Investigation into three-dimensional dry foam modelling using the boundary integral method

Understanding foam rheology relies on predictions of the foam structure and physical quantities associated with foam dynamics. In this work, we explore the modelling of dry foam dynamics using the boundary integral method, which can be used to predict the behaviour of dry foam in bulk or in confined geometries. The resultant equation for dry foam shows that the movement of foam films or lamellae is governed by the film curvature and the normal stress that the wall imposes on the fluid phase in bubbles and is characterized by three distinct motion modes: the background flow, the imposed flow due to the deformation of wall and the relaxation process of films. The singular integrals involved in the model are handled using a combined method of singularity subtraction and nonsingular contour integral. To demonstrate the validity of the method in potential applications, we consider two scenarios, for foam in bulk and in confined geometries, respectively. Dynamic foam motion is tracked using the model. The results show that the dry foam model has potentials applied in a variety of applications, such as foam flow in microfluidic devices and porous media.