Solidification and compositional convection of a ternary alloy

Abstract

We present the results of an experimental study on the solidification of aqueous solutions of potassium nitrate and sodium nitrate cooled from below. Upon cooling, two distinct mushy layers form, primary and cotectic, separated by an approximately planar horizontal interface. A density reversal between the two mushes causes the residual liquid in the upper, primary mush to be more buoyant than the melt overlying it, while the cotectic mush is compositionally stable. The unstable concentration gradient between the melt and primary mush causes convection that keeps the melt well-mixed and reduces the concentration gradient to zero after a finite time. At this point, the cotectic mush overtakes the primary mush and a transition from a convective regime to a diffusive regime occurs. Our measurements show that this transition is rapid and alters the growth rate of the single (cotectic) mush layer that remains. Concentration measurements taken from within the melt during convection and from within the mush during the diffusive regime show good agreement with the concentration evolution predicted by use of the equilibrium ternary phase diagram. We describe a global conservation model for solidification of a ternary alloy in this regime. Predictions from our model forced with empirical data for the heat and solute fluxes are in good agreement with the measured data for the interface positions of the two mushy layers. We also discuss how solid fractions vary with different melt concentrations in a non-convecting alloy and examine the influence of vertical solute transport in the convecting case. The identification of a density reversal in the solidification of a ternary alloy begins to address the complexities in solidification processes of multi-component alloys. IntroductionThe formation of solids by cooling a liquid melt is an integral part of many natural and industrial processes. Many of these solidification processes also generate fluid flows that are effective means of heat and mass transport and significantly influence the structure and growth rate of the solid phase. These fluid motions occur in liquid alloys owing to thermal convection caused by cooling the melt or to compositional convection caused by the removal of one or more components from the melt to form the solid phase. Preferential incorporation of components into the solid and rejection of others into the melt can also lead to constitutional supercooling, which † Present address:

Solidification using smoothed particle hydrodynamics

“…The method is simple to use and guarantees both energy conservation and the increase of entropy from both thermal conduction and from salt diffusion in the absence of sources. The method can be trivially extended to handle the solidification of ternary and higher order alloy systems, which are common in both industrial and natural contexts, but where investigation has only just begun [1,20].…”

On the mechanism responsible for unconventional thermal behaviour during freezing

“…Vigorous convective flow was observed during the solidification of water-Na 2 SO 4 , and water-CuSO 4 (Chen & Turner 1980;Huppert 1990;Bloomfield & Huppert 2003) under side and top cooled conditions. Thompson et al (2003) performed bottom-cooled experiments involving KNO 3 as one of the constituents and reported vigorous and random convection for a certain duration where KNO 3 was the primary solidifying component. Further, a gain in the bulk-fluid temperature was also observed at the end of convection in (Thompson et al 2003), which was attributed to the heat gained from the surroundings.…”

“…Thompson et al (2003) performed bottom-cooled experiments involving KNO 3 as one of the constituents and reported vigorous and random convection for a certain duration where KNO 3 was the primary solidifying component. Further, a gain in the bulk-fluid temperature was also observed at the end of convection in (Thompson et al 2003), which was attributed to the heat gained from the surroundings. This may not be necessarily true, as the distinguishing flow patterns with dendritic and faceted morphologies control the heat and mass transfer within the liquid.…”

Convective instabilities during the solidification of an ideal ternary alloy in a mushy layer

“…Other recent work has focused on aqueous ternary systems, whose equilibrium phase diagrams can be characterized relatively easily by a few simple formulas. Laboratory experiments on the aqueous system water-potassium nitrate-sodium nitrate (H 2 O-KNO 3 -NaNO 3 ) have revealed that in this ternary eutectic system two distinct mushy layers, referred to as the primary and secondary mushy layers, can form between the completely solid and completely liquid layers (Aitta, Huppert & Worster 2001a,b;Thompson et al 2003b). Convection and solidification of another aqueous ternary system H 2 O-CuSO 4 -Na 2 SO 4 has also been recently examined (Bloomfield & Huppert 2003).…”