Exterior foam drainage and flow regime switch in the foams

Abstract

The three-dimensional flow in exterior microscale foams including the Plateau borders and nodes are investigated by solving Navier-stoke and continuity equations. First, we show the effect of the interfacial mobility and film thickness on the dimensionless mean velocity of the exterior foams. The velocity of the exterior node-PB is similar to the velocity of single exterior Plateau border. Next, we calculated the pressure difference of each element separately and obtained their hydraulic resistances. We found out that the hydraulic resistance of the exterior Plateau border is always larger than the hydraulic resistance of the exterior node, resulting in a consistent channel-dominated regime. However, For the interior foams, there is a value of interfacial mobility where the node's resistance overcomes the channel's resistance, resulting in a switch from the channel-dominated regime to a node-dominated regime. This switching point is dependent on the relative length of the channels. Hence, we obtained an approximation of the interfacial mobility switching points versus the relative length of channels. Moreover, in a form of approximation master curve, we showed the dependence of mean velocities of foams and channels' hydraulic resistances to a dimensionless combined parameter of Λ^-1 that contains interfacial mobility and film thickness together. For both the exterior and interior nodes, the velocity and hydraulic resistance are almost constant for various Boussinesq numbers since interfacial mobility has a marginal effect on node's flow.

Keywords: Bubble; Exterior Plateau border; Exterior node; Foam; Hydraulic resistance; Interior Plateau border; Interior node.