Abstract
In this study we explore the one-dimensional drainage of a power-law fluid into a deformable porous material. Initially, the fluid is imbibed into the dry undeformed material due to capillary suction which in turn deforms the porous material and forms liquid and solid interfaces. Mixture theory is employed to study the movement of the liquid and solid phases. The zero-gravity model contains the similarity solution that is solved numerically. The stress gradient within the deformable porous material is induced from a pressure gradient that produces an evolving solid fraction and hence deformation. In the absence of gravity effects, the deformation of the solid seems in the same direction of imbibition. This is because of attraction of gravity. Note that these liquid and solid dynamics depend on both the power-law indexes n and μ. We performed the experiments to measure the drainage and deformations of deformable porous materials for two samples of silicon oil (polydimethylsiloxane) in a polyurethane foam. Our experiments show that the silicon with high viscosity drains slower than silicon oil with low viscosity. The theoretical and experimental results show the same qualitative trend.
Highlights
In this study we develop a model for the drainage of a power law liquid into deformable porous materials
In this present work we have presented a basic model for predicting the drainage of a power law liquid into a deformable porous material
We transform the capillary rise theory developed for power law liquids into deformable porous materials [24] to the drainage setting by specifying liquid height [25] via an equation based on conservation of liquid argument
Summary
In this study we develop a model for the drainage of a power law liquid into deformable porous materials. Enough, most of the fluids involved in these processes are not Newtonian in nature and should be incorporated in the complex dynamics of deformation To accommodate this need, we present a coupled model for deformation of porous material and drainage of power law fluids. The non-Newtonian modeling along with the mixture theory was studied by Siddique and Anderson [25] They studied the capillary rise of a power law fluid into a deformable porous material, where they assumed imbibition occurring from an infinite bath of power law fluid. This study mimics only one particular aspect of capillary rise; the need is to extend the current power law model along with mixture theory to explore many other physical settings. We hope that our preliminary efforts in this regard may lead to further investigate the additional features of flows in complex porous media
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