Abstract:

The Enskog-Vlasov equation is an extension of the Boltzmann equation that accounts for large densities through the Enskog collision term, and for long-range particle interaction through the Vlasov term [1][2][3]. The equation describes states from compressed liquid to non-ideal, or ideal, gas vapor, including diffusive phase interfaces. Thus, it provides an excellent tool for modeling of processes with liquid-vapor interfaces and adjacent Knudsen layers, and allows us to look at slip, jump and evaporation coefficients from a different perspective.

A set of 26 moment equations is derived from the Enskog-Vlasov equation by means of the Grad moment method [4]. The equations provide a meaningful approximation to the underlying kinetic equation, and include the description of compressible liquid and non-ideal gas behavior as well as fully resolved liquid-vapor interfaces. Moreover, the equations include rarefaction effects such as Knudsen layers, transpiration flow, thermal stresses or heat transfer without temperature gradients. This presentation focuses on numerical results for simple flow problems (Couette flow, heat transfer, forced evaporation) that highlight the richness of the equations. Results are discussed with emphasis on the behavior at interfaces, where the equations resolve temperature jumps, velocity slip, and evaporation processes, which appear not as jumps, but as steep changes. Comparison with classical sharp interface models gives insight into values for jump, slip and evaporation coefficients.
Joint work with A. Frezzotti (Milano) and H. Jahandideh (Victoria)

References:

[1] L. de Sobrino, On the Kinetic Theory of a van der Waals Gas, Can. J. Phys. 45, pp. 363-385, 1967.
[2] M. Grmela, Kinetic Equation Approach to Phase Transitions, J. Stat. Phys. 3, pp. 347-364, 1971.
[3] A. Frezzotti, L. Gibelli, and S. Lorenzani, Mean field kinetic theory description of evaporation of a fluid into vacuum, Phys. Fluids 17, 012102, 2005.
[4] H. Struchtrup, A. Frezzotti, 26 Moment Equations for the Enskog-Vlasov Equation, in preparation (2021).