Role of differential entropy inequality in chemically reacting flows

To our knowledge, today the differential entropy inequality appears to be always ignored in simulating chemically reacting flows. In addition to satisfying the differential mass, momentum, and energy balances, simulations of chemically/biochemically reacting systems must satisfy the entropy inequality (the second law of thermodynamics). Common types of material behavior (Newton's law of viscosity, Fourier's law, Fick's first law) satisfy the differential entropy inequality automatically, but common empirical descriptions of chemical/biochemical reactions do not. The issue is illustrated with three examples including a laminar methane flame for which data are available from the literature.

► Differential entropy inequality has same importance level as mass, momentum and energy balances.
► Differential entropy inequality must be imposed in any chemically reacting flow simulation.
► There is no theoretical justification for using a temperature limiter in reacting flow simulation.