Critical Conditions for Jumping Droplets

A droplet initially overstretched on a solid substrate pulls back to lower the contact area and may jump away from the substrate. The condition to realize such macroscopic behaviors is often dictated by microscopic characteristics, such as contact-line pinning, in nontrivial ways. Here we theoretically and experimentally reveal the hidden contribution of contact-line pinning in forming the critical condition for detachment of a droplet from a solid substrate, among other dominating hydrodynamical effects. Our results demonstrate the relation between classical theories on contact-line pinning and various droplet manipulating applications in microfluidics and bioprinting.

Figure 1

(a) Snapshots showing droplets retracting without jumping (top two panels), and droplets retracting and subsequently jumping from the substrate (bottom two panels). The scale bars represent 0.5 mm. (b) Plot showing the dependence of ${\theta }_{\mathrm{e}}$ (diamonds, left axis) and the corresponding jumping height $h$ (squares, right axis) on the applied voltage $V$. The viscosity of droplets is $\mu =1.0\mathrm{mPa}\mathrm{s}$.

Figure 2

Phase diagrams showing the detachable (open diamonds) and nondetachable regimes (solid diamonds) for droplets of (a) fixed viscosity ($\mu =1.0\mathrm{mPa}\mathrm{s}$), and (b) fixed radius ($R=0.5\mathrm{mm}$). The dashed-dotted line and dashed line are predictions of the transition to the detachable regime using Eq. (5) with $\gamma =55\mathrm{nm}$ and $\gamma =464\mathrm{nm}$, respectively.

Figure 3

(a) Snapshots showing the velocity field of a droplet having $R=0.5\mathrm{mm}$, $\mu =4.8\mathrm{mPa}\mathrm{s}$, and $\eta =1.28$ after the voltage is released. (b) Plot showing the dissipation rates at the boundary layer $\dot{T_{\mathrm{s}}}(t)$, at the CL $\dot{T_{\mathrm{c}}}(t)$, and in the bulk $\dot{T_{\mathrm{b}}}(t)$.

Figure 4

(a) A representative image obtained using AFM showing the surface morphology of a Teflon-coated substrate. (b) Plot showing the elevation $z$ along the dashed line in (a). (c) Phase diagram of detachable (open diamonds) and nondetachable (solid diamonds) regimes plotted using the variables $\eta \xi$ and $\alpha$. The shaded area shows the transitional extent caused by variation in $\gamma$.