Numerical simulations of mass transfer around rising bubbles in the presence of surfactants

  • Kentheswaran, Kalyani (Toulouse INP, LGC)
  • Dietrich, Nicolas (INSA, TBI)
  • Lalanne, Benjamin (Toulouse INP, LGC)

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The performances of many industrial processes involving bubble flows are related to the efficiency of the gas-liquid mass transfer. Such dispersed flows are generally contaminated with surrounding impurities or surfactants, which adsorb to the interfaces. They can have strong consequences on the flow features, and on the rates of heat and mass transfers. In this work, Direct Numerical Simulations are performed to investigate the mass transfer rate around a rising bubble contaminated by surfactants. The stagnant-cap regime is considered, for which the time of surfactant transfer between the bulk and the interface is much larger than that of surface convection. Numerical simulations are carried out with the in-house code DIVA, based on the Level-Set and the Ghost Fluid methods. The transport of surfactants is solved both in the bulk phase and along the bubble surface, by including adsorption/desorption fluxes. The Navier-Stokes equations are coupled with the Marangoni stresses, taken into account as a jump condition on the tangential viscous stress. The transfer of a passive scalar from the gas to the liquid is also computed, by considering that resistance to mass transfer lies in the liquid. The stagnant-cap regime is characterized by the contamination angle θcap formed by the advected surfactants at the bubble rear, which splits the interface into a mobile and an immobile zone. It is found that the transient phase of surfactant adsorption is a succession of quasi-steady states as soon as a cap angle exists. It is also revealed that the decrease of the maximal velocity of the fluid at the interface, u∗max, as compared to a clean bubble, is a signature of the decline of the interface mobility in the presence of surfactants. Regarding the mass transfer, the Sherwood number Sh lies between that for a clean bubble and a solid sphere. A local analysis shows that Sh is very sensitive to the hydrodynamics in the front of the interface where the flux is the highest. A correlation is proposed to predict Sh as a function of both global (Re, Sc) and local (θcap, u∗max) parameters, where Re and Sc are the Reynolds and Schmidt numbers (10 ≤ Re ≤ 100 and 1 ≤ Sc ≤ 500). This correlation, established from steady conditions, is shown to be valid even during the transient phase of adsorption. Finally, deformed bubbles are also considered, at higher Weber numbers. Surprisingly, the mass transfer rate is found to follow the same law as that developed for spherical bubbles.