CONICET | Buscador de Institutos y Recursos Humanos

Small pores formed on fluid sheets can contract, eventually closing the hole through the sheet, or can expand producing its rupture. This behavior has deep implications for important technological and industrial applications. For example, small particles can produce holes on the lamella of foams and to understand its dynamics is important to study the stability of several processes (separation operations, cleaning of industrial waste, etc.). Another example are fluid sheets expulsed from nozzles of atomizer devices, where the purpose is the breakup of the sheet in drops of controlled size [1]. Recent applications include the fabrication of precise biosensors for DNA sequencing [2].Pores are known to retract (open) with constant terminal speed $v_c = (2 sigma /( ho H))^{1/2}$, where $sigma$ is the surface tension, $ ho$ the fluid density and $H$ the unperturbed sheet thickness. This terminal speed was first deduced theoretically for the retraction of inviscid fluid sheets by Taylor [3], and more recently for the retraction of viscous fluid sheets by Savva and Bush [4] and Lu and coworkers [5]. Recently, Petit and coworkers [6] measured important deviations from $v_c$ on opening pores created on sheets of surfactants solutions. They also observed that, instead of the classical ring, surfactant laden pores expand forming an emph{aureole} where -apparently- strong accumulation of surfactant is produced.The aim of this work is to study the opening process of small pores in the presence of insoluble surfactants to uncover the mechanisms by which surfactants change the pore dynamics. For this purpose, we use the finite element method to solve the 3D axisymmetric Navier-Stokes equations on a moving mesh (Arbitrary Lagrangian Eulerian formulation), along with a front tracking interface technique to simultaneously compute the shape of the opening pore. The interfacial mass balance on the free surface is also solved to characterize the surfactant distribution and the resulting dynamic surface tension. Results show that the retraction of the pore and the convective fluid transport produce an important accumulation of surfactant on the retracting front (lobe) of the expanding pore. Thus, the equation of state used to relate surface tension and surfactant concentration, must be non-linear; we test several models but the well-known Langmuir-Hinshelwood kinetics and the Frumkin equation of state give the more reliable results.Our simulations show that in the absence of surfactants, a pronounced annular rim is formed on the tip front as the pore opens, and the pore velocity approaches the theoretical value $v_c$. We also observe a small capillary wave that connects the rim with the unperturbed sheet. By contrast, when surfactants are present: (i) the pore velocity is significantly reduced, as observed in previous experiments, (ii) a small lobe (not a rim) is formed at the tip front, and (iii) the mentioned small capillary wave is suppressed; however, a larger wave propagates on the free surface faster than the velocity of the pore tip, perturbing the free surface far away from the opening front. Results also show that, after a rapid initial increase, the surfactant concentration on the lobe remains essentially constant because the area contraction responsible for the surfactant accumulation is balanced by the tangential convection that drags surfactant away from the tip.