Cusps and cuspidal edges at fluid interfaces: Existence and application

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 91; no. 4; p. 043019
• Main Author: Krechetnikov, R
• Format: Journal Article
• Language: English
• Published: United States 01.04.2015
• ISSN: 1550-2376
• DOI: 10.1103/PhysRevE.91.043019

One of the intriguing questions in fluid dynamics is on the interrelation between dynamic singularities in the solutions of fluid dynamic equations - unboundedness of the velocity field in an appropriate norm - and the geometric ones - divergence of curvature at fluid interfaces. The present work focuses on two generic interfacial singularities - genuine cusps and cuspidal edges - found here in both two and three dimensions thus establishing a relation between real fluid interfaces and geometric singularity theory. The key finding is the necessary condition for the existence of geometric singularities, which is a variation of surface tension. It is also established here that the dynamic and geometric singularities entail each other only in the case of three-dimensional cusps. Explicit asymptotic solutions for the flow field and interface shape near steady-state singularities at fluid interfaces are developed as well. The practical motivation for the present study comes from the fundamental role interfacial singularities play in sustaining self-driven conversion of chemical into mechanical energy.