On modelling the drying of porous materials: Analytical solutions to coupled partial differential equations governing heat and moisture transfer.
On quasi-stationary models of mixtures of compressible fluids
We consider mixtures of compressible viscous fluids consisting of two miscible species. In contrast to the theory of non-homogeneous incompressible fluids where one has only one velocity field, here we have two densities and two velocity fields assigned to each species of the fluid. We obtain global classical solutions for quasi-stationary Stokes-like system with interaction term.
On solutions of the Gołab-Schinzel equation.
On the attenuation of waves propagating in fluid mixtures.
On the effect of temperature and velocity relaxation in two-phase flow models
We study a two-phase pipe flow model with relaxation terms in the momentum and energy equations, driving the model towards dynamic and thermal equilibrium. These equilibrium states are characterized by the velocities and temperatures being equal in each phase. For each of these relaxation processes, we consider the limits of zero and infinite relaxation times. By expanding on previously established results, we derive a formulation of the mixture sound velocity for the thermally relaxed model. This...
On the effect of temperature and velocity relaxation in two-phase flow models
We study a two-phase pipe flow model with relaxation terms in the momentum and energy equations, driving the model towards dynamic and thermal equilibrium. These equilibrium states are characterized by the velocities and temperatures being equal in each phase. For each of these relaxation processes, we consider the limits of zero and infinite relaxation times. By expanding on previously established results, we derive a formulation of the mixture sound velocity for the thermally relaxed model. This...
On the extremals of a subsidiary capillary problem.
On the inequalities associated with a model of Graffi for the motion of a mixture of two viscous, incompressible fluids
We demonstrate a theorem of existence and uniqueness on a large scale of the solution of a system of differential disequations associated to a Graffi model relative to the motion of two incompressible viscous fluids.
On the one-dimensional Boltzmann equation for granular flows
We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions.
On the one-dimensional Boltzmann equation for granular flows
We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions.
On the Stefan problem: the variational approach and some applications
On unsteady two-phase fluid flow due to eccentric rotation of a disk.
One-dimensional kinetic models of granular flows
One-dimensional kinetic models of granular flows
We introduce and discuss a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. Then, the behavior of the Boltzmann equation in the quasi elastic limit is investigated for a wide range of the rate function. By this limit procedure we obtain a class of nonlinear equations classified as nonlinear friction equations. The analysis of the cooling process shows that the nonlinearity on the relative velocity is of paramount importance...
Peculiarities of density distribution of a coupled fluid in capillary porous media.
Properties of the Gibbs potential and the equilibrium of a liquid with its vapor
Quando è possibile formare bolle in un fluido, e quando no
Bubbles are formed in a fluid by inflating a liquid film with a gas in which the pressure is a strictly decreasing function of the specific volume, unbounded as . We show that, if grows as fast or faster than as , then there is at least one stable equilibrium configuration of any such bubble, no matter how much gas has been used to inflate it. On the other hand, if grows as slowly or slower than as , then any such bubble has no equilibrium configuration, when the amount of gas within...
Relaxation and numerical approximation of a two-fluid two-pressure diphasic model
This paper is concerned with the numerical approximation of the solutions of a two-fluid two-pressure model used in the modelling of two-phase flows. We present a relaxation strategy for easily dealing with both the nonlinearities associated with the pressure laws and the nonconservative terms that are inherently present in the set of convective equations and that couple the two phases. In particular, the proposed approximate Riemann solver is given by explicit formulas, preserves the natural...
Relaxation models of phase transition flows
In this work, we propose a general framework for the construction of pressure law for phase transition. These equations of state are particularly suitable for a use in a relaxation finite volume scheme. The approach is based on a constrained convex optimization problem on the mixture entropy. It is valid for both miscible and immiscible mixtures. We also propose a rough pressure law for modelling a super-critical fluid.
Relaxation schemes for the multicomponent Euler system
We show that it is possible to construct a class of entropic schemes for the multicomponent Euler system describing a gas or fluid homogeneous mixture at thermodynamic equilibrium by applying a relaxation technique. A first order Chapman–Enskog expansion shows that the relaxed system formally converges when the relaxation frequencies go to the infinity toward a multicomponent Navier–Stokes system with the classical Fick and Newton laws, with a thermal diffusion which can be assimilated to a Soret...