Interfacial Tension

In this book, we will be concerned with the arrangement and displacement of multiple fluid phases in the pore space. The pore space could be the micron-sized interstices between grains in a rock or soil, the gaps between fibres in a tissue or blood vessels. The fluids could be water, oil, natural gas, carbon dioxide, blood plasma or electrolyte solution. Here we will present the basic equations before introducing the complex and fascinating geometry of the porous medium itself.

If we have two fluid phases, without a porous medium present, then the fluids arrange to minimize the surface area between them. For instance, a small droplet of water in air will be spherical, since this minimizes the area of contact with the air for a fixed volume, as shown in Fig. 1.1. For larger drops, the shape is perturbed by gravitational forces, which we ignore here for simplicity.

We define an interfacial tension, σ, which is the energy per unit area of the surface between the phases, or the change in free energy (in an open system with a defined pressure, this is the Gibbs free energy) for a change in area: σ = dF/dA. The two phases involved may be fluid or solid. It is the energy penalty of breaking the intermolecular interactions between the two phases and themselves only, and instead creating an interface between them; this energy is largest if one of the phases has strong intermolecular bonding with itself (such as a crystalline solid or metal) and lowest between two similar fluids (such as oil and a hydrocarbon gas at high pressure).

Note that sometimes, erroneously, the term surface tension is used: strictly this refers to the energy per unit area of a surface between a fluid or solid and its vapour in thermodynamic equilibrium, with no other components present. While surface tension is precisely defined, and is a useful concept for the discussion below, it is of little relevance in the majority of cases we will consider, where we have complex mixtures of many chemical components, at least two fluid phases and solid all present: in these cases the more general, and correct, expression interfacial tension should be used.