Numerical investigation of homogeneous cavitation nucleation in a microchannel

The physics of nucleation in water is an important issue for many areas, ranging from biomedical to engineering applications. Within the present study, we investigate numerically homogeneous nucleation in a microchannel induced by shock reflection to gain a better understanding of the mechanism of homogeneous nucleation. The liquid expands due to the reflected shock and homogeneous cavitation nuclei are generated. An Eulerian-Lagrangian approach is employed for modeling this process in a microchanel. Two-dimensional axisymmetric Euler equations are solved for obtaining the time evolution of shock, gas bubble, and the ambient fluid. The dynamics of dispersed vapor bubbles is coupled with the surrounding fluid in a Lagrangian framework, describing bubble location and bubble size variation. Our results reproduce nuclei distributions at different stages of homogeneous nucleation and are in good agreement with experimental results. We obtain numerical data for the negative pressure that water can sustain under the process of homogeneous nucleation. An energy transformation description for the homogeneous nucleation inside a microchannel flow is derived and analyzed in detail.

Figure 1

Schematic of the simulational setup. The laser-induced shock interacts with a free surface from distance. To save computational cost, we compute only the 2Daxisymmetric computational domain (light-gray region) and interpolate the results into 3D.

Figure 2

Sketch for bubble location initialization. The black circle indicates the nucleation region, in which nuclei generate. At the end of each computational time step, we generate $△N_{\text{nuclei}}$ nuclei, shown as red in the right figure. The location is a random selection, and the probability of each computation cell is defined based on Eq. (15).

Figure 3

Simulation results for the shock front and bubble-fluid interface locations with resolutions of $\left[256\times 228\right], \left[512\times 256\right], \left[1024\times 512\right]$, and experimental results of Ref. [12].

Figure 4

Snapshots of the pressure field at different time instants after shock reflection at the free surface. White color indicates minimum (negative) pressure.

Figure 5

Nucleation rate for water at room temperature and extreme negative pressure in CNT and PCNT. (a) Nucleation rate of pressures from $-55$ to $-100$ MPa, when ${\upsilon }_l/{\upsilon }_g$ ratio equals 0.01, 0.012, 0.015, 0.02, 0.05, and 0.1. (b) Comparison of nucleation rate of CNT and PCNT with ${\upsilon }_l/{\upsilon }_g=0.012\text{and}0.015$.

Figure 6

Numerical simulation of homogeneous nucleation in comparison with the experimental results [12]. The first line contains the results at 58 ns and the second row shows the results at 74 ns. Three numerical simulations with ${\upsilon }_l/{\upsilon }_g$ being 0.0126, 0.0128, and 0.013 are shown.

Figure 7

Nuclei in the nucleation region at different instances plotted with the background fluid pressure field. 3D vapor bubble distributions at each time instance are shown in the second row, with the color indicating the bulk fluid pressure at the each nucleus location.

Figure 8

(a) Time history of the nuclei number with the indications of the three stages of a general homogeneous nucleation process. (b) Time history of the nuclei number in the shock-bubble interaction case; here, $N_{\text{max}}$ is the number of the nuclei formed until the last stage of nucleation.

Figure 9

The nuclei radius distributions and Weibull fits at 64 and $76\text{ns}$. Here, $R^{*}=R/R_{\text{mean}}$. At $64\text{ns}, R_{\text{mean}}=2.10\mu \text{m}, \eta =1.11,$ and $\beta =3.5$, and at $76\text{ns}, R_{\text{mean}}=3.74\mu \mathrm{m}, \eta =1.06,$ and $\beta =7.3$.

Figure 10

The fitted Weibull distributions for nuclei at different time seconds ranging from 64 to 84 ns.

Figure 11

Time evolution of mean radius $R_{\text{mean}}$, scale $\eta$, and $\beta$ shape parameters. In general, mean radius and shape parameter increase with time. In reverse, scale parameter decreases with increasing time, but with a small change.

Figure 12

Pressure evolution in the nucleation region along the distance from the gas bubble center at 58, 60, and 62 ns.

Figure 13

Maximum of the nuclei number $N_{\text{max}}$ increases when initial shock amplitude inside the gas bubble increases from 5.8 to 6.1 GPa.

Figure 14

Time dependence of the dimensionless parameter $N_{\text{nuclei}}/N_{\text{max}}$ for different shock amplitudes.