[Paper Review] Phase-field theory of brine entrapment in sea ice: Short-time frozen microstructures

Silke Thoms, Bernd Kutschan+1 more|arXiv (Cornell University)|May 1, 2014

Arctic and Antarctic ice dynamics2 references3 citations

TL;DR

This paper develops a phase-field model to simulate the early-stage microstructure formation of brine entrapment in sea ice, coupling non-conserved order parameter dynamics with salt diffusion under mass conservation. The model predicts a dominant wavelength of ~198 μm in good agreement with observed sea ice platelet spacing, demonstrating that thermodynamic parameters like supercooling and freezing point directly govern microstructural length scales.

ABSTRACT

We analyze the early phase of brine entrapment in sea ice, using a phase field model. This model for a first-order phase transition couples non-conserved order parameter kinetics to salt diffusion. The evolution equations are derived from a Landau-Ginzburg order parameter gradient dynamics together with salinity conservation. The numerical solution of model equations by an exponential time differencing scheme describes the time evolution of phase separation between liquid water with high salinity and the ice phase with low salinity. The numerical solution in one and two dimensions indicates the formation of one dominant wavelength which sets the length scale of short-time frozen structures. A stability analysis provides the phase diagram in terms of two Landau parameters. It is distinguished an uniform ice phase, a homogeneous liquid saline water solution and a phase where solidification structures can be formed. The Landau parameters are extracted from the supercooling and superheating as well as the freezing point temperature of water. With the help of realistic parameters the distribution of brine inclusions is calculated and found in agreement with the measured samples. The size of the ice domains separating regions of concentrated seawater depends on salinity and temperature and corresponds to the size of sea ice platelets obtained from a morphological stability analysis for the solidification of salt water.

Motivation & Objective

• To understand the formation of brine inclusions during the initial stages of sea ice freezing, particularly under short-time frozen conditions.
• To develop a physically grounded phase-field model that conserves salt mass and captures the microstructural evolution of brine networks.
• To determine how thermodynamic parameters such as supercooling and freezing point influence the size and stability of ice-brine structures.
• To validate the model against experimental brine layer textures and observed sea ice microstructures, particularly platelet spacing.
• To establish a connection between Landau parameters and measurable physical properties of water and saltwater systems.

Proposed method

• Formulates a phase-field model based on Landau-Ginzburg gradient dynamics for a first-order phase transition, coupling order parameter evolution with salt diffusion.
• Derives coupled evolution equations from a generating functional to ensure conservation of salt mass, distinguishing it from non-conservative models like the Turing model.
• Uses an exponential time differencing scheme for numerical solution of the time-dependent partial differential equations in one and two dimensions.
• Performs linear stability analysis to derive a phase diagram in terms of two Landau parameters: freezing parameter (α₁) and structure parameter (α₃).
• Calibrates model parameters using physical properties: supercooling, superheating, and freezing point of water (T₀ = 233.15 K).
• Relates the critical domain size λc to the dominant wavelength via λc = 2π/κc, with κc derived from the stability analysis.

Experimental results

Research questions

• RQ1 What microstructural length scale emerges during the early phase of brine entrapment in sea ice, and how is it determined by thermodynamic conditions?
• RQ2 How do the freezing parameter and structure parameter in the phase-field model govern the formation of stable ice-brine patterns?
• RQ3 To what extent can the model reproduce experimentally observed brine layer textures and platelet spacings in natural sea ice?
• RQ4 How does the inclusion of salt mass conservation improve the physical realism of the phase-field model compared to non-conservative alternatives?
• RQ5 What is the relationship between the model’s critical domain size and the observed 200–500 μm ice lamellae spacing in real sea ice?

Key findings

• The model predicts a critical domain size of λc = 198 μm under realistic conditions (α₁ = 0.111482, α₃ = 1.99, T₀ = 233.15 K, ΔT = 0.032 K supercooling), matching observed sea ice platelet spacing.
• A dominant wavelength of ~198 μm emerges from the linear stability analysis, corresponding to the most unstable mode in the system.
• The model’s parameters are directly linked to physical properties: supercooling, superheating, and freezing point of water, enabling physical calibration.
• The critical domain size λc = 0.8 μm is obtained under high supercooling (ΔT = 6.3 K), consistent with morphological stability theory for saltwater solidification.
• The phase diagram derived from stability analysis identifies regions where spatial structures form, determined solely by α₁ and α₃, independent of diffusivity.
• Numerical simulations in two dimensions reproduce vertically oriented, sheet-like brine inclusions, matching the morphology of experimentally observed brine layers.