Incorporating the influence of wettability into models of immiscible fluid displacement through a porous media

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Abstract
One approach of assessing the influence of capillary forces on immiscible fluid displacement through porous media is to perform an analysis of the fluid on a length scale consisting of several pores. In order to perform such an analysis, a model must first be identified. This consists of specifying: the geometric structure of the pores and their interconnections; the material properties of the two immiscible fluids, e.g., whether or not they are Newtonian, the values of their viscosities and their interfacial tensions, and whether or not surface‐active‐agents are present; and, the wettability of the system. The objective of this presentation is to indicate a procedure by which wettability can be incorporated into such an analysis. The procedure is well‐defined and straight forward, containing only experimentally measurable properties of the system despite the current lack of understanding of the physics by which one fluid displaces another fluid across the surface of a solid. In section 1 the current status of dynamic wettability is reviewed from the perspective of fluid mechanics. A well‐posed boundary‐value problem whose solution describes the dynamics of a meniscus containing a contact line is identified in section 2. An example is presented in section 3. A summary and conclusions appear in section 4.

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