Combining a level-set method and a stabilized P1/P1 formulation for coupling transient Stokes-Darcy flows: application to particle deposition growth in suspension filtration
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Forming particle beds through suspension filtration is widely used method in the manufacturing processes of various industrial applications, such as for food, pharmaceutical or composite materials. Basically, particles carried in controlled flow first deposit on a filtrating membrane, and then keep on depositing afterwards on the so-called porous filter cake growing under the continuous deposition. Controlling this growth is of the utmost importance since it will yield the final particle cake geometry. From a modelling point of view, one has to describe a Stokes-Darcy flow, with two porous domains involved for the Darcy’s ruled region: the first one being static (membrane), and the second one changing in time (growing cake) as a function of the mass balance of suspension flowing across the cake moving boundary. In this work, we are interested in modelling the whole phenomena, using a coupled monolithic Stokes-Darcy approach with a special attention on the controlled moving boundary.
