Density stratification due to counterbuoyant flow along a vertical crystallization front

Abstract

Theoretical modelling and experimentation are used to analyze horizontal solidification of a double-diffusive, binary liquid in a confined rectangular cavity. For solutions which segregate the lighter component into the liquid, the composition and temperature gradients produced upon solidification lead to the onset of vertical counterbuoyant flow along the growing crystals. The counterflow progressively transforms the initially homogeneous liquid into a density-stratified fluid layer characterized by pronounced vertical gradients in solute concentration. The theoretical representation describes the coupling between the solidification and development of density stratification in the liquid in the interior of the cavity. The computed results and experimental observations indicate that for moderate horizontal temperature differences, the vertical stratification can effectively damp convection in the stratified portion of the bulk liquid. Increasing the temperature difference or lateral heat flux across the enclosure sufficiently, initiates formation of a series of horizontal double-diffusive convection layers. The nature of the fluid motion in the bulk is seen to have significant influence on solute redistribution and heat transfer, both at the growth interface and in the interior of the enclosure. The computed flow patterns, solid-liquid interface shapes, and rates of growth of the stratified region compare well with those observed experimentally for directionally-solidified solutions of sodium carbonate and water. The calculated and observed heights of the horizontal convection cells correlate well with theoretical predictions. Order-of-magnitude analysis is used to explore the theoretical limits of stability of the growing layer under the roof with respect to remixing with the underlying ‘bulk’ liquid.