Modelling foam flow through confined geometries

Despite their apparent simplicity, multiphase fluids such as liquid-foam exhibit a very rich dynamics, which is often difficult to predict, much more so than would be the case for single-phase fluids. The physics of liquid foams can be hard to capture mathematically, even in static and equilibrium systems. As external forces are applied on the foam structure, driving the system into motion, the amount of required information to characterize the system also increases, depending on factors such as the number of individual bubbles, and the geometry of the system’s container. This work takes a step forward into expanding the understanding of the nature of liquid-foam, where its physics, methods and techniques used to model its dynamics, and possible applications are reviewed. Two related models for modelling macroscale and bubble-scale liquid-foam dynamics, respectively, are further analysed. The first of these is the pressure-driven growth model, which aims to capture the location over time of a two-dimensional foam front propagating through a porous medium, in the context of foam improved oil recovery, particularly in the surfactant alternating gas process. It is shown that this model admits solutions containing sharp corners or kinks, in which a foam front reorients over a length scale small compared with the distance over which the front has propagated. The second of these is the viscous froth model, which is used to model bubble-scale foam flow of a layer of bubbles in a channel between closely spaced parallel flat plates, and hence is a two-dimensional foam model. It is shown that this model admits topological transformations in which sets of bubbles flowing in a channel exchange neighbours as the flow velocity increases.Despite their apparent simplicity, multiphase fluids such as liquid-foam exhibit a very rich dynamics, which is often difficult to predict, much more so than would be the case for single-phase fluids. The physics of liquid foams can be hard to capture mathematically, even in static and equilibrium systems. As external forces are applied on the foam structure, driving the system into motion, the amount of required information to characterize the system also increases, depending on factors such as the number of individual bubbles, and the geometry of the system’s container. This work takes a step forward into expanding the understanding of the nature of liquid-foam, where its physics, methods and techniques used to model its dynamics, and possible applications are reviewed. Two related models for modelling macroscale and bubble-scale liquid-foam dynamics, respectively, are further analysed. The first of these is the pressure-driven growth model, which aims to capture the location over time of a two-dimensional foam front propagating through a porous medium, in the context of foam improved oil recovery, particularly in the surfactant alternating gas process. It is shown that this model admits solutions containing sharp corners or kinks, in which a foam front reorients over a length scale small compared with the distance over which the front has propagated. The second of these is the viscous froth model, which is used to model bubble-scale foam flow of a layer of bubbles in a channel between closely spaced parallel flat plates, and hence is a two-dimensional foam model. It is shown that this model admits topological transformations in which sets of bubbles flowing in a channel exchange neighbours as the flow velocity increases