Numerical modeling of drop coalescence in the presence of soluble surfactants

• I. Bazhlekov ^[1] ; D. Vasileva ^[1]
  1. [1] Bulgarian Academy of Sciences

     Bulgarian Academy of Sciences

     Bulgaria

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 293, Nº 1 (February 2016), 2016, págs. 7-19
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.04.013
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• Resumen

  • The paper presents a numerical method for simulation of the effect of a soluble surfactant on the last stage of the drop coalescence (film formation, drainage and rupture). An axisymmetric interaction between drops is studied at small capillary and Reynolds numbers and small surfactant concentrations. The hydrodynamic part of the mathematical model includes the Stokes equations in the drop phase and their lubrication approximation in the gap between the drops (film phase), coupled with velocity and stress boundary conditions at the interfaces. The surfactant is considered soluble in both (drop and film) phases and the distribution of the surfactant concentration is governed by a convection–diffusion equation. A convection–diffusion equation is also used to model the distribution of the surfactant on the interfaces. The concentration in both phases is coupled with that on the interfaces via the adsorption isotherm and the fluxes between the interface and the bulk phases. The hydrodynamic and concentration parts of the mathematical model are related via the advection of the surfactant in the fluid phases and on the interfaces. On the other hand, a non-uniform surfactant concentration on the interfaces leads to a gradient of the interfacial tension which in turn leads to an additional tangential stress on the interfaces (Marangoni effects). For the flow in the drops a simplified version of Boundary integral method is used. Finite difference method is used for the flow in the gap, the position of the interfaces and the distribution of surfactant concentration on the interfaces, as well as in the fluid phases. Different approaches are used for an optimization of the numerical algorithm: Non-uniform meshes for space discretization in both (rr and zz) directions; Explicit and implicit first and second order time integration schemes with automatically adaptive time steps; A multiple time step integration scheme that can decrease significantly the computational time without loss of accuracy. Tests and comparisons are performed in order to investigate the accuracy and stability of the different numerical schemes.