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Abstract: We will discuss a recent result joint with In-Jee Jeong and Theo Drivas. We prove that twisting in Hamiltonian flows on annular domains, which can be quantified by the differential winding of particles around the center of the domain, is stable to general perturbations. In fact, we prove the all-time stability of the lifted dynamics in an L2 sense (though single particle paths are generically unstable). These stability facts are used to establish several results related to the long-time behavior of inviscid fluid flows.

Abstract: The Enskog-Vlasov equation extends the Enskog equation for the dense hard sphere fluid by accounting for the attractive forces between, and the finite volume of, the gas particles. Hence, it gives a van-der-Waals-like description of a non-ideal gas, including liquid-vapor phase change. Specifically, the equation describes the liquid phase, the vapor phase, and a diffusive transition region connecting both phases. Solutions of the Enskog-Vlasov equation exhibit all relevant phenomena occurring in the evaporation and condensation of rarefied or dense vapors.

Using Grad’s moment method we derived macroscopic transport equations—moment equations with 13 and 26 variables—from the Enskog-Vlasov equation, which describe liquid vapor and transition region in terms of a few macroscopic properties.

Focussing on 1-D heat and mass transfer problems, we compare moment solutions to DSMC solutions for transport across the interface, and the interplay between interface and Knudsen layers. Interface resistivities for jump interface conditions are determined from the simulations, which show marked differences to those found from classical kinetic theory, where dimensionless resistivities are constants. In contrast, the EV models give temperature dependent resistivities, some negative off-diagonal resistivities, and indicate non-linear behavior where resistivities depend on mass and heat fluxes through the interface.