Bubbles in the Hele-Shaw cell: Pattern selection and tip perturbations.

@article{Hong1988BubblesIT,
  title={Bubbles in the Hele-Shaw cell: Pattern selection and tip perturbations.},
  author={Hong and Family},
  journal={Physical review. A, General physics},
  year={1988},
  volume={38 10},
  pages={
          5253-5259
        }
}
We consider the motion of a symmetric finite bubble in a two-dimensional Hele-Shaw cell. In the absence of surface tension, the Saffman-Taylor solution contains two free parameters, U and \ensuremath{\lambda}, for a given bubble area J, where U is the dimensionless speed and \ensuremath{\lambda} is the dimensionless width of the bubble. It is shown that, in the presence of surface tension, a solution does not exist for Ug2 for any bubble area. We also derive the following scaling relations: (a… CONTINUE READING

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