Breakup Behavior of a Capillary Bridge on a Hydrophobic Stripe Separating Two Hydrophilic Stripes

The breakup dynamics of a capillary bridge on a hydrophobic area between two liquid filaments occupying two parallel hydrophilic stripes is studied experimentally. In addition calculations with the finite-element software \textit{Surface Evolver} are performed to obtain the corresponding stable minimal surfaces. Droplets of de-ionized water are placed on substrates with alternating hydrophilic and hydrophobic stripes of different width. Their volume decreases by evaporation. This results in a droplet shaped as the letter ``H'' covering two hydrophilic stripes separated by one hydrophobic stripe. The width of the capillary bridge $d(t)$ on the hydrophobic stripe during the breakup process is observed using a high-speed camera mounted on a bright-field microscope. The results of the experiments and the numerical studies show that the critical width $d_{\mathrm{crit}}$, indicating the point where the capillary bridge becomes unstable, mainly depends on the width ratio of the hydrophilic and hydrophobic stripes. It is found that the time derivative of $d(t)$ first decreases after $d_{\mathrm{crit}}$ has been reached. The final breakup dynamics then follows a $t^{\mathrm{2/3}}$ scaling.