A dynamical mother body in a Hele-Shaw problem

• Published in: Physica. D Vol. 240; no. 14; pp. 1156 - 1163
• Main Authors: Savina, T.V., Nepomnyashchy, A.A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15-07-2011; Elsevier
• Subjects: Algorithms; Boundaries; Cusps; Droplets; Exact sciences and technology; Fluid dynamics; Fluid flow; Fluids; Free boundary problem; Hele-Shaw cell; Physics; Schwarz function; Singularities; Hele-Shaw cell; Schwarz function; Free boundary problem; Circle; Algorithms; Droplets; Non linear phenomenon
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2011.04.002

It is well-known that in the framework of the internal Hele-Shaw problem the fluid cannot be fully removed through a single point sink because of a cusp formation occurring prior to the moving boundary reaching the sink unless the initial domain is a circle with a sink located in its center. We give a definition of a dynamical mother body and use it for developing an algorithm of complete removal of a fluid droplet having an algebraic boundary. To illustrate our theory we consider examples where fluid can be completely removed through the sinks distributed along arcs of curves and/or points.
► Formation of cusps is typical for Hele-Shaw problems. ► Only a circular droplet can be completely removed through a point sink. ► We introduce a special dynamics for the internal Hele-Shaw problem. ► We describe a way to avoid the formation of any kinds of singularities.