Consistent simulation of droplet evaporation based on the phase-field multiphase lattice Boltzmann method

In the present article, we extend and generalize our previous article [H. Safari, M. H. Rahimian, and M. Krafczyk, Phys. Rev. E 88, 013304 (2013)] to include the gradient of the vapor concentration at the liquid-vapor interface as the driving force for vaporization allowing the evaporation from the phase interface to work for arbitrary temperatures. The lattice Boltzmann phase-field multiphase modeling approach with a suitable source term, accounting for the effect of the phase change on the velocity field, is used to solve the two-phase flow field. The modified convective Cahn-Hilliard equation is employed to reconstruct the dynamics of the interface topology. The coupling between the vapor concentration and temperature field at the interface is modeled by the well-known Clausius-Clapeyron correlation. Numerous validation tests including one-dimensional and two-dimensional cases are carried out to demonstrate the consistency of the presented model. Results show that the model is able to predict the flow features around and inside an evaporating droplet quantitatively in quiescent as well as convective environments.

Figure 1

Schematic of the one-dimensional evaporation in an open end container.

Figure 2

Comparison between analytical solution and simulation results of nondimensional evaporative mass flux for different grid sizes.

Figure 3

Comparison between different strategies in solving advection-diffusion transport equations during evaporation.

Figure 4

The average nondimensional value of $Y_v\nabla ·\mathbf{u}$ inside the phase interface for various mass transfer numbers.

Figure 5

The average ratio of $\frac{\frac{D_{vg}}{c_s^2}\frac{\partial }{\partial t}\nabla ·\left(Y_v\mathbf{u}\right)}{Y_v\nabla ·\mathbf{u}}$ across the interface at (a) the initial stages of the simulation and (b) the developed phase of evaporation.

Figure 6

Schematic of the computational domain for nonisothermal static droplet evaporation.

Figure 7

Velocity vectors around the droplet interface ($t^{*}=1.7$).

Figure 8

(a) Temperature field and (b) Mass fraction field ($t^{*}=1.7$).

Figure 9

The temperature profile at different times for the drop and surrounding air.

Figure 10

Comparison between the computed wet-bulb temperature and the psychrometric chart value at the constant relative humidity of 40%.

Figure 11

Comparison between the computed wet-bulb temperature and the psychrometric chart value at the constant dry-bulb temperature of $298.15\mathrm{K}$.

Figure 12

Schematic view of the computational domain.

Figure 13

Comparison of the predicted Sherwood number and the empirical correlation.

Figure 14

Relative velocity streamlines and droplet shape for different dimensionless times.

Figure 15

Temperature field for surrounding air and droplet at various dimensionless times.