Oscillatory Instability, Limit Cycle, and Transition to Doublets in Directional Solidification

Abstract

An oscillatory instability is experimentally evidenced in directional solidification of nominally pure succinonitrile in a unity Péclet number regime. It involves long-time oscillations of both cell width and cell tip position in a nearly phase quadrature and at a wavelength equal to twice the cell spacing. The instability displays subcritical features and two instability domains, one at large cell spacing and the other at small cell spacing. Close to its upper stability boundaries, it succeeds in saturating onto a limit cycle; farther inside the unstable domains, it mediates a transition from cells to a different branch of solution, the doublets.