Influence of Soluble Surfactants and Deformation on the Dynamics of Centered Bubbles in Cylindrical Microchannels

In this study, we investigate, using direct numerical simulation, the motion of a small bubble in a horizontal microchannel filled with a liquid containing surfactants. In particular, we study the combined effect of surfactants and bubble deformability on the bubble shape, bubble-liquid relative velocity, velocity field in the liquid, liquid velocity on the gas-liquid interface, and surfactant distribution on the interface. The level-set method is used to capture the gas-liquid interface. The surfactant transport equation on the gas-liquid interface is solved in an Eulerian framework and is coupled to an equation describing the transport of surfactants inside the liquid phase. The Marangoni stress, induced by surfactant concentration gradients, is computed using the continuum surface force model. The simulation results give insights into the complexity of the coupling of the different phenomena controlling the dynamics of the studied system. For instance, the results show that for values of the capillary number much smaller than unity, that is, for spherical bubbles, the bubble velocity decreases as the bubble diameter increases. Moreover, surfactants tend to decrease significantly the bubble velocity, when compared with a bubble with a clean surface. Indeed, they accumulate at a convergent stagnation point/circle on the bubble surface and deplete at a divergent stagnation point/circle. As a consequence, the velocity of the liquid adjacent to the bubble is reduced in between the convergent and divergent stagnation points/circles because of Marangoni stresses. It is shown that regarding the bubble-liquid relative velocity, the bubble behaves as a rigid sphere when the Langmuir number is larger than unity, at least for the range of parameters explored in this study. For values of the capillary number of the order of unity, the bubble can take a "bullet shape". In this case, the bubble velocity increases as the bubble diameter increases. This increase of the bubble-liquid relative velocity is linked to a drastic change in the liquid flow structure near the bubble. Surfactants are swept to the rear of the bubble and have less influence on the bubble dynamics than for spherical bubbles. Finally, it is shown that increasing the amount of surfactants adsorbing to the surface eventually leads to the bursting of the bubble.