Squeeze flow of multiply-connected fluid domains in a Hele-Shaw cell
Squeeze flow of multiply-connected fluid domains in a Hele-Shaw cell
复制标题
Hele-Shaw 单元中多重连接流体域的挤压流动
作者：
D. Crowdy;Hyun
本文利用代数曲线和求积域理论，构造了Hele-Shaw胞腔中多连通流体域挤压流问题的精确解。这些解是精确的，因为它们可以用一组有限的随时间变化的参数来表示。该方法是非常普遍的，适用于任何有限连通的流体域。通过实例，明确地计算了具有两个和四个空气孔的流体域的演化。对于单连通区域，挤压流问题是适定的。相比之下，多连通域的挤压流问题不一定是适定的，并且解决方案可以在有限时间内通过在封闭的空气孔的边界上形成尖点而分解。
SummaryThe theory of algebraic curves and quadrature domains is used to construct exact solutions to the problem of the squeeze flow of multiply-connected fluid domains in a Hele-Shaw cell. The solutions are exact in that they can be written down in terms of a finite set of time-evolving parameters. The method is very general and applies to fluid domains of any finite connectivity. By way of example, the evolution of fluid domains with two and four air holes are calculated explicitly. For simply connected domains, the squeeze flow problem is well posed. In contrast, the squeeze flow problem for a multiply connected domain is not necessarily well-posed and solutions can break down in finite time by the formation of cusps on the boundaries of the enclosed air holes.