Numerical study of surfactant effects on the buoyancy-driven motion of a drop in a tube

We present results of our numerical study of the effect of surfactants on buoyancy-driven motion of drops in a tube at intermediate Reynolds numbers. The drop and bulk phases are treated as incompressible Newtonian fluids and simulated using a front-tracking method. The steady shapes and velocity-volume curves for drops ranging in drop size from 0.2 to 1.3 of tube radius are determined numerically. At small Bond numbers, the velocity-volume curve shows a maximum before the velocity plateaus for large drops. As the Bond number increases, the maximum in the velocity-volume curve disappears with elongated, more streamlined drop shapes consistent with previous experimental studies. For increasing Weber numbers, the rear of the drop shows a flattening followed by the development of a negative curvature. Surfactants are modeled using a Langmuir equation of state in the adsorption-desorption limit and the effect of surfactant mass transfer, fractional coverage of surfactants, and the interfacial Peclet number on the velocity-volume curve is determined. Marangoni stress generated due to the non-uniform distribution of surfactants at the interface reduces drop mobility. Reduced drop mobility is more prominent for drop sizes that are comparable to the tube diameter and is maximum when mass transfer to and from the interface is inhibited. As the fractional coverage of soluble surfactants, or the interfacial Peclet number increases, larger Marangoni stresses are generated along the interface that lead to greater retardation of the drop motion.