Modes and break periods of electrowetting liquid bridge

In this paper, we propose a microscale liquid oscillator using electrowetting-on-dielectric (EWOD). Specifically, a mesoscale liquid bridge (LB) between two horizontal surfaces with EWOD is considered. When EWOD is applied, the solid surface becomes more hydrophilic, and hence the contact angle (CA) is reduced. Following the activation of EWOD, the LB can remain connected or it can break into either symmetric or asymmetric shapes depending on the initial liquid volume and wettability of the two surfaces. The LB dynamics activated by EWOD is studied using the multibody dissipative particle dynamics (MDPD) method. Our numerical results show that the behavior of an LB under EWOD can be interpreted via three modes. In the first mode, the LB does not break after applying EWOD. In the second mode, the LB breaks and does not reform. The third mode happens when, depending on the interplay of the volume of the liquid and CA manipulation, the LB continuously breaks, recoils, and reforms. For asymmetric cases, it was observed that the LB may completely detach from one surface and may not reform. It was also observed that decreasing the wettability of a surface, for cases with a continuous breaking and reformation behavior, increases the connecting time interval and decreases the breaking time interval in one break-reform cycle. The results provided in this investigation facilitate fundamental understanding of LB dynamics and their application for the design of microscale liquid oscillators using EWOD.

Figure 1

Schematic of the liquid bridge and its disruption due to electrowettability phenomenon. (a) Symmetric and (b) asymmetric induced electrowetting. (c) The solution algorithm of MDPD, and the present LB-EWOD models. The LB-EWOD examples in (c) include the configuration and dimensional parameters of the present MDPD simulation, and two cases when $B_r=0$ and $B_r=1$.

Figure 2

Comparison of the contact angle of a droplet on a wall using the present MDPD method and provided data by Chang et al. [56].

Figure 3

Center of mass (CM) for different models of the electro-wetting bridge. (a–c) Modes 1 to 3, respectively. (d) Example unstable liquid bridge for high original CA. The CM position shown as red, blue, and green curves are for the complete bridge and the upper and lower portions of the droplet, respectively.

Figure 4

Dynamic contact angles for different models of the electro-wetting bridge. (a–c) Modes 1 to 3, respectively. (d) Example unstable liquid bridge for certain original CAs.

Figure 5

Mode maps for three different cases. (a) Case 1 and (b) Cases 2 and 3. Blue squares indicate Mode 1; Red deltas indicate Mode 2; Green circles indicate Mode 3; Black diamonds indicate unstable liquid bridge.

Figure 6

Period of complete bridge, ${\tau }_c$, bridge break, ${\tau }_b$, and one cycle, ${\tau }_t$, for Mode 3 using different liquid bridge height, $H_{\mathrm{LB}}$. For all cases, $H_{\mathrm{LB}}^3/N=0.253$ and $A_{s\ell }^i=-30({\theta }^i={81}^{\circ }),A_{s\ell }^f=-40({\theta }^f={26}^{\circ })$, as shown in mode's map.

Figure 7

Break height, H' (a), and mass ratio, $R$ (b), for Mode 3 using different cases and $A_{s\ell }^i\left({\theta }^i\right)$. Red square, green triangle, and blue diamond are for Cases 1 to 3, respectively. For all cases, $A_{s\ell }^f=-40\left({\theta }^f={26}^{\circ }\right)$ as shown in mode map.

Figure 8

Center of mass (CM) for Case 1 using $A_{s\ell }^i=-25\left({\theta }^i={107}^{\circ }\right)$ and $A_{s\ell }^f=-40({\theta }^f={26}^{\circ })$. (a) The different behavior of the liquid bridge at different times due to the effect of randomness originating from the smaller number of liquid beads compared with other cases. (b) A detailed illustration of the cycles.

Figure 9

Center of mass (CM) for two different asymmetric case studies (a, c), and an illustration of one cycle for each case (b, d).

Figure 10

Period of complete bridge, ${\tau }_c$, bridge break, ${\tau }_b$, and one cycle, ${\tau }_t$, for subcase 4 with different height, $H_{\mathrm{LB}}$, and $H_{\mathrm{LB}}^3/N=0.253$.

Figure 11

Break height (a) and mass ratio (b) for Mode 3 in Cases 2 and 3 with wettability given in Table 5. Green triangles and blue diamonds are for cases 2 and 3, respectively.