Modelagem Matemática e Simulação Computacional de Escoamentos Bifásicos com a Presença de Surfactante Insolúvel

Abstract

When it comes to two-phase ows, it is inevitable to talk about surfactants. Surfactants are surface-active agents that may be present in systems, as impurities, or deliberately added to the mixture to control interfacial physical efects. Surfactants are widely used in many engineering applications; for instance, they are used to generate emulsions, to handle drops and bubbles in microchannels, or to stabilize droplets suspended in an immiscible medium, they are also used in the process of water purification, etc. The main functions of surfactants are to reduce surface tension and prevent coalescence. The presence of these active agents can critically afect the dynamics of interfacial two-phase ows. Surfactants adhered to the interface result in a decrease, in a non-uniform way, of the surface tension; which makes the capillary force non-linear and introduces the Marangoni force. By using the front-tracking method and adaptive meshes locally refined, this work aims to study the efect of insoluble surfactant in interfacial two-dimensional

ows. Since the surfactant is assumed to be insoluble, there is no net mass transport between the interface and the bulk uid. Therefore, the transport of surfactant is only done on the interface and for that, the transport equation for the surfactant concentration is solved in the Lagrangian mesh. This equation was implemented in the AMR2D code developed by Villar (2007). In the first step, the numerical code was validated by an analitical expression developed to calculate the drag coeficient for two-dimensional bubbles, then, the analytical and numerical results were compared. The implementation of surfactant concentration equation was verified through convergence analysis. It was simulated one and two bubbles immersed in a shear ow seeking to make a comparison between clean and contaminated interfaces. For that, it was evaluated the efects of surfactant on the dynamics of these ows. Moreover, for the case of two bubbles, the efects of surfactant in the interaction between bubbles were also investigated. After that, it was demonstrated the presence of the Marangoni efect in contaminated ows through a test in which the interface moves only because of the Marangoni force. Finally, a study of moving contact lines is presented. This study is about the modeling of the contact point, where there is the interaction of the three phases present in the ow and, in this context, the surfactant acts by modifying the value of contact angle. This is also a problem of great industrial interest. It appears in the processes of wetting, coating and many biological applications and it has been in the focus of study by many researchers for several decades.