Linear and Weakly Nonlinear Stability of Marangoni Convection in a Liquid Bridge

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概要

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• Marangoni convection arising in a liquid column, bridging between concentric circular parallel plates with different but uniform temperatures, is examined on its linear and weakly nonlinear stability. The analyses are conducted for the Prandtl number P ranging from 0.001 to 10. Our attention is focused on a relatively low liquid bridge with r_{*}/h=1 where h is the height and r_{*} is the radius of the bridge. The buoyancy effect is ignored entirely and the perfectly insulating condition is imposed on the non-deformable surface. It is revealed that linear critical conditions are given by azimuthal wavenumbers m=1, 2, and 3 depending on the Prandtl number. The critical modes are found to be steady for 0.001\leq P<0.0578 while they are oscillatory for P>0.0578. The weakly nonlinear analysis identifies the stable region of the secondary solutions bifurcating off the linear critical curve.

• 2013-07-15

著者

• Fujimura Kaoru

  Department Of Applied Mathematics And Physics Faculty Of Engineering Tottori University

• Fujimura Kaoru

  Department of Applied Mathematics and Physics, Tottori University, Tottori 680-8552, Japan

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