The Lewis number under supercritical conditions

Abstract

An effective Lewis number is calculated for situations where temperature and mass fraction gradients are very large by defining effective thermal and mass diffusivities; such situations may occur in systems where there is more than one chemical component, and in particular under supercritical conditions. The definitions evolve from a model assuming that derivatives of certain functions are small with respect to those of the dependent variables. In the model, Soret and Dufour effects are included and Shvab–Zeldovich-like variables are defined to remove the coupling between the operators of the differential equations for temperature and mass fractions. Results from calculations using binary systems of chemical components, using both isolated fluid drops and interacting fluid drops, show that under supercritical conditions, depending upon the compounds, the effective Lewis number can be 2–40 times larger than the traditionally calculated Lewis number and that the spatial variation of the two numbers is different. For the values of the thermal diffusion factor used in the calculations, the Soret and Dufour effects are negligible; the discrepancy between the traditional and effective Lewis numbers is due to the combined effect of the small mass diffusion factor and the difference between the specific enthalpies of the two compounds. Parametric variations show that the effective Lewis number increases with increasing pressure and decreasing surrounding gas temperature. Closer drop proximity in clusters results in sharper peaks in the effective Lewis number due to the increased gradients of the dependent variables.