Flow of yield-stress fluids through porous media

O Tammisola

Royal Institute of Technology (KTH), Sweden

Abstract

This talk will present numerical and theoretical studies of flows of yield-stress materials through porous media. We will bring two new effects into the picture: how the resulting flow and pressure drop are affected by a) elasticity of the yield-stress material (an elastoviscoplastic fluid), and b) the fluids ``apparent” sliding nature (e.g. microgels) over the solid surfaces of the porous medium.

First, we compare non-sliding viscoplastic and elastoviscoplastic flows in the same model porous media. Elastic effects are found to increase the pressure drop and also the size of unyielded regions in the flow, which is the consequence of different stress solutions compare to viscoplastic flows. Yet, the velocity fields and pressure drops in the viscoplastic and elastoviscoplastic flows are comparable for small elastic effects at moderate Bingham numbers. When the elastic effects increase, the elastoviscoplastic flow becomes time-dependent and oscillations in the flow can be observed.

Yield-stress fluids are known to slip over solid surfaces if the tangential stress exceeds the ``sliding yield stress”. The sliding may occur due to various microscopic phenomena and leads to a stick-slip law at the wall complicating the modelling. Here, viscoplastic flows through model and randomized porous media are simulated. The randomized configuration is chosen to capture a more sophisticated aspect of the yield-stress fluid flow in porous media at the yield limit: channelization. A simple model that is able to find the first open channel at the yield limit in a no-slip porous media will be presented.

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