Microscopic and Macroscopic Structure of the Precursor Layer in Spreading Viscous Drops

We study the spreading of viscous nonvolatile liquids on smooth horizontal substrates using a phase-modulated interference microscope with sufficient dynamic range to enable the simultaneous measurement of both the inner (“microscopic”) length scale and the outer (“macroscopic”) flow scale in addition to the intermediate matching region. The resulting measurements of both the apparent contact angle and the lateral scale of the precursor “wetting” film agree quantitatively with theoretical predictions for a van der Waal’s liquid over a wide range of capillary numbers.

Figure 1

Schematic of macroscopic and microscopic features in the vicinity of an advancing contact line of a perfectly wetting van der Waals fluid spreading slowly over a smooth dry substrate.

Figure 2

Evolution in the profile of a silicone oil drop spreading on a smooth dry silicon substrate at $Ca=2\times {10}^{-6}$. Symbols (○) show the local thickness of the drop (in $\mu \mathrm{m}$) and the solid line is the visibility of the interference fringes, $m$. The inset shows an enlarged view of the precursor film detected in front of the moving contact line. Each symbol is drawn to the scale of the lateral resolution of the psLFI system ($\Delta x\sim \pm 0.8\mu \mathrm{m}$).

Figure 3

(a) Drop profile, $h(x)$, and the spatial derivative, $dh/dx$, for different values of capillary number ($Ca=1\times {10}^{-4}$ and $Ca=7\times {10}^{-4}$). The maximum value of the slope corresponds to the macroscopic dynamic contact angle, ${\theta }_a$. (b) Dynamic contact angle, ${\theta }_a$, as a function of capillary number. The inset shows the de Gennes model fit to the same set of data (solid line) when the reduced angle ${\theta }_a^3/Ca$ is plotted as a function of $\ln (Ca)$. The slope of the solid line is $1/3$.

Figure 4

Length of the precursor film, $L_P$ (in meters), as a function of capillary number. The solid line is the regression to the experimental results (●), $L_P=7.2\times {10}^{-10}C{a}^{-0.98\pm 0.16}$, and the dashed line is the theoretical prediction for an “adiabatic” precursor layer, $L_P=6.1\times {10}^{-10}C{a}^{-1}$. The dash-dotted line is the diffraction limited lateral resolution of our system. The inset shows the average thickness of the precursor film, $H_P$, as a function of capillary number, $Ca$.