Convective instability in ammonium chloride solution directionally solidified from below

Abstract

The stabilities of salt-finger and plume convection, two major flows characterizing the fluid dynamics of NH4Cl solutions cooling from below, are investigated by theoretical and experimental approaches. A linear stability analysis is implemented to study theoretically the onset of salt-finger convection. Special emphasis is placed on the competition between different instability modes. It is found that in most of the cases considered, the neutral curve consists of two separated monotonic branches with a Hopf bifurcation branch in between; the right-hand monotonic branch corresponding to the boundary-layer-mode convection is more unstable than the left-hand monotonic branch corresponding to the mushy-layer mode. We also conducted a series of experiments covering wide ranges of bulk fluid concentration C∞ and bottom temperature TB to study the stability characteristics of plume convection. From the measurement of both temperature and concentration of the interstitial fluid in the mushy layer, we verify that during the progress of solidification the melt in the mush is in a thermodynamic equilibrium state except at the melt/mush interface where most of the solidification occurs. The critical Rayleigh number of the onset of plume convection is found to be Rccm = 1.1 × 107Π* (see (22)), where Π* is the permeability of the mush. This relation is believed to be valid up to supereutectic NH4Cl solutions.