Nicoletta Ianiro

Stationary nonequilibrium solutions of model Boltzmann equation

We give an explicit solution of a model Boltzmann kinetic equation describing a gas between two walls maintained at different temperatures. In the model, which is essentially one-dimensional, there is a probability for collisions to reverse the velocities of particles traveling in opposite directions. Particle number and speeds (but not momentum) are collision invariants. The solution, which depends on the stochastic collision kernels at the walls, has a linear density profile and the energy flux satisfies Fouriers law.

Phase coexistence in consolidating porous media

The appearance of the fluid-rich phase in saturated porous media under the effect of an external pressure is investigated. For this purpose we introduce a two field second gradient model allowing the complete description of the phenomenon. We study the coexistence profile between poor and rich fluid phases and we show that for a suitable choice of the parameters nonmonotonic interfaces show up at coexistence.

Effects of the Centrifugal Forces on a Gas Between Rotating Cylinders

The gas e ow between two concentric rotating cylinders is investigated over a wide range of governing dimensionless products. Analytic solutions are given for the free molecular e ow, for the Bhatnagar ‐Gross‐Krook model up to the e rst-order approximation, and for the hydrodynamic limit in the Chapman ‐Enskog expansion. The slip e ow boundary conditionsareextensively discussed, and a constructivesolution to the transitional e ow is proposed. Numerical direct simulation data are obtained and adopted as exact reference experimental results.

Allen-Cahn and Cahn-Hilliard-like equations for dissipative dynamics of saturated porous media

Abstract We consider a saturated porous medium in the solid–fluid segregation regime under the effect of an external pressure applied on the solid constituent. We prove that, depending on the dissipation mechanism, the dynamics is described either by a Cahn–Hilliard or by an Allen–Cahn-like equation. More precisely, when the dissipation is modeled via the Darcy law we find that, provided the solid deformation and the fluid density variations are small, the evolution equation is very similar to the Cahn–Hilliard one. On the other hand, when only the Stokes dissipation term is considered, we find that the evolution is governed by an Allen–Cahn-like equation. We use this theory to describe the formation of interfaces inside porous media. We consider a recently developed model proposed to study the solid–liquid segregation in consolidation and we give a complete description of the formation of an interface between the fluid-rich and the fluid-poor phase.

Kink localization under asymmetric double-well potentials.

We study diffuse phase interfaces under asymmetric double-well potential energies with degenerate minima and demonstrate that the limiting sharp profile, for small interface energy cost, on a finite space interval is in general not symmetric and its position depends exclusively on the second derivatives of the potential energy at the two minima (phases). We discuss an application of the general result to porous media in the regime of solid-fluid segregation under an applied pressure and describe the interface between a fluid-rich and a fluid-poor phase.

Phase transition in saturated porous media: Pore-fluid segregation in consolidation

Abstract Consider the consolidation process typical of soils; this phenomenon is expected not to exhibit a unique state of equilibrium, depending on external loading and constitutive parameters. Beyond the standard solution also, pore-fluid segregation can arise. Pore-fluid segregation has been recognized as a phenomenon typical of the short time behavior of a saturated porous slab or a saturated porous sphere, during consolidation. In both circumstances, the Biot three-dimensional model provides time increasing values of the water pressure (and fluid mass density) at the center of the slab (or of the sphere), at early times, if the Lame constant μ of the skeleton is different from zero. This localized pore-fluid segregation is known in the literature as the Mandel–Cryer effect. In this paper, a nonlinear poromechanical model is formulated. The model is able to describe the occurrence of two states of equilibrium and the switching from one to the other by considering a kind of phase transition. Extending the classical Biot theory, a more than quadratic strain energy potential is postulated, depending on the strain of the porous material and the variation of the fluid mass density (measured with respect to the skeleton reference volume). When the consolidating pressure is strong enough, the existence of two distinct minima is proven.

A model for the compressible flow through a porous medium

A model for a continuum gas flowing through a porous matrix is proposed where the gas kinetics is governed by the Boltzmann equation and the solid phase by the energy equation. In the Boltzmann equation the integral relative to the gas–solid collisions is evaluated as for the collisions of hard spheres molecules against much heavier and longer straight particles (Lebowitz model of a sticks gas), randomly distributed in space according to a Maxwellian function with zero mean velocity. The mean flow is one-dimensional but the molecules are free to move in all three space dimensions. In the continuum limit, the moments of the Boltzmann equation provide the mass continuity, energy and momentum equations, the last one expressing the Darcy law for a compressible gas. The transport coefficients are analytically evaluated and a few examples are dealt with.

Kinetic models for a gas filled porous matrix. WAVE PROPAGATION

The propagation of small perturbation in a gas filled porous matrix is investigated. The skeleton is supposed rigid and governed by the energy balance equation, where the heat exchanged between the two phases is taken into account. The Boltzmann equation is written for the gas where the integrals of the collisions between gas and solid particles are evaluated as those for the particles of a mixture. Different choices of the time and space scales lead to models equations which hold for different rarefaction regimes. The wave propagation characteristics are then dealt with in various situations.

HYDRODYNAMICS OF A MODEL GAS IN A SLAB

The stationary Boltzmann equation is considered for the Lebowitz model gas of sticks in a slab in the presence of a nonconstant external field. It is proved that the solution is close in L∞ norm to a local “Maxwellian” distribution, the “parameters” of which satisfy the equations of hydrodynamics.

Compacton formation under Allen–Cahn dynamics

We study the solutions of a generalized Allen–Cahn equation deduced from a Landau energy functional, endowed with a non–constant higher order stiffness. We analytically solve the stationary problem and deduce the existence of so-called compactons, namely, connections on a finite interval between the two phases. The dynamics problem is numerically solved and compacton formation is described.