Tuesday, 1 November 2005 - 9:30 AM
171g
Gravity-Driven Motion of a Drop or Bubble near an Inclined Wall at Low Reynolds Number
Andrew J. Griggs, Alexander Z. Zinchenko, and Robert H. Davis. Department of Chemical and Biological Engineering, University of Colorado at Boulder, 424 UCB, Boulder, CO 80309-0424
Dynamical simulations for the creeping motion of a three-dimensional deformable drop or bubble in the vicinity of an inclined wall are performed. The main purpose is to study the steady-state drop/bubble velocity as a function of the Bond number, drop-to-medium viscosity ratio, and the wall inclination angle. The major difficulty is that for moderate-to-small deformations (the range where most experimental results are available), the drop/bubble is able to approach the wall very closely (to less than 1% of drop radius) in steady motion, and there is an extended lubrication region which has a strong effect on the solution that requires high resolution, even for moderate Bond numbers. Also, most experimental data are for very low viscosity ratios (bubbles), making such a numerical solution very demanding. We have developed a novel algorithm that is a combination of the boundary-integral and economical multipole techniques. In the boundary-integral formulation, the Green function for the half-space above an infinite plane wall is used, which circumvents discretization of the wall. A multipole acceleration allows calculations with as many as 20000-40000 boundary elements and many thousand time steps to reach a steady state. The steady drop-to-wall separation and drop velocity depend heavily on the Bond number and viscosity ratio for intermediate-to-large inclination angles (i.e. 30-75 degrees above horizontal). With decreasing Bond number, homoviscous drops travel increasingly closer to the wall. Viscous drops maintain smaller separations and deform more than bubbles at fixed Bond number over a large range of inclination angles. For small inclination angles, the steady drop velocity decreases due to increased proximity to the wall. Simulations for drop motion near a vertical plane wall have also been conducted and compare well with previous experimental and theoretical results.
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