Abstract
Hele-Shaw cells where the top plate is moving uniformly at a prescribed speed and the bottom plate is fixed have been used to study interface related problems. This paper focuses on interfacial flows with linear and nonlinear kinetic undercooling regularization in a radial Hele-Shaw cell with a time dependent gap. We obtain some exact solutions of the moving boundary problems when the initial shape is a circle, an ellipse or an annular domain. For the nonlinear case, a linear stability analysis is also presented for the circular solutions. The methodology is to use complex analysis and PDE theory.
Reference63 articles.
1. P. H. A. A NJOS , E. O. D IAS AND J. A. M IRANDA , Kinetic undercooling in Hele-Shaw flows, Phys. Rev. E, 92
2. (2015), 043019.
3. J. M. B ACK , S. W. M C C UE , M. N. H SIEH , AND T. J. M ORONEY , The effect of surface tension and kinetic
4. undercooling on a radially-symmetric melting problem, Appl. Math. Comp., 229 (2014), 41-52.
5. G. C ARVALHO , H. G AD ˆ ELHA , AND J. M IRANDA , Elastic fingering in rotating Hele–Shaw flows, Phys. Rev. E, 89 (2014), 053019.