Nearly two decades ago, Couder (1981) and Gharib & Derango (1989) used soap films
to perform classical hydrodynamics experiments on two-dimensional flows. Recently
soap films have received renewed interest and experimental investigations published
in the past few years call for a proper analysis of soap film dynamics. In the present
paper, we derive the leading-order approximation for the dynamics of a flat soap film
under the sole assumption that the typical length scale of the flow parallel to the film
surface is large compared to the film thickness. The evolution equations governing
the leading-order film thickness, two-dimensional velocities (locally averaged across
the film thickness), average surfactant concentration in the interstitial liquid, and
surface surfactant concentration are given and compared to similar results from the
literature. Then we show that a sufficient condition for the film velocity distribution
to comply with the Navier–Stokes equations is that the typical flow velocity be
small compared to the Marangoni elastic wave velocity. In that case the thickness
variations are slaved to the velocity field in a very specific way that seems consistent
with recent experimental observations. When fluid velocities are of the order of the
elastic wave speed, we show that the dynamics are generally very specific to a soap
film except if the fluid viscosity and the surfactant solubility are neglected. In that
case, the compressible Euler equations are recovered and the soap film behaves like a
two-dimensional gas with an unusual ratio of specific heat capacities equal to unity.
The dynamics of a viscous soap film with soluble surfactant
