MARANGONI EFFECTS OF ADSORPTION-DESORPTION CONTROLLED SURFACTANTS ON THE LEADING END OF AN INFINITELY LONG BUBBLE IN A CAPILLARY

The leading end of an infinitely long gas bubble which displaces a vis cous surfactant solution in a capillary tube is studied. The surfactan t is present at elevated concentration and has sorption controlled mas s transfer. The displaced fluid wets the wall, forming a continuous li quid film between the bubble and the capillary wall. Both the thicknes s of this film and the additional pressure required to aspirate the bu bble depend upon the Marangoni stresses caused by non-uniform surfacta nt adsorption along the interface. The equations governing this flow a re solved at asymptotically small capillary number for the case where the balances of momentum and mass transfer are coupled to leading orde r. As the Marangoni effect is increased over several orders of magnitu de, the additional pressure and the wetting-layer thickness increase a bove the stress-free interface values found by Bretherton (1961) and a pproach an upper bound of 4(2/3) times the Bretherton values. Accompan ying changes in the surface tension, Marangoni stress and surface velo city profiles as this upper bound is approached are described. Finally , surface viscosities that are intrinsic to the interfacial region are incorporated in the analysis. When small departures from surface equi librium states are considered, the terms representing surface viscous effects have the same functional form as the Marangoni stresses and re sult in thicker films and higher additional pressures.