The Brinkman model is a unified law governing the flow of a viscous fluid in cavity (Stokes equations) and in porous media (Darcy equations). In this work, we explore a novel mixed formulation of the Brinkman problem. Introducing the flow’s vorticity as additional unknown, this formulation allows for a uniformly stable and conforming discretization by standard finite elements (Nédélec, Raviart-...

The Brinkman model is a unified law governing the flow of a viscous fluid in cavity (Stokes equations) and in porous media (Darcy equations). In this work, we explore a novel mixed formulation of the Brinkman problem by introducing the flow’s vorticity as an additional unknown. This formulation allows for a uniformly stable and conforming discretization by standard finite element (Nédélec, Ravi...

Number of Papers published in peer-reviewed journals: Number of Papers published in non peer-reviewed journals: Final Report: Computational Study of Colloidal Droplet Interactions with Three Dimensional Structures Report Title The colloidal droplet spreading on and sorption into a porous medium is important to 3D printing technology. In this study, we conducted numerical simulation to investiga...

The electrohydrodynamic plane Couette–Poiseuille flow instability of two superposed conducting and dielectric viscous incompressible fluids confined between rigid horizontal planes under the action a normal electric field pressure gradient through Brinkman porous medium has been analytically investigated. lower is stationary, while upper one moving with constant velocity. details base state mat...

This study examined the relationship between stresses and couple within context of stress fluid theory. The application effective medium approach, based on Brinkman equation, is also discussed under effect slip spin surface solid sphere immersed in porous fluid. motion generated by moving a at constant speed. Using Stokesian assumptions, equation ignores nonlinear terms. conditions for fluids h...

The pressure drop in microchannels filled with porous media formed by square arrays of cylinders (micro-porous channels) is investigated. Combining the Brinkman equation and the existing models for permeability of regular arrays of cylinders, the pressure drop in the considered micro-porous channels is calculated theoretically. Soft lithography method is used to fabricate several Polydimethylsi...

The method of matched asymptotic expansions is used to investigate the problem thermophoresis migration an aerosol spherical particle immersed in a porous medium saturated by viscous fluid at small non-zero Péclet number Pe. A uniform temperature gradient imposed on system parallel diameter opposite direction z axis. It assumed that Knudsen range slip flow through pores and compatible with assu...

A semi-analytical study is presented for the thermophoretic migration of a spherical particle located at an arbitrary position in porous medium inside cavity. uniformly applied temperature gradient parallel to line connecting and cavity centers. The modeled as Brinkman fluid with characteristic Darcy permeability K that can be obtained directly from experimental data. assumed homogenous isotrop...

We present a well-posed model for the Stokes/Brinkman problem with a family of jump embedded boundary conditions (J.E.B.C.) on an immersed interface with weak regularity assumptions. It is issued from a general framework recently proposed for fictitious domain problems. Our model is based on algebraic transmission conditions combining the stress and velocity jumps on the interface S separating ...