Bubble formation in freezing droplets

Water droplet icing on solid surfaces has been intensively studied in recent years but still with many mechanisms unrevealed. Here, we report a bubble formation phenomenon that always occurs in freezing droplets, from millimeter-sized sessile droplets to microscale condensed droplets, during icing and condensation frosting. In the second stage of icing (the first stage is nucleation and recalescence), air dissolved in liquid water is separated out in the ice front, forming many isolated bubbles. Coupled with the droplet icing physics, a theoretical model was proposed to predict the bubble formation and elucidate its influencing factors. Due to the bubble formation, the final ice droplet is actually a porous medium, rather than a complete solid ice. These results bring new insight into icing physics, helping modify icing models and improve anti-icing and deicing techniques.

Figure 1

(a) Direct observation of bubble formation during freezing of a sessile droplet from top view. In the second stage of icing, bubbles constantly appear. These bubbles are of micron scale. The partial enlarged drawing shows these bubbles more clearly. (b) Proof of bubble formation in freezing droplets via observing its melting process of an ice droplet from top view. From the partial enlarged drawings, one can see many tiny bubbles surrounding or embedded in the unmelted ice cover. (c) Proof of bubble formation in freezing droplets via observing the melting process from side view with many bubbles moving quickly from the unmelted ice cover.

Figure 2

(a) Direct observation of bubble formation in freezing droplets during condensation frosting. From the partial enlarged drawing, one can see the differences between the ice droplets behind the frost front and the water droplet ahead. Those tiny, dark-blue dots are bubbles entrapped in ice droplets. (b) Proof of bubble formation in freezing droplets during condensation frosting via observing the defrosting process. The partial enlarged drawing shows clearly that there are many bubbles (blue dots) embedded in the unmelted ice covers of droplets.

Figure 3

(a) Bubble formation mechanism determination through a controlled reicing process of a partially melted ice droplet. One can see bubbles constantly separated out in the ice front. (b) Schematic of bubble formation in freezing droplets. $h$ is the ice front height, $dh$ is the moving distance of the ice front during $dt$ time, $r$ is the ice front radius, and φ is the contact angle at the ice-water-gas triple line; $R$ is the droplet curvature radius, $b$ is the droplet base radius, and $b=R\sin \theta$, where θ is the surface contact angle.

Figure 4

(a) Variation of ice front height. We extracted the experimental results from the experiments by Marin et al. [9] and obtained the theoretical results by integrating Eq. (3). (b) Variation of ice front radius. The experimental results are from the experiments by Marin et al. [9] and the theoretical results are from Eq. (5). (c) Variation of bubble volume. For the experimental results, we obtained a 2D bubble area by processing the images captured by Marin et al. [9] and then transformed the 2D bubble area to 3D bubble volume through a mathematical process, while the theoretical bubble volume is an integration of Eq. (6).

Figure 5

(a) Calculation method of water droplet volume, $V_{\mathrm{water}}$, and ice droplet volume, $V_{\mathrm{ice}}$. The droplet profiles are extracted first and then integrations are performed along the $y$ axis to get the droplet volumes. The bubble volume fraction in an ice droplet is equal to $1-V_{\mathrm{water}}/\left(\nu V_{\mathrm{ice}}\right)$, where ν is the ratio of ice and water densities. (b) Bubble volume fraction data in ice droplets under different supercooling on surfaces S1 and S2.