Marangoni-driven freezing dynamics of supercooled binary droplets

TL;DR

The paper addresses how concentration gradients in supercooled ethanol–water droplets influence freezing dynamics. It combines experiments with a concentration-dependent model to predict the migration speed of dispersed ice particles, $v_{\text{ice}}$, and their growth rate, $\dot{R}_{\text{ice}}$, via solutal Marangoni flow and latent-heat balance, respectively, and demonstrates that the final wrapping state depends on ethanol concentration $c_0$ through the supercooling $\Delta T=T_m(c_0)-T_s$. Key scalings $v_{\text{ice}}/v_{\text{diff}} \sim Ma$ and $\dot{R}_{\text{ice}}/v_{\text{diff}} \sim Ma\cdot St$ are validated, with $Ma=\frac{\Delta\gamma h}{2\mu D_0}$ and $St=\frac{c_p\Delta T}{L_f}$. The findings provide mechanistic insight into interfacial hydrodynamics during multicomponent phase transitions and suggest routes to control droplet-based solidification patterns in engineering applications.

Abstract

Solidification of droplets is of great importance to various technological applications, drawing considerable attention from scientists aiming to unravel the fundamental physical mechanisms. In the case of multicomponent droplets undergoing solidification, the emergence of concentration gradients may trigger significant interfacial flows that dominate the freezing dynamics. Here, we experimentally investigate the fascinating interfacial freezing dynamics of supercooled ethanol-water droplets, accompanied with the migration and growth of massive ice particles. We reveal that these unique freezing dynamics are driven by solidification-induced solutal Marangoni flow within the droplets. Our model, which incorporates the temperature- and concentration-dependent properties of the ethanol-water mixture, quantitatively predicts both the migration velocity and the growth rate of the ice particles. The former is determined by the solutal Marangoni flow velocity, while the latter is governed by a balance between the latent heat release and the enhanced thermal dissipation by the Marangoni flow. Moreover, we show that the final wrapping state of droplets can be modulated by the concentration of ethanol. Our findings may pave the way for novel insights into the physicochemical hydrodynamics of multicomponent liquids undergoing phase transitions.

Figures (12)

• Figure 1: Schematic diagrams illustrating droplet freezing dynamics. (a) For warm droplets, the liquid phase temperature $T_\text{d}$ remains above the freezing point $T_\text{m}$, so the released latent heat at the freezing front is primarily dissipated via ice-phase conduction. (b) In contrast, supercooled droplets (with $T_\text{d}<T_\text{m}$) enable additional heat dissipation through the supercooled liquid during freezing. (c) Substrate temperature profiles over time comparing warm (blue) and supercooled (red) droplet freezing scenarios. (d) Temperature profiles along the dashed line in (a,b) during solidification for warm (blue) and supercooled (red) droplet freezing, showing distinct thermal behaviors.
• Figure 2: Schematic view of the experimental setup. In the experiments, the droplet is gently deposited onto the copper substrate, with both the droplet and substrate preconditioned to room temperature. Subsequently, the substrate undergoes progressive cooling down to $T_\text{s}=-20 ^\circ$C by a semiconductor cooler.
• Figure 3: Side view for the freezing dynamics of supercooled droplets. (a) In the case of pure water droplets ($V_0=150~\upmu$L), the explosive nucleation phenomena (recalescence) is observed, when the substrate temperature $T_\text{s}$ is cooled down to about $-14 ^\circ$C. (b) By contrast, the ethanol-water droplets ($c_0=0.05$, $V_0=150~\upmu$L) can remain unfrozen for several minutes, with the substrate temperature maintaining $T_\text{s}=-20 ^\circ$C. Subsequently, dispersed ice particles are observed at the droplet-air interface, migrating uni-directionally and growing slowly, which is quite different from that of pure water case.
• Figure 4: Top-down view for the freezing dynamics of supercooled ethanol-water droplets. (a,b) Sketch for two typical freezing processes observed in experiments, corresponding to the experimental snapshots (c,d). Since the ice nucleation process is stochastic, it can occur at the solid-liquid interface (a) and near the solid-liquid-air triple point (b). (c) When the ice nucleation occurs at the solid-liquid interface ($c_0=0.15$, $V_0=500~\upmu$L, $T_\text{s}=-20~^\circ$C), an expanding ice disk can be observed from the top-down view. Subsequently, the migrating ice particles are observed, moving away from the center of the ice disk. (d) When the ice nucleation occurs near the solid-liquid-air triple point ($c_0=0.20$, $V_0=500~\upmu$L, $T_\text{s}=-20~^\circ$C), the ice disk becomes much smaller than that of the former case. Subsequently, the migrating ice particles are observed, moving towards the other side of the droplet.
• Figure 5: Thermal imaging for the freezing supercooled ethanol-water droplets. (a) Top-down view for the case of ice nucleates at the solid-liquid interface ($c_0=0.15$, $V_0=500~\upmu$L, $T_\text{s}=-20~^\circ$C). (b) Top-down view for the case of ice nucleates near the solid-liquid-air triple point ($c_0=0.20$, $V_0=500~\upmu$L, $T_\text{s}=-20~^\circ$C). (c,d) Temperature distribution along the white dash line in (a,b), respectively. The temperature of the supercooled liquid $T_\text{d}$ is almost equal to the substrate temperature $T_\text{s}=-20~^\circ$C. The white dotted lines in (a,b) and the red circles in (c,d) for the ice-water interface.