Expediting viscous spreading with liquid-infused solids

Here we discuss how the use of textured liquid-infused solids can expedite the dynamics of spreading of viscous drops, when the subjacent oil layer is less viscous. We characterize the nature and amplitude of the effect, and the laws governing the spreading at short time. More generally, our findings affirm the universality of the early dynamics of viscous contact, found to hold for drops that coalesce, spread, or even, like here, slip on their substrate.

Figure 1

Top: Schematic of a glycerol drop with radius $R$ brought in contact (at $t=0$) with a transparent infused surface. Down: Top-view time lapse of $1\mu \mathrm{l}$ glycerol droplets spreading on a transparent LIS for oil viscosities ${\eta }_0=9\mathrm{mPa}\mathrm{s}, {\eta }_0=96\mathrm{mPa}\mathrm{s}$, and ${\eta }_o=970\mathrm{mPa}\mathrm{s}$, or on a hydrophobic glass slide (down row). We note that the contact, with radius $r$ and orange in the photos, propagates faster when the solid is infused; the lower the oil viscosity, the faster the wetting. For a more complete series of oil viscosities, see the Supplemental Material movie.

Figure 2

(a) Contact radius $r$ between a glycerol drop (volume $1\mu \mathrm{l}$) and its substrate, as a function of time $t$, either on a hydrophobic solid (gray data), or on a LIS with ${\eta }_0=5\mathrm{mPa}\mathrm{s}$ (red), $9\mathrm{mPa}\mathrm{s}$ (purple), $19\mathrm{mPa}\mathrm{s}$ (blue), $48\mathrm{mPa}\mathrm{s}$ (orange), $96\mathrm{mPa}\mathrm{s}$ (green), $485\mathrm{mPa}\mathrm{s}$ (yellow), and $970\mathrm{mPa}\mathrm{s}$ (brown). Solid lines show the ELS law (introduced in the text), $r=A(\gamma t/\eta )ln(R/r)$, where $A$ is a prefactor treated as an adjustable parameter in the fits. Its value is found to vary with the oil viscosity. (b) The same data collapse after normalizing $r$ by the drop radius $R$, and $t$ by the visco-capillary time $\tau =\eta R/A\gamma$ of glycerol including the parameter $A$. (c) Time ${\tau }_r$ observed to reach a given radius $r=100\mu \mathrm{m}$ (black data) or $r=200\mu \mathrm{m}$ (red data). Both plots exhibit the same trend and show that spreading is accelerated by a factor $\sim 4$ when the oil viscosity falls from 970 to $5\mathrm{mPa}\mathrm{s}$.

Figure 3

(a) Schematic of a viscous drop (in blue) contacting a flat substrate. Inset shows the initial profile of the drop (dotted line), and the profile after the solid-liquid contact has propagated by a distance $r$ at a velocity $V$ (full line). The characteristic height of the region close to the contact line is denoted as δ. (b) The slip factor $A$ extracted from the fits in Fig. 2 is plotted as a function of the ratio ${\eta }_{0}R/\eta h$ for glycerol drops (1 µl, black data and 4 µl, red data) spreading on a LIS with $h=20\mu \mathrm{m}$ and infused with oil of viscosity between 5 and $970\mathrm{mPa}\mathrm{s}$. The dashed line shows the behavior expected from the model.