Crystallization-Induced Convection

• Crystallization-induced convection is the process by which phase change, through latent heat release and solute redistribution, initiates fluid motion and complex flow patterns.
• This phenomenon governs dynamics in systems ranging from geophysical interiors and white dwarfs to mesoscale nanofluid droplets and industrial crystallizer setups.
• Key parameters such as the Peclet, Rayleigh, Marangoni, and phase-change numbers dictate the convection regimes and interface dynamics critical to material and astrophysical processes.

Crystallization-induced convection refers to the fluid motion and associated transport phenomena initiated or fundamentally altered by the formation of a crystalline phase within a liquid or multiphase medium. This process plays a central role in diverse contexts, from geophysical and planetary interiors undergoing solidification (e.g., Earth's inner core, white dwarfs) to mesoscale and laboratory systems such as nanodroplets, functional materials, and industrial crystal growth. The defining feature is the coupling between phase change (with associated latent heat and compositional fluxes) and convective fluid motion—often giving rise to interplay between advection, diffusion, instabilities, and feedback upon the evolving crystal morphology.

1. Theoretical Principles and Governing Parameters

Crystallization-induced convection results from the interplay of thermal and compositional gradients generated at the moving solid-liquid interface. The release (or absorption) of latent heat and the redistribution of solutes or phase-separating species during crystallization produce buoyancy forces that can drive convection. In many contexts, the effective convective regime is characterized by dimensionless numbers:

• Peclet Number ($\mathrm{Pe}$): $\mathrm{Pe} = v_c \ell / \kappa_T$, where $v_c$ is the convective velocity, $\ell$ the mixing length, and $\kappa_T$ the thermal diffusivity. Pe measures the relative importance of advective to diffusive (thermal) transport.
• Phase-Change Number ($\mathcal{P}$): $$\mathcal{P} = (\text{phase-change time}) / (\text{viscous relaxation time})$$, controlling boundary permeability via melting/freezing efficiency (Deguen, 2013).
• Rayleigh and Marangoni Numbers: Measuring bulk thermally driven convection and surface-tension-gradient-driven flows, especially relevant in droplets and thin films.
• Composition Flux Parameter ($\tau$): Dictates convective regime by comparing the timescale of thermal diffusion to that of composition injection (Fuentes et al., 2023).

Crystallization can drive either classical overturning convection (when buoyancy overcomes stabilizing gradients, Pe $\gg$ 1), or “fingering”/thermohaline convection (where slow compositional buoyancy acts in a thermally stable background and Pe $\ll$ 1) (Castro-Tapia et al., 2 Feb 2024, Fuentes et al., 6 Feb 2024).

2. Morphological Instabilities and Interface Dynamics

Crystallization-induced convection frequently interacts with morphological instability of the solid-liquid interface. Canonical examples include the formation of ripples on icicles (Ueno et al., 2011), where heat removal is modulated by both conduction and natural convection airflow. When convection is present in the airflow above a supercooled water film, the temperature gradient at the water–air interface steepens and becomes non-uniform:

$$-K_l \left. \frac{\partial \bar{T}_l}{\partial y} \right|_{y=h_0} = -K_a \left. \frac{\partial \bar{T}_a}{\partial y} \right|_{y=h_0}$$

The increased non-uniform latent heat loss amplifies interface disturbances, enhancing the growth rate of interfacial ripples. However, the selected wavelength of the most unstable mode remains robust (e.g., $\lambda \approx 1$ cm)—anchored by the balance between destabilizing (convective) heat loss and stabilizing gravity/surface tension. The convective enhancement also impacts phase velocity and the migration direction of surface patterns, with the possibility of direction reversal under varying environmental conditions.

Analogous interface-buoyancy couplings arise in forced convection crystallizers for fine chemicals (Tan et al., 2023), where heat released at the solid-liquid front raises local temperatures by up to $\sim$1.5°C, thereby modulating both vortex structures and the anisotropy of crystal habit via the interplay of the Reynolds number, imposed flow, and thermal gradients.

3. Compositionally Driven Convection in Planetary and Stellar Interiors

Earth’s Inner Core and Spherical Shells

Crystallization at the inner core boundary (ICB) creates density stratification via partitioning of light elements (e.g., O, S). The controlling parameter, the phase-change number ($\mathcal{P}$), determines whether boundaries behave as permeable (efficient phase-change, $\mathcal{P}\ll1$) or impermeable ($\mathcal{P}\gg1$) (Deguen, 2013, Deguen et al., 2013). The regime with low $\mathcal{P}$ enables global translation modes (degree-one convection) where the entire core or shell shifts bodily, with melting on one side and freezing on the other, and minimal internal deformation:

$$\mathcal{P} = \frac{\Delta \rho \, g_{icb} \, r_{ic} \, \tau_\phi}{\eta}$$

$$V \sim \left(\frac{6}{5} \frac{Ra}{\mathcal{P}}\right)^{1/2} \frac{\kappa}{r_{ic}}$$

The resulting compositional convection can be substantially more efficient than thermally driven convection when the stratification is unstable and the viscosity is high.

White Dwarfs and Neutron Stars

Carbon–oxygen white dwarfs develop convection zones as oxygen-rich crystals form and carbon-rich liquid becomes buoyant (Ginzburg et al., 2022, Fuentes et al., 2023, Blatman et al., 2023). Two key convective regimes are again defined by the composition flux parameter $\tau$ and the Peclet number:

• Fast Convection: At the onset of crystallization, Pe $\gg 1$, convection is overturning and efficient. Convective velocities reach up to $10^3$ cm s$^{-1}$ and drive intense magnetic dynamos, supporting fields $\sim 10^6$–$10^8$ G independent of rotation period (Castro-Tapia et al., 2 Feb 2024, Fuentes et al., 6 Feb 2024).
• Slow (Thermohaline) Convection: As crystallization proceeds and $\tau$ drops, convection becomes diffusive, Pe $\ll 1$; velocities plummet ($10^{-6}$–$10^{-5}$ cm s$^{-1}$), and field generation efficiency drops sharply. The heat flux/composition flux ratio is then independent of Pe due to thermal leakage being precisely offset by a reduction in the required composition gradient (Fuentes et al., 2023).

Convective motions generate magnetic fields by a dynamo process in the so-called MAC (Magnetic–Archimedean–Coriolis) balance regime. However, the transition from fast to slow convection is rapid ($\sim10$ Myr timescale); thus, the surface fields observed today reflect both early intense generation and later diffusive decay modulated by the growth of the solid core, changes in conductivity, and the initial size of the convective mantle (Castro-Tapia et al., 3 Jun 2024).

4. Crystallization-Induced Convection in Mesoscale and Laboratory Systems

Droplet and Nanofluid Phenomena

In evaporating droplets—whether in protein crystallization (Pradhan et al., 2020) or surfactant-laden multicomponent systems (Li et al., 2020)—crystallization-induced convection is primarily driven by evaporation-induced concentration or temperature gradients, leading to buoyancy (Rayleigh) and Marangoni (surface tension) convection. For example:

• Protein Crystallization: Confining geometry suppresses evaporative surface area and reduces natural convection, creating a more quiescent, diffusion-dominated regime favoring higher crystal quality.
• Surfactant Crystallization: Evaporation of water localizes supersaturation and precipitates crystals at the droplet edge, which then “shield” the interface and modulate internal Marangoni and buoyancy-driven flows, often halting further evaporation.

Enhanced crystallization kinetics due to nanoparticle additives in levitated nanofluid droplets (McElligott et al., 11 Sep 2024) lead to increased mass transport, rapid crystal shell formation, elevated internal pressures, and more extensive interfacial cracking. Upon melting, vertical temperature gradients drive transient Bénard–Marangoni convection, but improved fluid thermal conductivity (from the nanoparticles) suppresses sustained circulatory motion.

Nanoscale Additive Manufacturing

In LIFT printing of silicon nanoparticles (Liang et al., 6 Apr 2025), latent heat release from crystallization and nonuniform nucleation sites (typically sub-surface, within 5 Å) create strong local thermal gradients, which can drive internal Marangoni convection. Nano-confinement modifies the convective landscape: in larger droplets, convection can efficiently redistribute latent heat and maintain a uniform crystallization front; in ultrasmall systems, Laplace pressure suppresses convection and leads to size-dependent nucleation thresholds.

5. Scaling Laws, Model Frameworks, and Field Evolution

Crystallization-induced convection is quantitatively described by coupled advection–diffusion–phase-change models, mixing-length theory (MLT) extended to include composition gradients and thermal diffusion, and in some systems (e.g., white dwarfs) by magnetohydrodynamic (MHD) dynamo scaling:

• MLT Extended for Composition: Incorporates an extra term in the buoyancy and convective flux for composition, leading to a quintic polynomial for the convective efficiency parameter and naturally reproducing both thermally and compositionally driven regimes (Castro-Tapia et al., 2 Feb 2024).
• Thermal and Compositional Fluxes: The convective heat and composition fluxes can be written as $F_H \sim \rho v_c c_P DT$ and $F_X \sim \rho v_c DX$. For Pe $\ll 1$, $F_H/F_X$ remains invariant.
• Dynamo Scaling: Under MAC balance, the field strength scales as $$B \sim v_c^{3/4}(2\Omega H_P)^{1/4}(4\pi\rho)^{1/2}$$, predicting saturation-level fields in the efficient phase but order-of-magnitude reduction at the surface due to later Ohmic and turbulent magnetic diffusion (Castro-Tapia et al., 2 Feb 2024, Castro-Tapia et al., 3 Jun 2024).
• Evolutionary Effects: As the solid fraction grows, electrical conductivity of the core increases, slowing Ohmic diffusion. This "freezes in" the internal field and prevents its efficient outward transport, strongly limiting the final observable field (Castro-Tapia et al., 3 Jun 2024).

6. Applications, Limitations, and Astrophysical/Materials Implications

Crystallization-induced convection underpins the understanding of diverse phenomena:

• Geophysics: Explains large-scale convective translation in planetary cores, hemispherical asymmetries in Earth’s inner core, F-layer stratification, and possibly coupling to dynamo/magnetic processes (Deguen, 2013, Deguen et al., 2013).
• Astrophysics: Connects white dwarf and neutron star cooling, core magnetism, and the timing of observable magnetic field "breakout" to the initial C/O profile and crystallization-front propagation (Blatman et al., 2023).
• Materials and Nanotechnology: Determines microstructure evolution, defect clustering, and uniformity in LIFT printing, colloidal crystallization, and nanoparticle-doped fluid systems via controlled convective and phase behaviors (Liang et al., 6 Apr 2025, McElligott et al., 11 Sep 2024).
• Crystallizer Design: Hybrid lattice Boltzmann and finite-difference models quantify the impact of advection, local heat generation, forced convection, and growth asymmetry, supporting the engineering of baffle positions or flow rates for habit control in fine chemical and pharmaceutical crystallization (Tan et al., 2023).

Important limitations include the strong dependence of magnetic field generation on the ratio of conduction to convection (Pe), initial convective mantle depth, and phase evolution kinetics. Frequent model assumptions of well-mixed layers or instant latent heat removal may overestimate the convective efficiency, especially in stellar or planetary contexts where Ohmic diffusive timescales and solid-phase conductivity arrest further field amplification or transport (Castro-Tapia et al., 3 Jun 2024).

7. Outlook and Open Problems

While key scaling relations and theoretical frameworks are now established, uncertainties remain regarding:

• The transition kinetics between efficient (overturning) and slow (thermohaline) convection in evolving interiors.
• Feedback among phase separation, nonlinear convection, and magnetic field growth or diffusion, particularly in multidimensional or turbulent regimes.
• The determination of initial compositional profiles and their influence on the timing and morphology of convective-magnetic breakout events in stellar remnants.
• Nanoconfinement and surface effects on nucleation, latent heat redistribution, and convective flows in meso- and nanoscale droplets.

Ongoing work integrates multiphysics numerical modeling, microfluidic experimentation, and astrophysical observation to refine understanding of crystallization-induced convection across scales. The phenomenon remains a paradigmatic example of the coupling of phase transitions and fluid dynamics with ramifications in planetary science, astrophysics, and advanced material fabrication.