Freezing and ice aging dynamics in saline water under natural convection

TL;DR

This work addresses the long-term evolution of saline mushy ice under natural convection, focusing on how desalination and porosity changes feed back to thermal and mass transport to modulate ice thickness. It combines top-down Rayleigh-Bénard experiments with a 1D quasi-equilibrium model that couples heat transfer, salt conservation, and porosity evolution, using the porosity at maximum ice thickness as a key input. The main findings show that after rapid initial growth, desalination reduces porosity, weakens mushy-ice convection, and drives slow thinning of the ice layer; the model successfully predicts $h$, $\phi$, and $S_{bulk}$ over time and across wider parameter ranges defined by $\phi_{max}$, $T_c$, and $H$. These results shed light on sea-ice aging mechanisms and provide a tractable framework for predicting the coupled phase-change and transport processes in saline systems under convection, with potential applicability to geophysical and industrial contexts. The study also identifies avenues for deeper flow visualization and numerical simulations to refine transport properties and capture more complex environmental conditions.

Abstract

Understanding the coupled dynamics of liquid-solid phase change and fluid flows is crucial in a wide range of geophysical and industrial applications. When freezing occurs in saline water, the newly formed ice is mushy, with a porous structure that traps the brine within the ice. In this work, which combines experiments and theoretical analyses, we investigate the long-term evolution of saline ice, comprehensively accounting for the coupled dynamics of multiscale fluid flow, heat and mass transfer, and phase change. We show that in a closed convective system the rapid formation of a mushy ice layer is followed by desalination (i.e, the expulsion of salt from the ice) processes that might lead to a slow asymptotic decrease of the ice thickness. Desalination of mushy ice reduces its porosity, which alters the dynamic thermal equilibrium and ice thickness by weakening buoyancy-driven convection within the mushy layer. In turn, changes in brine convection and ice thickness affect the further desalination of the ice. The long-term dynamics of the system can be accurately predicted by a one-dimensional model based on appropriate parameterizations of global heat and mass transfer properties. Furthermore, within the same theoretical model we explore the ice dynamics across a broader parameter space. Our findings advance the understanding of the coupled phase-change physics of saline solutions in the presence of convective fluid flows and provide a basis for explaining and predicting real-world phenomena such as the aging of sea ice.

Figures (8)

• Figure 1: Evolution of the mushy ice in salty water. (a) Sketch of the experimental system. The experiments adopt a cuboidal cell with aspect ratio $L/H=2$. The cell is initially filled with salty water of salinity $S_{bulk}|_{t=0}\approx3.5\%$. The cold top plate is maintained at $T_c=-12.1\ ^\circ$C, 10 $^\circ$C below the initial freezing point $T_0(S_{bulk}|_{t=0})$. The hot bottom plate temperature $T_h$ decides a dimensionless parameter $\Theta_i=(T_h-T_0(S_{bulk}|_{t=0}))/(T_h-T_c)$. A salinity sensor is embedded near the bottom plate. An expansion vessel is connected to compensate for the volume change. (b) Image at the start of the experiment. (c-e) Images of the ice layer for $\Theta_i=0.44$ ($T_h=5.9$$^\circ$C) at day 1 (c), day 4 (d) and day 8 (e). (f-h) Images of the ice layer for $\Theta_i=0.29$ ($T_h=1.9$$^\circ$C) at day 2 (f), day 8 (g) and day 16 (h).
• Figure 2: Space-time diagram for the ice layer profile at different horizontal positions $x=H$ (a), $x=0.5H$ (b) and $x=1.5H$ (c), in the experiment with $\Theta_i=0.29$. The dashed arrows in (a) are drawn to guide the eye for the stripes.
• Figure 3: Velocity fields in the ice layer at $t=4$ day (a), 6 day (b), 8 day (c), 10 day (d), 11 day (e) and 12 day (f) for $\Theta_i=0.29$. The color contour shows the magnitude of the migration velocity. The direction and length of the white arrows indicate the direction and magnitude of the migration velocity.
• Figure 4: Velocity fields in the ice layer at $t=2$ day (a), 3 day (b), 4 day (c) in the experiment of long-term ice evolution in a vertical convection system with $\Theta_i=0.5$. The original images are from Ref. du2025sea. The color contour shows the magnitude of the migration velocity. The direction and length of the white arrows indicate the direction and magnitude of the migration velocity.
• Figure 5: Experiment results (symbols) and theoretical predictions (lines) on mean ice thickness $h/H$ (a,d, black), salinity measured by the sensor $S$ (b,e, yellow) and mean ice porosity $\phi$ (c,f, red) as function of time. The ice porosity in the experiments (red diamonds in c,f) is calculated with mass conservation inputting the measured ice thickness and salinity. The top axes exhibit the dimensionless time $t/t_D$, where $t_D=(h^*)^2/D_{brine}$ is the solutal diffusive time scale, $h^*$ is the spatial-temporal mean ice thickness and $D_{brine}$ is the salt diffusivity. (a-c) Experiment results and theoretical predictions for $\Theta_i=0.44$, with $t_D\approx8.3$ days. (d-f) Experiment results and theoretical predictions for $\Theta_i=0.29$, with $t_D\approx50.7$ days.