Effects of surfactant on terminal velocity of a Taylor bubble in a vertical pipe

Abstract

Effects of soluble surfactant on the terminal velocity of a Taylor bubble rising through a vertical pipe are investigated using an interface tracking method. A level set method is utilized to track the interface. Transport of surfactant in the bulk liquid and at the interface is taken into account. The amount of adsorption and desorption is evaluated using the Frumkin and Levich model. The normal component of surface tension force is computed using a ghost fluid method, whereas the tangential component, i.e., the Marangoni force, is evaluated by making use of the continuum surface force model. Simulations of small air bubbles contaminated with soluble surfactant are carried out for validation. The Marangoni effects on the bubbles, i.e., the surface immobilization and the increase in drag coefficient, are well predicted. Then Taylor bubbles rising through vertical pipes filled with contaminated water at a low Morton number are simulated for various Eötvös numbers, various bulk surfactant concentrations and two different surfactants, i.e., 1-pentanol and Triton X-100. As a result, the following conclusions are obtained: (1) the reduction of surface tension near the bubble nose is the cause of the increase in terminal velocity, (2) the surfactant does not affect the terminal velocities of high Eötvös number bubbles since the bubbles at high Eötvös numbers are independent of surface tension, (3) the terminal velocity of a low Morton number Taylor bubble can be evaluated by making use of available correlations for clean Taylor bubbles, provided that the degree of contamination near the bubble nose is known and the Marangoni effect in the nose region is negligible, and (4) the Hatta number, which is the ratio of the adsorption velocity to the bubble velocity, is a primary factor governing the degree of contamination in the bubble nose region.