周辺支持の液滴・気泡の粘性による非回転的減衰振動

概要

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A spherical liquid drop or a gas bubble makes oscillations of a characteristic frequency and mode shape, due tosurface tension. When the drop is pinned on a circle of contact, the mode shapes change and the frequencies are shifted, asshown by Bostwick and Steen (Physics of Fluids 21, 032108, 2009). Their linear stability problem of inviscid, axisymmetric,volume-preserving oscillations of a liquid drop under the constraint is extended here to include effects of viscosity using themethod of Viscous Potential Flow (VPF). Eigen functions are obtained analytically and the series expansion may be taken upto the 15-th term. The eigen values can be obtained well for low viscosity, but those become complex for high viscosity. Theirrotational decay due to viscosity can be found to arise at high frequency modes.
2010-01-31