Coalescence-induced droplet detachment on low-adhesion surfaces: A three-phase system study

Coalescing water droplets on superhydrophobic surfaces can detach from the surface without the aid of any external forces. This self-propelled droplet detachment mechanism is useful in many applications, such as phase change heat transfer enhancement, self-cleaning surfaces, and anti-icing and antidew coatings. In this article, the coalescence-induced droplet jumping in a three-phase system is numerically investigated. The gaps between the surface structures are filled with a liquid that is immiscible with water, e.g., lubricant. A mass-conserving lattice Boltzmann method is implemented to study the effects of several parameters, such as interfacial tensions, droplet size, and surface wettability on the jumping process. The numerical results show that for relatively high values of lubricant-water interfacial tensions and large surface-water contact angles ($>{150}^{\circ }$) the water droplets are capable of detaching. The critical droplet size for jumping is also highly dependent on the lubricant-water interfacial properties. The results of this study provide insights into the fluid-fluid and fluid-solid interactions and shed light on the underlying mechanisms involved in the droplet coalescence process on such surfaces.

Figure 1

Different equilibrium states for a droplet with an initial contact angle of ${90}^{\circ }$; the lines represent ${\varphi }_1=0.5$.

Figure 2

Simulated and analytical dimensionless droplet height for different equilibrium contact angles. The solid black line shows the theory [Eq. (45)], and the square symbols show the simulation results.

Figure 3

Capillary rise of liquid under zero gravity condition. The solid line shows the theoretical height given by the Lucas-Washburn equation, and the obtained numerical height is shown by square symbols. $R_t=0.1\mathrm{mm}, {\theta }^{\mathrm{eq}}={47}^{\circ }, {\eta }_l=6\times {10}^{-4}\mathrm{Pa}\times \mathrm{s}, {\rho }_l=750\mathrm{kg}\times {\mathrm{m}}^{-3}, {\sigma }_{lg}=2.5\times {10}^{-3}\mathrm{N}\times {\mathrm{m}}^{-1}$. $l$ denotes the liquid properties.

Figure 4

Schematic of the problem setup for (a) two-phase system and (b) three-phase system.

Figure 5

Time evolution of coalescence-induced droplet jumping for the water-air system, ${\theta }_1^{\mathrm{eq}}={160}^{\circ }$ and $\mathrm{Oh}=0.017$.

Figure 6

(a) Droplet jumping velocity as a function of initial droplet radius. The numerical result is shown by the solid line with square symbols, the triangles represent the experimental results by Ref. [10], and the dashed line is the theoretical value. (b) Dimensionless droplet jumping velocity as a function of initial droplet radius.

Figure 7

Snapshots of droplet shape evolution in water-lubricant-air system for ${\sigma }_{12}^{*}=0.75$ and ${\sigma }_{23}^{*}=0.4.$

Figure 8

Time evolution of the dimensionless droplet velocity and stages of the jumping process before departure in the three-phase system for ${\sigma }_{12}^{*}=0.75$ and ${\sigma }_{23}^{*}=0.4$.

Figure 9

Dimensionless droplet velocity in the three-phase system for ${\sigma }_{23}^{*}=0.4$ and ${\sigma }_{12}^{*}=0.7–0.95$.

Figure 10

Dimensionless droplet velocity in the three-phase system for ${\sigma }_{12}^{*}=0.9$ and ${\sigma }_{23}^{*}=0.4–0.7$.

Figure 11

Effect of initial droplet radius on dimensionless droplet velocity in the three-phase system for ${\sigma }_{12}^{*}=0.8$ and ${\sigma }_{23}^{*}=0.4.$

Figure 12

Dimensionless droplet jumping velocity as a function of initial droplet radius for the three-phase system.

Figure 13

The effect of surface wettability on jumping velocity at $\mathrm{Oh}=0.017$. The surface wettability is quantified by specifying the equilibrium contact angle ${\theta }^{\mathrm{eq}}$, which is varied from $140{}^{\circ }$ to $170{}^{\circ }$.

Figure 14

The effect of lubricant viscosity on jumping velocity of the merged droplet.

Figure 15

Dimensionless droplet velocity $U_j^{*}$, comparison between two-phase and three-phase systems. $U_j^{*}$ is shown by the solid line for the three-phase systems, and for the two-phase system is shown by the dashed line. The work of adhesion is also shown for the two cases.

Figure 16

Velocity field in two-phase and three-phase systems. The two-phase and three-phase systems are shown in the left and right halves of each frame, respectively. The dotted blue line is the droplet shape in the two-phase, and the solid red is for the three-phase system. The lines represent ${\varphi }_1=0.5$.