A viscous–inertial model of foam drainage

The common factor that links various current methods of estimating drainage rate through a gas–liquid foam is that all losses of pressure due to flow are assumed to be entirely viscous. However, by drawing analogy with liquid flow through a packed bed, it is apparent that, for foams that are relatively wet or have relatively high Galileo number, there is a significant inertial loss. This is further demonstrated by determining, using computational fluid dynamics, the pressure losses at a constant expansion with fluid flow boundaries. A foam drainage equation that accounts for inertial pressure losses is proposed by adapting the functional form of the Ergun equation for pressure loss due to flow in a packed bed. This is tested against forced drainage data for foam stabilised by SDS with a mono-dispersed bubble size distribution from the literature. It is shown that the model accurately predicts the results with the use of only one adjustable constant, which is, in fact, the number of inertial velocity heads lost due to flow through a slice of foam of one bubble radius in thickness.