Pinning-depinning of the contact line during drop evaporation on textured surfaces: A lattice Boltzmann study

The evaporation of the liquid droplet on a structured surface is numerically investigated using the lattice Boltzmann method. Simulations are carried out for different contact angles and pillar widths. From the simulation for the Cassie state, it is found that the evaporation starts in a pinned contact line mode. Then, when the droplet reaches the receding state, the contact line jumps to the neighboring pillar. Also, the depinning force decreases with increasing the contact angle or the pillar width. In the Wenzel state, the droplet contact line remains on the initial pillar for all of its lifetime.

Figure 1

Boundary conditions and pillar properties.

Figure 2

Variation of the droplet height with contact angle. Solid line is given by Eq. (41) and triangular symbol shows the numerical result.

Figure 3

Equilibrium shape of the droplet, (a) in Wenzel state and (b) in Cassie state.

Figure 4

Comparison of the numerical results with $D^2$ law.

Figure 5

Evaporation of the droplet on the pillars with $\theta =100$, $\mathrm{St}=0.4$ on a surface with $h=15\mathrm{lu}$, $w=4\mathrm{lu}$, and $g=4\mathrm{lu}$.

Figure 6

Streamlines during evaporation of the droplet on the pillars with $\theta =100$, $\mathrm{St}=0.4$ on a surface with $h=15\mathrm{lu}$, $w=4\mathrm{lu}$, and $g=4\mathrm{lu}$.

Figure 7

Evaporation of the droplet initially in the Cassie state on substrate with $h=15\mathrm{lu}$, $w=4\mathrm{lu}$, $g=4\mathrm{lu}$ and $\theta ={100}^{\circ }$. (a) Variation of contact angle and contact radius. (b) Initial position of the droplet. Contact line is pinned on the pillar. (c) Evaporation causes change in contact angle, but contact line is still stuck to the pillar. (d) Slipping starts and depinning occurs. (e) Change in the contact line position is clear.

Figure 8

Evaporation for the droplet initially in the Cassie state on substrate with $h=15\mathrm{lu}$, $w=4\mathrm{lu}$, $g=4\mathrm{lu}$, and $\theta ={120}^{\circ }$.

Figure 9

Variation in ${\theta }_r$, ${\theta }_a$, and $F_D$ with contact angle.

Figure 10

Nondimensional mass versus time in two different contact angles.

Figure 11

Evaporation for the droplet initially in the Cassie state on substrate with $h=15\mathrm{lu}$, $w=8\mathrm{lu}$, $g=4\mathrm{lu}$, and $\theta ={100}^{\circ }$. (a) Variation of contact angle and contact radius. (b) Initial position of the droplet. Contact line is pinned on pillar. (c) Slipping starts and depinning occurs. Droplet goes to the CCA mode. (d) Droplet slips on the pillar in CCA mode.

Figure 12

Variation in ${\theta }_r$, ${\theta }_a$, and $F_D$ with pillar width.

Figure 13

Streamlines during evaporation of the droplet in the Wenzel state, with $\theta =120$, $\mathrm{St}=0.4$ on a surface with $h=15\mathrm{lu}$, $w=4\mathrm{lu}$, and $g=4\mathrm{lu}$.

Figure 14

Evaporation for the droplet initially in the Wenzel state on substrate with $h=15\mathrm{lu},w=4\mathrm{lu},g=4\mathrm{lu}$, and $\theta ={120}^{\circ }$. (a) Variation of contact angle and contact radius. (b) Initial position of the droplet. Contact line is pinned on pillar. (c) Contact line slips very slightly toward the inner corner of the pillar. (d) Droplet slips on the pillar. (e) Contact line is stuck and contact angle decreases over time.

Figure 15

Evaporation for the droplet initially in the Wenzel state on substrate with $h=15\mathrm{lu}$, $w=4\mathrm{lu}$, $g=4\mathrm{lu}$, and $\theta ={100}^{\circ }$.