A dual-reciprocity boundary element method for evaluating bulk convective transport of surfactant in free-surface flows

We present a dual-reciprocity boundary element method (DRBEM) to investigate bulk surfactant transport dynamics in a free-surface flow system under steady-state conditions. This free-surface flow system consists of semi-infinite bubble progression in a rigid axisymmetric capillary tube. Once adsorbed to the air-liquid interface with a surface concentration Gamma surfactant alters the interfacial surface tension gamma. As the interfacial stress balance, which governs the fluid mechanics, is a function of gamma, a strong coupling exists between surfactant transport dynamics and the fluid mechanics (physicochemical hydrodynamics). To model this problem over a range of bulk concentrations, C-o the bulk convective/diffusive transport of surfactant to the interface must be calculated. In this paper, DRBEM is used to simulate the bulk convection-diffusion relationship while the boundary element method (BEM) is used to solve Stokes flow, and a finite-difference method is used to solve the surface transport equation under steady-state conditions. A nonlinear Langmuir adsorption model is used to determine the surfactant equation of state gamma = f (Gamma). The validity of the DRBEM is first demonstrated by comparing computational and analytical solutions for a test problem. Next, the computational algorithm is used to calculate the bulk concentration field surrounding the bubble as a function of the far-downstream quantity of surfactant, C-o and its influence on interfacial dynamics. These profiles clearly demonstrate the importance of accurately calculating the bulk concentration field under moderate C-o conditions. In addition, the variation of mechanical proper-ties of this system as a function of C-o indicates that the interfacial pressure jump can be significantly larger when the bulk transport of surfactant to the interface is limited. (C) 2001 Academic Press.