“Fast” and “slow” pressure waves electrically induced by nonlinear coupling in Biot-type porous medium saturated by a nematic liquid crystal

In this paper, it is proposed a model for deformable porous media saturated by compressible nematic liquid crystal subjected to slowly varying electric fields. from a mechanical point of view, we assume that such a system can be described by means of a Biot-type model and that the mechanical action of the NLC on the solid matrix can be modeled by means of a suitable modification of Biot constitutive equations for pore pressure only. The nonlinear nature of NLCs and the presence of bifurcations make the analysis particularly challenging. We prove that suitable electrical stimulus applied on the NLC specimen may induce both type of Biot waves, fast and slow, along with shear waves in the porous matrix. This effect may be of use when one may wish to damp mechanically induced pressure waves using Darcy dissipation.