Foam flowing vertically upwards in pipes through expansions and contractions

The drift-flux analysis of one-dimensional two-phase flow of Wallis (Wallis, G.B., 1969. One-dimensional two-phase flow. McGraw-Hill Book Company, New York.) is utilised for the first time to model the behaviour of pneumatic foam flowing vertically through an expansion or an contraction. It is demonstrated that, although a sudden contraction of flow area decreases the liquid fraction, it does not affect the volumetric liquid over-flow rate. It is also demonstrated that a sudden expansion of flow area decreases both the liquid fraction and the volumetric liquid over-flow rate. The liquid fraction of a foam stabilised by 2.92 g/L sodium dodecyl sulphate (SDS) solution flowing through a sudden contraction or expansion was measured by an improved pressure gradient method. The results were found to be consistent with the theoretical analysis. This study has implications for foam fractionation device design, optimisation and process intensification.