Figure 1

(a) The initial condition for the experiments and the numerical simulations, where a drop held at the tip of a needle is brought into contact with a dry solid substrate. The dashed box in shows the field of view in the experiments. (b) and (c) The drop shape near the substrate at times $t=0.15$ ms, $t=0.60$ ms, and $t=0.90$ ms, after initial contact. Each panel shows a composite of experiment (left) and simulation (right). The black solid line in the right half of the panel that is plotted on top of the simulation result illustrates experimental interface shape. (b) A water drop spreading on an oxidized Si wafer (${\theta }_e={20}^{\circ }$, viscosity ${\mu }_{{\mathrm{H}}_2\mathrm{O}}=1$ mPa s). (c) Glycerin $82.5\%$ drop spreading on an oxidized Si wafer (${\theta }_e\sim {20}^{\circ }$, viscosity ${\mu }_{{\mathrm{glycerin}}_{82.5\%}}=85$ mPa s).Reuse & Permissions

Figure 2

The spreading radius in time on an oxidized Si wafer for two drop sizes, $R\approx (0.3\pm 0.02)$ mm (open symbols) and $R\approx (0.5\pm 0.02)$ mm (solid symbols) for different mass fractions of glycerin as indicated in the legend. (a) Dimensional units. (b) Viscous scaling. (c) Inertial scaling. (d) Contact-line friction scaling.Reuse & Permissions

Figure 3

Nondimensional spreading radius based on a contact-line friction scaling on the different substrates: oxide (black), silane [red (light gray)], and teflon [blue (dark gray)]. Open symbols denote $R=0.3$ mm), and solid symbols denote $R=0.5$ mm. (a) Linear axis. (b) Logarithmic axis.Reuse & Permissions

Figure 4

The dimensionless contact-line velocity function from phase field theory $u_{cl}=\frac{{\mu }_f}{\sigma }{\widehat{u}}_{cl}=[\cos \left({\theta }_e\right)-\cos \left(\theta \right)]/\sin \left(\theta \right)$. The inset shows the velocity predicted from the linearized molecular kinetic theory $u_{\mathrm{MKT}}=({\mu }_f/\sigma ){\widehat{u}}_{\mathrm{MKT}}=\cos \left({\theta }_e\right)-\cos \left(\theta \right)$. The input in these two functions is the experimentally measured dynamic contact angle $\theta$ for two different drop sizes on the oxidized Si wafer. The mass fraction of glycerin is indicated in the legend. Open symbols denote small drops ($R=0.3$ mm), and solid symbols indicate large drops ($R=0.5$ mm).Reuse & Permissions