Demetrius Papageorgiou
Department of Methematics, New Jersey Institute of Technology
| When small bubbles or drops rise or fall in a viscous liquid, it is observed experimentally that they behave as if they were solid spheres. This is seen by measuring rise velocities, for example, and computing the drag experienced at steady state. The reason fo this is that trace amounts of impurities (surfactants) have a dramatic influence on the global hydrodynamics through their exchange with the bubble interface and their ability, in many regimes, to rigidify the surface. This talk will present the complete model for this problem in the limit of large surface tension (small Weber number) that eeps the bubbles spherical. Different regimes will be identified as well as the possibility of utilizing the surfactant concentration in a controled manner, to influence the resulting drag. We will show through numerical simulations based on the Navier-Stokes equations, that if the surfactant has a fast kinetic exchange with the interface, then the bubble can be completely remobilized, i.e. the drag is reduced to that of a rising bubble with a tangentially free interface. In the other extreme where kinetic exchange is slow, the bubble can be partially covered and is comprised of a clean fron and a solid-like back end - the stagnant cap regime. We present simulations and experiments that bring out this behavior and make direct comparisons between theory and experiment. This approach is a promising method for measuring surfactant kinetic constants which are hard to obtain using other methods (e.g. pendant bubble apparatus). |
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