Capillary surfaces: stability from families of equilibria with application to the liquid bridge
Capillary surfaces: stability from families of equilibria with application to the liquid bridge
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DOI：
10.1098/rspa.1995.0051
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发表时间：
1993-08
期刊：
影响因子：
--
通讯作者：
B. Lowry;P. Steen
中科院分区：
文献类型：
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作者：
B. Lowry;P. Steen
确定一般静态毛细管表面的稳定性的方法示出的应用程序的液体桥。在重力作用下具有固定接触线的轴对称桥梁由三个量参数化：桥梁长度L、桥梁体积V和Bond数B。该方法提供：（i）定压和定容扰动的{L，V，B}参数空间中的稳定性包络（产生新的和恢复的经典结果），（ii）一旦一个平衡态的稳定性已知，任何平衡态（不稳定状态）的不稳定模式的数量（e. G.的领域）的基础上（三）证明，所有已知的家庭平衡连接。该方法使用“首选”分叉图，体积V对压力p的曲线图。相对于其邻居的平衡形状的不稳定状态是立即从这个图。此外，一个不变的波数分类介绍和用于标记的众多家庭的液体桥平衡。基于Jacobi方程性质的优选图方法给出了比经典分歧理论更强的结果。其他毛细管表面，包括液滴和非轴对称形状的应用进行了讨论。
A method for determining the stability of general static capillary surfaces is illustrated by application to the liquid bridge. Axisymmetric bridges with fixed contact lines under gravity are parametrized by three quantities: bridge length L, bridge volume V, and Bond number B. The method delivers: (i) stability envelopes in the {L, V, B} parameter space for constant-pressure and constant-volume disturbances (generating new and recovering classical results), (ii) the number of unstable modes for any equilibrium (state of instability) once the stability of one equilibrium state is known (e. g. that of the sphere) based on (iii) a demonstration that all known families of equilibria are connected. The method uses ‘preferred’ bifurcation diagrams, a plot of volume V against pressure p. The state of instability of an equilibrium shape relative to its neighbours is immediate from this plot. In addition, an invariant wavenumber classification is introduced and used to label the numerous families of liquid bridge equilibria. The preferred diagram method, which is based on properties of the Jacobi equation, gives stronger results than classical bifurcation theory. Application to other capillary surfaces, including drops and non-axisymmetric shapes, is discussed.