The geometric shape of flowing soap film channels

A flowing soap film channel is usually constructed using a pair of nylon wires, which are initially intact and pulled away from each other to create a soap film between them. When a soap film is present, these flexible wires are bent toward each other due to the action of the surface tension. This feature is used to measure the surface tension of flowing soap films [Sane et al., J. Fluid Mech. 841, R2 (2018)] by assuming that the variation of the channel width is not large enough to alter the flow. The current study investigates a more generalized case where the bending curvature is large enough to alter the flow. In soap films, the flow speed and the thickness are coupled, and therefore so do the surface tension and the bending curvature. We numerically solve for the geometric shape of the channel by using theoretical and empirical relations and find that the solution is biquadratic to the longitudinal coordinate.