Influence of Wettability and Dynamic Fluid-Fluid Displacement in Micromodels

The radial displacement of a viscous fluid by a less viscous fluid in micromodel porous media leads to a beautiful array of flow patterns. Here, emerging patterns depend on the capillary number (Ca), viscosity contrast (M), pore structure, and wettability of the system. In the limit of low Ca, the invading pattern grows asymmetrically through either capillary fingering, cooperative pore filling, or corner flow mechanisms as the substrate wettability changes from strong drainage to strong imbibition. As Ca increases, and for M<1, the invading fluid becomes more radially symmetric and forms viscous fingers, whose widths increase as the substrate becomes more wetting to the invading fluid.

We model the immiscible fluid-fluid displacement in patterned microfluidic cells through a novel ``moving capacitor'' network model, which considers pore-scale instability events of Cieplak and Robbins and corner flow events. In our model, we approximate the flow geometry through a pore network where interfaces are treated as moving electric capacitors. The model reproduces the invading fluid patterns observed experimentally under a wide range of Ca and substrate wettabilities, which demonstrates its potential as a predictive pore-scale modeling tool for more complex pore geometries.