Abstract
The flow of fluids with pressure-dependent viscosity in free-space and in porous media is considered in this study. The interest is to employ the physical model of flow through a porous layer down an inclined plane in order to derive velocity expressions that can be used as entry conditions in the study of two-dimensional flows through free-space and through porous channels. The generalized equations of Darcy, Forchheimer and Brinkman are used in this work. Â
Highlights
The realization that viscosity of a fluid depends on pressure can be traced back to the nineteenth century and works of Stokes, [1] and Barus, [2], [3]
Flow between parallel plates and flow in pipes and two-dimensional channels, and flow over circles provide us with the necessary benchmarks to better understand the full three-dimensional flow
These situations provide us in part with motivations for this work in which we derive and document expressions for the entry conditions into two-dimensional channels when the flow is that of a pressure-dependent viscosity, and the channel is either free-space or filled with a porous material
Summary
The realization that viscosity of a fluid depends on pressure can be traced back to the nineteenth century and works of Stokes, [1] and Barus, [2], [3]. The past quarter of a century, has witnessed an increasing interest in this type of flow through porous media This stems from the many applications in enhanced oil recovery and carbon sequestration, [11], [12], in filtration problems, [13], and in the pharmaceutical industry [14]. Uniform flow assumptions might no longer be valid as entry conditions to a porous channel bounded by solid walls, and the popular parabolic entry profiles of the Navier-Stokes equations are approximations at best in flow of fluids with pressure-dependent viscosities through porous channels These situations provide us in part with motivations for this work in which we derive and document expressions for the entry conditions into two-dimensional channels when the flow is that of a pressure-dependent viscosity, and the channel is either free-space (as in the case of Navier-Stokes flow) or filled with a porous material. We provide concluding remarks and plans for future work
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