CONICET | Buscador de Institutos y Recursos Humanos

Soap films have drawn attention since ancient times. The study of their integrity is today relevant in several areas, like foams and bubbles stability, coating flows, spray formation processes, or micro-pore sensors. When a small orifice is produced in a freely standing liquid sheet, this hole could either close or expand, depending on its initial diameter. In this work we are interested in the latter case: pores that expand after its creation. After a certain transient period, low viscosity films quickly attain a constant retraction speed v0. From a balance of inertial and surface tension force, Taylor (1959) and Culick (1960) independently predicted a retraction speed v0 = vTC sqrt(2 sigma / rho h), sigma, rho and h being the surface tension, density and thickness of the liquid sheet, respectively. This prediction (today know as the Taylor-Culick velocity) is quite accurate as long as elastic effects of surfactants usually present in liquid sheets are weak. However, this is not always the case. In a series of recent experiments, Petit et al. (2015) found that the retraction speed of orifices produced in freely standing liquid films made of surfactant solutions decreases relative to vTC. Specifically, they found that v0=vTC = f(Ma), f being a decreasing function of the Marangoni number (Ma). In our work we modeled the pore retraction process by solving numerically the axisymmetric Navier-Stokes equations, along with the convection-diffusion equation, in order to calculate the flow field and the surfactant distribution simultaneously. Our results also show that v0=vTC decreases as Ma increases, tough not to the extent of the experimental results of Petit et al. (2015). The numerical results also reproduce other phenomena observed in experiments, as the so-called aureole that surrounds the expanding orifice, as well as allow to explain the diverse process that take place simultaneously and lead to the decrease of the retraction speed.

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