Self-similar relaxation dynamics of a fluid wedge in a Hele-Shaw cell

Details Self-similar relaxation dynamics of a fluid wedge in a Hele-Shaw cell Self-similar relaxation dynamics of a fluid wedge in a Hele-Shaw cell

2006-05-13

arxiv.org/abs/physics/0605112v1

Physics

Fluid Dynamics

4 pages, 4 figures, to appear in Phys. Rev. E (Rapid Communications)

Scientific paper

10.1103/PhysRevE.73.065302

Let the interface between two immiscible fluids in a Hele-Shaw cell have, at t=0, a wedge shape. As a wedge is scale-free, the fluid relaxation dynamics are self-similar. We find the dynamic exponent of this self-similar flow and show that the interface shape is given by the solution of an unusual inverse problem of potential theory. We solve this inverse problem analytically for an almost flat wedge, and numerically otherwise. The wedge solution is useful for analysis of pinch-off singularities.

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