Channelized convection and solidification of a binary melt cooled from below: an experimental and theoretical study

Aqueous salt solutions are the simplest systems in which to study multicomponent solidification with the mushy-layer growth [1]. The reactive melting/dissolution often leads to the formation of so-called chimneys, narrow channels devoid of solid through which the buoyant fluid escapes the mush. In sea ice, the channels provide the flux of saltier water into the ocean [2]. Tabular dunite bodies are believed to provide the evidence for channel formation due to the reactive dissolution of the partially molten mantle [3]. The channelized transport of volatiles is relevant for magma chamber evolution [4].

Modelling coupled with experiments play a crucial role in the investigation of mushy layers. Of importance is the relationship between the initial conditions, the cooling history and the evolution of the mush. The full model of transient evolution of a mushy layer with chimneys is too complicated even for numerical treatment ([5], [6]). To date, most of the theoretical studies focused on the steady-state mushy layers with constant growth rate. We aim at understanding some aspects of the evolution of the channelized mushy-layer convection related to the more realistic situations, namely finite extent of the domain and time-dependent cooling.

We report on a combined experimental and theoretical study directed to investigate the interaction of chimney convection and solidification in a binary fluid cooled from below. The experiments with aqueous ammonium chloride are conducted in a tank where temperature, concentration, and mush thickness have been monitored.  We quantify a solute flux between the mush and the liquid, and determine a relationship between the time-dependent cooling rate, the released potential energy, the porosity and the mush height, describing the temporal evolution of the system towards a steady state. To understand the behavior of the system, we develop a model of the evolution of the gross characteristics of the mush/liquid system, where the velocity of the fluid leaving the chimney is a function of the difference between the concentration in the liquid and the vertically averaged  concentration in the mush.

This research was funded by the Mobility Plus Project supported by the Czech Academy of Sciences (SAV-23-06) and the Slovak Academy of Sciences (CAS-SAS-2022-01). We thank J. Šimkanin for technical assistance with the experiments.

 

[1] Kumar, V., Sakalkale, K., Karagadde, S., Convection-induced bridging during alloy solidification. Phys. Fluids 34, 053605, 2022

[2] Anderson, D. M. and Guba P., Convective phenomena in mushy layers. Annu. Rev. Fluid Mech. 52, 93-119, 2020

[3] Rees Jones, D. W. and Katz, R. F., Reaction-infiltration instability in a compacting porous medium. J. Fluid Mech. 852, 5-36, 2018

[4] Annen, C. and Burgisser, A., Modeling water exsolution from a growing and solidifying felsic magma body. Lithos 402-403, 105799, 2021

[5] Wells, A. J., Hitchen, J. R. and Parkinson, J. R. G., Mushy-layer growth and convection, with application to sea ice. Phil. Trans. R. Soc. A 377, 20180165, 2019

[6] Katz, R. F. and Worster, M. G., Simulation of directional solidification, thermochemical convection, and chimney formation in a Hele-Shaw cell. J. Comput. Phys. 227, 9823-9840, 2008