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We theoretically investigate the deformation of a perfect dielectric drop suspended in a second dielectric liquid subject to a uniform electric field. Axisymmetric equilibrium shapes are found by solving simultaneously the Young–Laplace equation at the interface and Laplace equation for the electric field. Analytical solutions are constructed for the governing nonlinear boundary-value problem using domain perturbation method together with a special type of Hermite–Pade approximation. The results show the existence of a critical electric capillary number beyond which no axisymmetric figure is possible.

In this work, we perform preliminary group classification of equations governing the flow of a thermo-dependent fluid in a porous medium. The detailed model is a coupled system of nonlinear partial differential equations containing two arbitrary functions. The principal Lie algebra admitted by the coupled system is given. The study also demonstrates that the forms of arbitrary functions provide an extension of this algebra via an optimal system of one-dimensional Lie subalgebras.

This paper investigates axisymmetric shapes of a ferrofluid drop immersed in a uniform magnetic field. Approximate solutions are constructed for the governing nonlinear boundary value problem using the domain perturbation method. Bifurcation and turning points are located by applying a special type of Hermite–Pade approximation.

We study the homogenization of a slow viscous two-phase incompressible flow in a domain consisting of a free fluid domain, a porous medium, and the interface between them. We take into account the capillary forces on the fluid-fluid interfaces. We construct boundary layers describing the flow at the interface between the free fluid and the porous medium. We derive a macroscopic model with a viscous two-phase fluid in the free domain, a coupled Darcy law connecting two-phase velocities in the porous medium, and boundary conditions at the permeable interface between the free fluid domain and the porous medium.

This paper deals with the homogenization of a composite material built with an elastic matrix periodically reinforced by elastic notched fibres. We assume that the Lame constants in the fibres are highly contrasted with respect to those of the matrix. We derive a class of energy functionals involving additional degrees of freedom implying nonlocal description of localized geometrical discontinuities due to the fibre-notches, nonlocal effects associated with thin boundary layer phenomena, and nonlocal terms including macroscopic fields of extension or flexion.

This paper investigates axisymmetric shapes of an incompressible inviscid fluid bubble in a uniform flow. Approximate solutions are constructed for the governing nonlinear boundary value problem using the domain perturbation method. Bifurcation and turning points are located by applying a special type of Hermite-Pade approximation.

International audience; The aim of this work is to apply the homotopy perturbation method for solving the steady state equations of the exothermic decomposition of a combustible material obeying Arrhenius, Bimolecular, and Sensitised laws of reaction rates. These equations are formulated on some Class A geometries (an infinite cylinder, an infinite slab, and a sphere). We also investigate the effect of Frank-Kamenetskii parameter on bifurcation and thermal criticality by means of the Domb-Sykes graphical method.