Generalized Navier Boundary Condition and Geometric Conservation Law for surface tension

We consider two-fluid flow problems in an Arbitrary Lagrangian Eulerian (ALE) framework. The purpose of this work is twofold. First, we address the problem of the moving contact line, namely the line common to the two fluids and the wall. Second, we perform a stability analysis in the energy norm for various numerical schemes, taking into account the gravity and surface tension effects. The problem of the moving contact line is treated with the so-called Generalized Navier Boundary Conditions. Owing to these boundary conditions, it is possible to circumvent the incompatibility between the classical no-slip boundary condition and the fact that the contact line of the interface on the wall is actually moving. The energy stability analysis is based in particular on an extension of the Geometry Conservation Law (GCL) concept to the case of moving surfaces. This extension is useful to study the contribution of the surface tension. The theoretical and computational results presented in this paper allow us to propose a strategy which offers a good compromise between efficiency, stability and artificial diffusion

Some qualitative properties of the solutions of the Magnetohydrodynamic equations for nonlinear bipolar fluids

In this article we study the long-time behaviour of a system of nonlinear Partial Differential Equations (PDEs) modelling the motion of incompressible, isothermal and conducting modified bipolar fluids in presence of magnetic field. We mainly prove the existence of a global attractor denoted by \A for the nonlinear semigroup associated to the aforementioned systems of nonlinear PDEs. We also show that this nonlinear semigroup is uniformly differentiable on \A. This fact enables us to go further and prove that the attractor \A is of finite-dimensional and we give an explicit bounds for its Hausdorff and fractal dimensions.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s10440-014-9964-

A mathematical model for unsteady mixed flows in closed water pipes

We present the formal derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipe. In the case of free surface incompressible flows, the \FS-model is formally obtained, using formal asymptotic analysis, which is an extension to more classical shallow water models. In the same way, when the pipe is full, we propose the \Pres-model, which describes the evolution of a compressible inviscid flow, close to gas dynamics equations in a nozzle. In order to cope the transition between a free surface state and a pressured (i.e. compressible) state, we propose a mixed model, the \PFS-model, taking into account changes of section and slope variation

Weak and strong solutions of equations of compressible magnetohydrodynamics

International audienceThis article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions. Then, existence of strong solutions in the neighbourhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted : the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques

Gating of aquaporins by heavy metals in Allium cepa L. epidermal cells

Changes in the water permeability, aquaporin (AQP) activity, of leaf cells were investigated in response to different heavy metals (Zn2+, Pb2+, Cd2+, Hg2+). The cell pressure probe experiments were performed on onion epidermal cells as a model system. Heavy metal solutions at different concentrations (0.05 μM–2 mM) were used in our experiments. We showed that the investigated metal ions can be arranged in order of decreasing toxicity (expressed as a decrease in water permeability) as follows: Hg>Cd>Pb>Zn. Our results showed that β-mercaptoethanol treatment (10 mM solution) partially reverses the effect of AQP gating. The magnitude of this reverse differed depending on the metal and its concentration. The time course studies of the process showed that the gating of AQPs occurred within the first 10 min after the application of a metal. We also showed that after 20–40 min from the onset of metal treatment, the water flow through AQPs stabilized and remained constant. We observed that irrespective of the metal applied, the effect of AQP gating can be recorded within the first 10 min after the administration of metal ions. More generally, our results indicate that the toxic effects of investigated metal ions on the cellular level may involve AQP gating