Two-dimensional slow viscous flows with time-dependent free boundaries driven by surface tension
Two-dimensional slow viscous flows with time-dependent free boundaries driven by surface tension
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表面张力驱动的具有随时间变化的自由边界的二维慢粘性流
DOI：
10.1017/s0956792500000796
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发表时间：
1992
影响因子：
1.9
通讯作者：
S. Richardson
中科院分区：
文献类型：
--
作者：
S. Richardson
我们考虑了不可压缩牛顿流体的二维准定常Stokes流，它占据了一个由自由面为边界的含时单连通区域。运动是由作用在自由边界上的恒定表面张力驱动的，因此，忽略重力的影响，人们预计随着时间的推移，边界将接近圆形。结果表明，如果在某个初始时刻，流体所占据的区域是由单位圆盘的有理保角映射给出的，那么只要该区域保持单连通，它就一定保持这一性质。此外，它的演化可以解析地描述；在简单的情况下，这种描述是明确的，但在更复杂的问题中，可能需要对一阶微分方程组进行数值积分。
We consider the two-dimensional quasi-steady Stokes flow of an incompressible Newtonian fluid occupying a time-dependent simply-connected region bounded by a free surface. The motion is driven by a constant surface tension acting at the free boundary so that, with the effects of gravity ignored, one expects the boundary to approach a circular form as time evolves. It is shown that, if at some initial instant the region occupied by the fluid is given by a rational conformal map of the unit disc, then it must retain this property as long as the region remains simply-connected. Moreover, its evolution may be described analytically; in simple cases this description is explicit, but in more complicated problems the numerical integration of a system of first order differential equations may be required.