Effects of surfactants in the opening of holes in freely suspended liquid films. Numerical analysis

RODRÍGUEZ CACIK, EUGENIA SOFÍA; CAMPANA, DIEGO MARTÍN; LU, JIAKAI; CORVALÁN, CARLOS; UBAL, SEBASTIÁN

Cordoba

Congreso; II Brazil-Argentine Microfluidics Congress / V Congreso de Microfluídica Argentina; 2019

UNC

Soap films have drawn attention since ancient times. The study of their integrity is todayrelevant in several areas, like foams and bubbles stability, coating flows, spray formationprocesses, or micro-pore sensors. When a small orifice is produced in a freely standingliquid sheet, this hole could either close or expand, depending on its initial diameter. Inthis work we are interested in the latter case: pores that expand after its creation. Aftera certain transient period, low viscosity films quickly attain a constant retraction speedv0. From a balance of inertial and surface tension force, Taylor (1959) and Culick (1960)independently predicted a retraction speed v0 = vTC ≡p2σ/ρh, σ, ρ and h being the sur-face tension, density and thickness of the liquid sheet, respectively. This prediction (todayknow as the Taylor-Culick velocity) is quite accurate as long as elastic effects of surfac-tants usually present in liquid sheets are weak. However, this is not always the case. In aseries of recent experiments, Petit et al. (2015) found that the retraction speed of orificesproduced in freely standing liquid films made of surfactant solutions decreases relative tovTC. Specifically, they found that v0/vTC = f(M a), f being a decreasing function of theMarangoni number (M a). In our work we modeled the pore retraction process by solvingnumerically the axisymmetric Navier-Stokes equations, along with the convection-diffusionequation, in order to calculate the flow field and the surfactant distribution simultaneously.Our results also show that v0/vTC decreases as M a increases, tough not to the extent ofthe experimental results of Petit et al. (2015). The numerical results also reproduce otherphenomena observed in experiments, as the so-called aureole that surrounds the expandingorifice, as well as allow to explain the diverse process that take place simultaneously andlead to the decrease of the retraction speed.[1] Taylor, G. I. (1959). The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets. Pro-ceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 253(1274),313-321.[3] Culick, F. E. C. (1960). Comments on a ruptured soap film. Journal of Applied Physics, 31(6),1128-1129.[3] Petit, P. C., Le Merrer, M., & Biance, A. L. (2015). Holes and cracks in rigid foam films.Journal of Fluid Mechanics, 774.