Dissolution process of a single bubble under pressure with a large-density-ratio multicomponent multiphase lattice Boltzmann model

A large-density-ratio and tunable-viscosity-ratio multicomponent multiphase pseudopotential lattice Boltzmann model is used to study the dissolution process of a bubble under pressure. The multi-relaxation-time collision operator, exact-difference-method external force scheme, and scaling coefficient $k$ are applied to ensure the numerical stability of the model. The influence of $k$ in the equation of state (EOS) and intermolecule interaction strength on the stationary bubble evolution process are discussed, and the effect of $k$ on thermodynamic consistency is also analyzed. The results indicate that adjusting the scaling coefficient in the EOS changes the surface tension and interface thickness, and that the gas-liquid interface width $w$ is proportional to $1/\sqrt{k}$. Considering the effect of $k$ on the surface tension, interface thickness, and thermodynamic consistency, the scaling coefficient should be between 0.6 and 1. Furthermore, the dissolution process of a single bubble under pressure is studied using the developed model, and it is found that the dissolution mass and concentration of dissolved gas increase linearly with increases in the pressure difference, and that the concentration of dissolved gas is proportional to the gas pressure after the fluid system reaches equilibrium. These results are consistent with Henry's law.

Figure 1

Schematic diagram for Laplace’s law and bubble dissolution, where the rectangular area with dashed box is the computational domain.

Figure 2

Density distribution after bubble reaches equilibrium ($k=0.6,R_0=50$): (a) component 1 density distribution, (b) component 2 density distribution, and (c) total density distribution.

Figure 3

Relationship between pressure difference inside and outside the bubble and drop radii for five different $k$ values.

Figure 4

The distribution of (a) density field of component 1 and component 2 with the different intermolecule interaction strength $G_{\alpha ,\alpha }$ at $y=100\mathrm{lu}$. The velocity distribution in the computation domain with (b)$G_{\alpha ,\alpha }=-0.5$, (c)$G_{\alpha ,\alpha }=-1$, and (d)$G_{\alpha ,\alpha }=-40$.

Figure 5

The distribution of (a) density field of component 1 and component 2 with the different intermolecule interaction strength $G_{\alpha ,\overline{\alpha }}$ at $y=100\mathrm{lu}$. The velocity distribution in the computation domain with (b)$G_{\alpha ,\overline{\alpha }}=0.0002$, (c)$G_{\alpha ,\overline{\alpha }}=0.0003$, and (d)$G_{\alpha ,\overline{\alpha }}=0.0005$.

Figure 6

Density profile after bubble reaches equilibrium of different components at $y=100\mathrm{lu}$ with different $k$ values.

Figure 7

Comparison of thermodynamic curves in theoretical solution with the EDM force scheme combined with different scale coefficient $k$ values.

Figure 8

Pressure distribution after bubble reaches equilibrium at $y=100\mathrm{lu}$ with different $k$ values.

Figure 9

Distribution of spurious currents with $R_0=50$ with different values of $k$: (a) $k=0.05$, (b) $k=0.3$, (c) $k=0.6$, and (d) $k=1$.

Figure 10

Relationship between interface thickness or surface tension and scaling coefficient $k$ of EOS .

Figure 11

Relationship between interface thickness and the scaling coefficient $k$ of the EOS.

Figure 12

Chemical potential distribution after bubble reaches the equilibrium at $y=100\mathrm{lu}$ with different $k$ values.

Figure 13

(a) The comparison of the surface obtained from theoretical analysis and Laplace law. (b) The contribution of the intermolecule and intramolecule interaction forces on surface tension.

Figure 14

Influence of different gas-liquid viscosity ratios on the gas and liquid component density distribution at $y=100\mathrm{lu}$: (a) variation of liquid viscosity; (b) variation of gas viscosity.

Figure 15

Velocity distribution of fluid system during bubble dissolution process with $k=0.6$ and $\mathrm{\Delta }p=0.01356\mathrm{mu}\mathrm{l}{\mathrm{u}}^{-1}\mathrm{t}{\mathrm{u}}^{-2}$ at different time steps: (a) $t=0$, (b) $t=1000\mathrm{tu}$, (c) $t=2000\mathrm{tu}$, (d) $t=3000\mathrm{tu}$, (e) $t=4000\mathrm{tu}$, and (f) $t=15000\mathrm{tu}$.

Figure 16

Variation in the radius of the bubble with time when $k=0.6$ and $\mathrm{\Delta }p=0.01356\mathrm{mu}\mathrm{l}{\mathrm{u}}^{-1}t{\mathrm{u}}^{-2}$.

Figure 17

Variation in dissolved gas mass with time when $k=0.6$ and $\mathrm{\Delta }p=0.01356\mathrm{mu}\mathrm{l}{\mathrm{u}}^{-1}\mathrm{t}{\mathrm{u}}^{-2}$.

Figure 18

Influence of initial pressure difference on gas component density, liquid component density, and total density at $y=100\mathrm{lu}$ ($k=0.6$): (a) gas component density distribution, (b) liquid component density distribution, and (c) total density distribution.

Figure 19

Relationship between the mass and concentration of dissolved gas and the initial pressure difference with $k=0.6$ and $\mathrm{\Delta }p=0.01356\mathrm{mu}\mathrm{l}{\mathrm{u}}^{-1}\mathrm{t}{\mathrm{u}}^{-2}$.

Figure 20

Relationship between the dissolved gas concentration and partial pressure of component 1 in the surrounding liquid after the fluid system reaches equilibrium.