Macroscale balance relations for bulk, interfacial and common line systems in multiphase flows through porous media on the basis of molecular considerations

A new molecular-based approach is employed to derive balance relations for multiphase flow through porous media. Criteria are prescribed which identify, instant by instant, precisely which molecules are considered to reside in each bulk, interfacial, and contact line phase. Continuum balance relations for mass, momentum and energy are established for each of these phases (which consist of ever-changing molecular populations) at the scale of representative elementary volumes (REVs). All fields in these balance relations are related to space–time averages of molecular quantities, and complete account is taken of molecular transport within and between phases. This is a one-step procedure, as opposed to the two-step approach commonly used in averaging (first going from molecular scale to an intermediate scale, at which common lines, interfaces and pore geometry are manifest, and thence to a macro/REV-scale). In this way consideration of `excessʹ quantities is avoided. Simplifications and constitutive considerations are discussed.