Air Entrainment by Contact Lines of a Solid Plate Plunged into a Viscous Fluid

The entrainment of air by advancing contact lines is studied by plunging a solid plate into a very viscous liquid. Above a threshold velocity, we observe the formation of an extended air film, typically 10 microns thick, which subsequently decays into air bubbles. Exploring a large range of viscous liquids, we find an unexpectedly weak dependence of entrainment speed on liquid viscosity, pointing towards a crucial role of the flow inside the air film. This induces a striking asymmetry between wetting and dewetting: while the breakup of the air film strongly resembles the dewetting of a liquid film, the wetting speeds are larger by orders of magnitude.

Figure 1

Air entrainment by a contact line when a solid plate is plunged into a viscous liquid. (a) Sketch of dynamical meniscus below the threshold of air entrainment, and (b) above the threshold of air entrainment, where a film of thickness $h$ develops. A high-speed camera is placed perpendicularly to the substrate. (c),(d) Front views of the air film entrained into a viscous silicone oil (${\eta }_{\ell }=0.1\mathrm{Pa}·\mathrm{s}$). (c) The extended air film is formed behind the contact line and moves downwards into the bath (taken 70 ms after plunging). The film is destroyed by the formation of “rewetting” bridges. The diagonal dark line is the reflection of a straight wire that gives an impression of the interface profile. (d) Zoom of the rewetting bridge, which is the inverse of the dewetting of a liquid film. Once the oil reestablishes contact with the solid, a growing circular zone invades the air film.

Figure 2

(a) Contact line velocity $U_{\mathrm{cl}}$ (triangles) as a function of the plate velocity $U_p$, for ${\eta }_{\ell }=0.1\mathrm{Pa}·\mathrm{s}$. The relative velocity $U_p-U_{\mathrm{cl}}$ (circles) is independent of the plate speed. (b) Entrainment speed $U_e$ for different liquid viscosities ${\eta }_{\ell }$, measured in two ways: the diamonds represent the relative velocity with respect to the plate, $U_p-U_{\mathrm{cl}}$, while the circles are the bridge rewetting speeds [see Fig. 1d]. (c) Film thickness $h$ for different ${\eta }_{\ell }$, taken at constant plate velocity $U_p=0.67\mathrm{m}·{\mathrm{s}}^{-1}$. The open circle was taken for a liquid jet of glycerol entraining air at the same speed [3]. The error bars are determined from a set of independent measurements.

Figure 3

Dimensionless entrainment speed, ${\mathrm{Ca}}_e=U_e{\eta }_{\ell }/\gamma$, versus the viscosity ratio ${\eta }_g/{\eta }_{\ell }$ for: silicon-oil/air (•, ◇, present data), silicon-oil/air (▪ after 18) and various liquids/air (▴ after [36]). Curves: numerical results discussed in the Supplemental Material [23]. Corresponding parameters: oil slip lengths ${\lambda }_{\ell }={10}^{-5}{\ell }_{\gamma }$, and air slip lengths ${\lambda }_g={10}^{-4}{\ell }_{\gamma }$ (solid line) and ${10}^{-2}{\ell }_{\gamma }$ (dotted line), corresponding to mean free paths ${\ell }_{\mathrm{mfp}}=70\mathrm{nm}$ (solid) and $7\mu \mathrm{m}$ (dotted). The theoretical curves do not suggest a definite exponent.

Figure 4

Streamlines in a perfect wedge [31] of angle $\theta$ for (a) a receding contact line (with $\theta$ close to 0), and for (b) an advancing contact line (with $\theta$ close to $\pi$). In the advancing case, the viscous dissipation in the gas phase will dominate over the liquid phase due to the strongly confined circulation in the gas wedge. (c) Shape of the curved interface near the entrainment threshold. In a range of thickness $h$ between the molecular scale and the scale ${\ell }_{\gamma }$ of the bath, the local angle $\theta$ is close to $\pi$ so that dissipation is dominated by air. Inset: When the mean free path ${\ell }_{\mathrm{mfp}}$ is comparable to $h$, then air behaves as a Knudsen gas.