Electric field-triggered Cassie-Baxter-Wenzel wetting transition on textured surface

Understanding the critical condition and mechanism of the droplet wetting transition between Cassie-Baxter state and Wenzel state triggered by an external electric field is of considerable importance because of its numerous applications in industry and engineering. However, such a wetting transition on a patterned surface is still not fully understood, e.g., the effects of electrowetting (EW) number, geometry of the patterned surfaces and droplet volume on the transition have not been systematically investigated. In this paper, we propose a theoretical model for the Cassie-Baxter-Wenzel wetting transition triggered by an external voltage applied to a droplet placed on a mirco-pillared surface or a porous substrate. It is found that the external field applied lowers the energy barrier for the droplet to cross over and complete the wetting transition. Our calculations also indicate that for a fixed droplet volume, the critical EW number (voltage) will increase (decrease) along with the surface roughness for a micropillar-patterned (porous) surface, and if the surface roughness is fixed, a small droplet tends to ease the critical EW condition for the transition. Besides, three-dimensional phase diagrams in terms of EW number, surface roughness, and droplet volume are constructed to illustrate the wetting transition. Our theoretical model can be used to explain the previous experimental results about the Cassie-Baxter-Wenzel wetting transition reported in the literature.

Figure 1

(a) Schematic 3D picture of a microstructured surface with cylindrical pillars of radius $R$, height $H$, and gap pitch $P$ on a periodic square lattice with pillar-to-pillar spacing $S$. Schematic (b) top view and (c) side view of a regular array of pores of radius $R$, depth $H$, gap pitch $P$, and center-to-center pore spacing $S$. Different wetting states of a droplet on a microtextured surface in the presence of an external electric voltage: (d) CB state, (e) intermediate composite state, and (f) W state.

Figure 2

(a) Variation of the total interfacial free energy with respect to the invading depth. (b) Theoretical wetting phase diagram in the parameter space spanned by $R$ and $S$ for a droplet placed on a micropillar-patterned surface.

Figure 3

Representative total interfacial free energies of the CB and the intermediate states of a droplet on a micropillar-patterned surface: $G_{\mathrm{CB}}$ and $G_{\mathrm{inter}}$, respectively, as a function of EW number. The inset shows their difference, $\mathrm{\Delta }G=G_{\mathrm{inter}}-G_{\mathrm{CB}}$, which gives the critical EW number (critical external electric voltage) for the wetting transition when $\mathrm{\Delta }G=0$.

Figure 4

The critical EW number ${\eta }_c$ for the CB-W transition vs (a) aspect ratio $R/H$, (b) surface roughness $r$, (c) solid fraction ${\varphi }_s$, and (d) $P/H$, where the black square dot curve and the red circle dot curve stand for micropillar- and pore-patterned surfaces, respectively.

Figure 5

The critical EW number ${\eta }_c$ for the CB-W transition vs droplet volume $V_0$, where the black square dot curve and the red circle dot curve represent micropillar- and pore-patterned surfaces, respectively.

Figure 6

3D phase diagrams in terms of the critical EW number ${\eta }_c$, surface roughness $r$, and droplet volume $V_0$ for (a) a micropillar-patterned surface and (b) a pore-patterned surface.

Figure 7

(a) Illustration of the side view of a droplet in the intermediate composite state with a sagging height and the contact angle between the liquid-vapor interface and the micropillar side walls; (b) the equivalent circle of the projection of the 3D liquid-air interface in a unit cell.