Deformation-driven flow in homogenized fluid-saturated porous periodic structures: Nonlinearity and dynamic effects

Abstract

: The paper deals with the homogenization-based modelling of periodic porous structures saturated by a Newtonian fluid and locally controlable due to embedded piezoelectric segments which can induce a peristaltic deformation of the microchannels, in response to prescribed propagating voltage waves. To respect dynamic effects of the flow in bulged pores, where the advection term of the acceleration is important, two time scales are considered and an appropriate time scaling of the fast-slow dynamics is introduced in a proportion to the spatial scaling. The two-scale homogenized problem is nonlinear by the consequence of the advection term in the flow model. Further nonlinearity is introduced by deformation-dependent homogenized coefficients of the macroscopic equations. For this, a linear expansions based on the sensitivity analysis of the homogenized coefficients with respect to the deformation induced by the macroscopic quantities is employed.