Freezing of axisymmetric liquid bridges

The solidification of liquid bridges plays an important role in many applications. Previous research on droplet solidification has found that supercooling and gravity have certain effects on physical properties and droplet shape during solidification. In this paper, axisymmetric water bridge solidification is studied from theory and experiment. A fixed contact line model, considering both the effects of supercooling and gravity, is developed to describe the freezing behavior of a liquid bridge. In the experiment, two horizontal cold coaxial circular end plates are cooled simultaneously, and a liquid bridge starts freezing from the contact surfaces with the end plates and finally forms an asymmetric ice ring in the middle. A correlation expression of the three-phase contact line height evolution determined by theory and experiment is developed. Comparisons between the calculation and experiment are made, and good agreement is obtained in the first freezing stage.

Figure 1

Schematic of experimental system: (A) computer, (B) CCD camera, (C) long distance microscope, (D) ring cold light, (E) power supply, (F) cooling bath, (G) semiconductor cooler, (H) copper plate, (I) thermocouple, (J) copper end plate, and (K) temperature acquisition unit.

Figure 2

Schematic of liquid bridge between equal end plates: (a) nucleation-recalescence; (b) freezing stage. $T_F$ is the mushy zone temperature, and $T_C$ is the end plate temperature, which can be regarded as the nucleation temperature $T_N$.

Figure 3

Evolution of heights and radii of upper and lower freezing fronts of liquid bridges with different shapes: (a) slender ($R_p=1\mathrm{mm},H=2.5\mathrm{mm},V_0=5\mu \mathrm{l}$), (b) undulation ($R_p=1\mathrm{mm},H=2.5\mathrm{mm},V_0=7.5\mu \mathrm{l}$), and (c) rotund ($R_p=1\mathrm{mm},H=2.5\mathrm{mm},V_0=10\mu \mathrm{l}$), during the freezing process. The insets represent the shapes of the liquid bridges before freezing.

Figure 4

Freezing process of a liquid bridge ($R_p=1\mathrm{mm},H=2.75\mathrm{mm},V_0=5.5\mu \mathrm{l}$). (a)–(d) Nucleation-recalescence stage; (d)–(k) freezing stage; (l) sketch of ice ring. Red arrow points out the nucleation position and yellow arrows indicate the direction of recalescence, while yellow circle in (h) indicates the single azimuthal bulge.

Figure 5

Evolution of liquid bridge profile during freezing process ($R_p=1\mathrm{mm},H=2.75\mathrm{mm},V_0=5.5\mu \mathrm{l}$).

Figure 6

Evolution of liquid bridge volume and expansion rate during freezing process ($R_p=1\mathrm{mm},H=2.75\mathrm{mm},V_0=5.5\mu \mathrm{l}$).

Figure 7

Evolution of freezing front average heights at different liquid bridge volumes and nucleation temperatures during the first freezing stage ($R_p=1\mathrm{mm},H=2.5\mathrm{mm}$): (a) experimental data; (b) normalized results and fitting results. The black and red dotted fitting lines in (b) are $X=0.92\left(R^2=0.9932\right)$ and $1\left(R^2=0.9911\right)$, respectively.

Figure 8

The parameters of liquid bridges when the single azimuthal bulge is about to form are depicted on the stability diagram of a liquid bridge. The experimental points are basically distributed on the stability limit of the liquid bridge, so it can be judged that the liquid bridges are unstable.

Figure 9

Evolution of liquid bridge profiles obtained from calculation and experiment ($R_p=1\mathrm{mm}$, $H=2\mathrm{mm}$, $V_0=5.5\mu \mathrm{l}$).

Figure 10

Comparison between calculation and experiment of the evolution of triple-phase contact line height and radius ($R_p=1\mathrm{mm}$, $H=2\mathrm{mm}$, $V_0=5.5\mu \mathrm{l}$).