Kinetic Effects in Dynamic Wetting

The maximum speed at which a liquid can wet a solid is limited by the need to displace gas lubrication films in front of the moving contact line. The characteristic height of these films is often comparable to the mean free path in the gas so that hydrodynamic models do not adequately describe the flow physics. This Letter develops a model which incorporates kinetic effects in the gas, via the Boltzmann equation, and can predict experimentally observed increases in the maximum speed of wetting when (a) the liquid’s viscosity is varied, (b) the ambient gas pressure is reduced, or (c) the meniscus is confined.

Figure 1

Flow configuration (left) and close-up of the thin-film region (right) showing that (a) the height $h(x)$ and speed in the liquid $U_{fs}(x)$ vary with $x$, (b) there is a Couette-Poiseuille flow profile $u_g$ in the gas, and (c) the free surface bends to attain its contact angle $\theta$. At the upper and lower boundaries of the domain, a distance $4L$ apart, is a stationary solid.

Figure 2

(a) Predictions of the flow coefficients $Q(\text{Kn})$ from Eq. (1). (b) Curves of $r$, defined in Eq. (2), and demonstration (inset) that the slip model diverges from the Boltzmann solution for larger Kn.

Figure 3

Maximum speed of wetting (dimensionlessly a capillary number $C{a}_{\max }={\mu }_l{U}_{\max }/\sigma$) of water-glycerol solutions in air as a function of viscosity ratio ${\mu }_g/{\mu }_l$.

Figure 4

(a) Maximum speed of wetting, for silicone oil in helium, as ambient pressure $P$ is reduced. (b) Local pressure $p$ relative to its far-field value and normalized by the ambient value $P=0.06P_{\mathrm{atm}}$, at a contact line speed ${\mu }_{l}U/\sigma =0.5$, just before the no-slip model predicts entrainment. The distance along the free surface $s$ starts in the thin-film region.