Pinch-off singularities in rotating Hele-Shaw flows at high viscosity contrast.
We study the evolution of a family of dumbbell-shaped liquid patches surrounded by air inside a rotating Hele-Shaw cell with lubrication methods and numerical simulations. Depending on initial conditions, the dumbbell either stretches to infinity, pinches off at the neck to form a droplet, or collects into a circular drop at the center of rotation. Whether or not pinch-off occurs results from a subtle interplay between centrifugal and capillary forces. In particular, rotation may delay or even prevent pinch-off from occurring owing to stretching and smoothing of the fluid neck. However, frequently rotation may have the opposite effect leading to pinch-off where the relaxation toward a circular drop would be observed in an ordinary Hele-Shaw cell.
Alvarez-Lacalle
E
E
Departament de Física Aplicada, Universitat Politècnica de Catalunya, Marañon 50, E-08028 Barcelona, Spain.
Casademunt
J
J
Eggers
J
J
D000388:Air; D000465:Algorithms; D002498:Centrifugation; D008962:Models, Theoretical; D010363:Pattern Recognition, Automated; D010825:Physics / Q000379:methods*; D012212:Rheology; D014783:Viscosity