Related papers: A general existence result for isothermal two-phas…
Theoretical models for the liquid-vapor and metal-nonmetal transitions of alkali fluids are investigated. Mean-field models are considered first but shown to be inadequate. An alternate approach is then studied in which each statistical…
In this paper we consider the evolution of two fluid phases in a porous medium. The fluids are separated from each other and also the wetting phase from air by interfaces which evolve in time. We reduce the problem to an abstract evolution…
This work reconsiders the Becker-Doering model for nucleation under isothermal conditions in the presence of phase transitions. Based on thermodynamic principles a modified model is derived where the condensation and evaporation rates may…
In the present study we investigate analytically the process of velocity and energy relaxation in two-phase flows. We begin our exposition by considering the so-called six equations two-phase model [Ishii1975, Rovarch2006]. This model…
The generalized hydrodynamics (GHD) equation is the equivalent of the Euler equations of hydrodynamics for integrable models. Systems of hyperbolic equations such as the Euler equations usually develop shocks and are plagued by problems of…
The fluid flow across an unbounded horizontal plate embedded with uniform mass diffusion is studied in this article together with the impacts of the chemical reaction and parabolic motion, while the temperature and concentration of the…
According to the dynamic van der Waals theory, we propose a thermodynamically consistent model for non-isothermal compressible two-phase flows with contact line motion. In this model, fluid temperature is treated as a primary variable,…
We show that the multi-dimensional compressible Euler system for isothermal flow of an ideal, polytropic gas admits global-in-time, radially symmetric solutions with unbounded amplitudes due to wave focusing. The examples are similarity…
In this paper, we consider the global existence and uniqueness of the classical solutions for the 3D viscous liquid-gas two-phase flow model. Initial data is only small in the energy-norm. Our main ideas come from [15] where the existence…
The Euler equation of an ideal (i.e. inviscid incompressible) fluid can be regarded, following V.Arnold, as the geodesic flow of the right-invariant $L^2$-metric on the group of volume-preserving diffeomorphisms of the flow domain. In this…
The importance of contact discontinuities in 2D isothermal flows has rarely been discussed, since most Riemann solvers are derived for 1D Euler equations. We present a new contact resolving approximate Riemann solver for the isothermal…
We formulate a well posed interface formulation for canonical one-dimensional evaporation two-phase model problems (the Stefan and Sucking problems) commonly used to validate production codes. We focus on the interface between the vapor and…
We consider particles in ${\Bbb R}^d, d \geq 2$, interacting via attractive pair and repulsive four-body potentials of the Kac type. Perturbing about mean field theory, valid when the interaction range becomes infinite, we prove rigorously…
In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…
In this work, we study the behaviour of saturation fronts for two phase flow through a long homogeneous porous column. In particular, the model includes hysteresis and dynamic effects in the capillary pressure and hysteresis in the…
We study information geometry of the thermodynamics of first and second order phase transitions, and beyond criticality, in magnetic and liquid systems. We establish a universal microscopic characterization of such phase transitions via the…
Due to the limited cell resolution in the representation of flow variables, a piecewise continuous initial reconstruction with discontinuous jump at a cell interface is usually used in modern computational fluid dynamics methods. Starting…
We introduce a new class of non-isothermal models describing the evolution of nematic liquid crystals and prove their consistency with the fundamental laws of classical Thermodynamics. The resulting system of equations captures all…
We show that H\"{o}lder continuous incompressible Euler flows that satisfy the local energy inequality ("globally dissipative" solutions) exhibit nonuniqueness and contain examples that strictly dissipate kinetic energy. The collection of…
We propose a model describing the liquid-vapour phase transition according to a phase-field approach. The model takes up a setting proposed by the second author, where a phase field is introduced whose equilibrium values 0 and 1 are…