Coupled gas and bubble dynamics at the solidification front

TL;DR

The paper investigates how gas bubbles form, grow, and are engulfed at the solidification front under directional solidification with a fixed temperature gradient $G$ and variable front velocity $V_{sf}$. Using in situ cryo-confocal fluorescence microscopy on carbonated water in a constrained Hele-Shaw cell, the authors uncover a characteristic nucleation time $t_{plateau}$ governed by gas diffusion, front advancement, and nucleation/growth kinetics, and they estimate a homogeneous nucleation concentration $C_n^*$ around $8.4 \pm 3.1$ g/L. They find that roughly 73% of bubbles nucleate at the front (heterogeneous) while the rest nucleate in the bulk (likely homogeneous), with a mean bulk-nucleation distance $d_{sf}=27 \pm 25~\mu$m, and that nucleation dynamics and engulfment times $t_n$ and $t_e$ depend on $V_{sf}$ but the critical concentration remains largely velocity-independent. These results advance understanding of bubble-induced porosity control in solidification and offer quantitative benchmarks for managing gas entrapment in industrial processes.

Abstract

The formation and entrapment of gas bubbles during solidification significantly influence the microstructure and mechanical properties of materials, from metallic alloys to ice. While gas segregation at the solidification front is well-documented, the real-time dynamics of bubble nucleation, growth, and engulfment-and their dependence on solidification velocity-remain poorly understood. In this study, we use in situ cryo-confocal fluorescence microscopy to investigate the coupled gas-bubble dynamics at the solidification front of carbonated water, systematically varying the solidification velocity ($V = 1-20 μm/s$) while maintaining a constant thermal gradient ($G = 15 K/mm$). Our experiments reveal that bubble nucleation is governed by a characteristic nucleation time, which emerges from the interplay between gas diffusion ahead of the front, nucleation kinetics, and bubble growth, all competing with the advancing solidification front. These results allow us to estimate the critical gas concentration for bubbles nucleation in carbonated water. These results offer a detailed understanding of the mechanisms controlling bubble nucleation and entrapment during solidification at constant thermal gradient. They contribute to the development of strategies to control bubble formation in industrial processes where the presence of bubbles can either be detrimental or intentionally harnessed.

Figures (9)

• Figure 1: Experimental setup for cryo-confocal microscopy. A constant temperature gradient $\Delta T = T_h - T_c$ is created between the Peltier modules, specifically within the gap ($d=2mm$). The sample is translated through the temperature gradient at a constant velocity $V_{sf}$, thereby inducing ice crystal growth at a velocity $V_{sf}$. Consequently, the interface remains at a fixed position within the observation frame. The samples possess a thickness of $100\mu m$, and $T_f$ denotes the liquid's freezing point. Due to differing thermal conductivities, the temperature gradient in the ice is greater than in the liquid. Within the study, the reported magnitude of the temperature gradient $\Delta T$ corresponds to the temperature difference between the two Peltier modules.
• Figure 2: Representative images obtained through confocal cryomicroscopy. These time-lapse sequences of typical two-dimensional confocal images illustrate the freezing process of carbonated water. In each image, the lower, darker region corresponds to the ice phase, whereas the upper, lighter region corresponds to the liquid phase. Bubbles, being non-fluorescent, appear as dark regions within the liquid. (A) The time-lapse sequences display typical 2D cryo-confocal images demonstrating the nucleation, interaction, and engulfment of bubbles during the solidification process. Velocity of the solidification front $V_{sf} = 20 \mu m/s$. The bubble formation in these images is ascribed to nucleation induced by gas accumulation at the advancing solidification front, attributed to gas segregation. (B), (C) The sequences also illustrate the formation and evolution of cylindrical bubbles at the solidification front during solidification for $V_{sf} = 20 \mu m/s$ (B) and $V_{sf} = 1 \mu m/s$ (C).
• Figure 3: Evolution of the nucleation rate of bubbles as a function of the velocity of solidification $V_{sf}$. Measurement were done with similar sample and identical experimental conditions but with either an increasing or a decreasing solidification front velocity.
• Figure 4: Cumulative number of nucleated bubbles as a function of solidification duration under varying velocities. Multiple experiments were performed at solidification velocities of $V_{sf} = 10\mu m/s$ and $V_{sf} = 15\mu m/s$ to validate the reproducibility of the measurements. The plateau length indicates the lag period $t_{plateau}$ between successive bubble nucleation events.
• Figure 5: Evolution of the area occupied by bubbles and the sum of nucleated bubbles in the field of view of the microscope as a function of the duration of the solidification. (A), (C) Cumulative number of nucleated bubbles as a function of time (A) for $V_{sf}=5\mu m/s$ and (C) $V_{sf}=10\mu m/s$. (B), (D) Area occupied by nucleated bubble in the liquid as a function of the time for (B) $V_{sf}=5\mu m/s$ and (D) $V_{sf}=10\mu m/s$