in the section Mass Balance Equation Derivation will help explain why this is the case.īeside the time derivative part both PDEs are made up of several components. Typically, the non-conservative formulation is appropriate for incompressible fluids where the concentration field is expected to be smooth. The partial differential equation (PDE) model describes how chemical species are transported over time in a solid or fluid medium. The dependent variable in the mass balance equation is the species concentration, which varies with time and position.
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