Wetting over pre-existing liquid films

Wetting of a liquid over another, pre-existing liquid film governs several natural phenomena and technical applications, such as coating and oil recovery. The dynamics of this everyday process are poorly understood due to the lack of space and time-resolved techniques, which can discriminate between the two liquids. Here we image a water front moving on a micrometer-thick film of a solid supported silicone oil using laser scanning confocal microscopy. The silicone oil forms a meniscus around the water front. We resolve the spreading dynamics within the meniscus in 3D using tracer microparticles. Capillary suction induces local thinning of the oil film adjacent to the meniscus. When moving the water front forward, viscous forces deform the oil meniscus, giving rise to a wavelike film profile with local backflows. For high velocities, the film profile can be modeled within the Landau-Levich-Bretherton framework. The theory fails to predict the film profile at low velocities where strong capillary-suction-induced backflows occur.

Figure 1

Silicone oil meniscus and the oil film around a water drop or a piece of glass on a smooth glass substrate. (a) Illustration of a water drop deposited on the oil film. (b) A confocal microscopy image compiled from individual vertical micrographs in $xh$ plane (side-view) shows a 0.5-$\mu \mathrm{l}$ water drop (cyan, fluorescently dyed with WS-PDI) resting on a silicone oil film (yellow, dyed with Coumarin 6, initial film thickness $h_0\approx 10\mu \mathrm{m}$) on glass. The micrographs were captured 1–2 min after placing the drop on the oil film. Yellow dotted arrows demonstrate circulative convection of the oil within the meniscus. $r_1$ corresponds to the vertical radius of the meniscus at $\sim 10\mu \mathrm{m}$ height. Inset: top-view image (horizontal slice), where $r_{\mathrm{drop}}$ and $r_2$ correspond to the horizontal radius of the drop and the oil meniscus at $\sim 10\mu \mathrm{m}$ height, respectively. (c) Confocal microscope reflection images of the meniscus (on the left-hand side) and the depletion zone in $xh$ plane few minutes, 1 h, 5 h, and 4 days after placing a piece of glass ($3\times 3\times 1\mathrm{m}{\mathrm{m}}^3$) on the oil film $h_0\approx 8\mu \mathrm{m}$. The imaging position was adjusted to follow the depletion zone during growth of the meniscus.

Figure 2

Silicone oil meniscus advancing over the pre-existing silicone oil film in the flow cell. (a) Schematic illustration of the flow cell (length, $x=17$ mm; width, $y=3.8$ mm; height, $h=0.5$ mm) setup on the confocal microscope. The oil meniscus ahead of water front is driven to the right. (b) Schematic drawing of the advancing oil meniscus and the film profile in the middle of the cell. $r_1$ and $r_2$ indicate curvature of the meniscus. (c) A confocal microscopy image compiled from individual vertical micrographs in $xh$ plane (side-view) shows the meniscus and the film profile advancing in the flow cell at $v\approx 15\mu \mathrm{m}/\mathrm{s}$ ($h_0\approx 11\mu \mathrm{m}$, $h_{\min }\approx 3.5\mu \mathrm{m}$, and $h_{\max }\approx 17\mu \mathrm{m}$). The micrograph reveals approximately $1/3(\sim 170\mu \mathrm{m})$ of the total height of the flow cell. Time resolution for the confocal microscopy was 0.85 s.

Figure 3

Approximated Laplace and hydrostatic pressures acting at the silicone oil meniscus $\eta =50$ mPa s and the curved oil film while advancing in the flow cell at $v\approx 15\mu \mathrm{m}/\mathrm{s}$. Curvature of the oil meniscus is characterized by two negative radii (Fig. 2), vertical $r_1\approx -190\mu \mathrm{m}$ and horizontal $r_2\approx -1100\mu \mathrm{m}$ yielding approximated Laplace pressure of $-132$ Pa. Elsewhere in the film the effect of $r_2$ is considered to be negligible, thus the curvature $r_1$ determines the Laplace pressure at the given areas from left to right in the image as follows (calculated Laplace pressure, related curvature $r_1$): 3.7 Pa, $5700\mu \mathrm{m}$; 0.9 Pa, $24000\mu \mathrm{m}$; 0.3 Pa, $60000\mu \mathrm{m}$; $-36\mathrm{Pa},-590\mu \mathrm{m};39\mathrm{Pa},540\mu \mathrm{m}$. At the smooth film region, where the curvature of the oil interface is zero, the Laplace pressure is zero.

Figure 4

Silicone oil meniscus $\eta =50$ mPa s at rest in the flow cell. When stopping movement of the meniscus, the local minimum film height $h_{\min }$ in front of the meniscus and the concave curvature remained constant over the follow-up period of 60 min. Inset: magnification of the film profile at $h_{\min }$. The gradual decrement of the film height can be associated with the capillary suction of the liquid in the meniscus of the oil plug and in the menisci at the walls of the flow cell.

Figure 5

Characterization of advancing silicone oil meniscus and the oil film profile in the flow cell. (a) Oil meniscus $\eta =50$ mPa s advancing at $v\approx 15\mu \mathrm{m}/\mathrm{s}$ ($\mathrm{Ca}=3.6\times {10}^{-5}$) over the oil film $h_0\approx 11\mu \mathrm{m}$. $W$ and $A$ denote the half-wavelength and amplitude, respectively, of the primary minimum and maximum. Inset: magnification of the secondary minimum and maximum (red solid line is to guide eye). Film profile and theoretical fit (black solid line) with (b) the lowest ($v\approx 14\mu \mathrm{m}/\mathrm{s},\eta =5$ mPa s, $\mathrm{Ca}=3.9\times {10}^{-6}$) and (c) the highest ($v\approx 290\mu \mathrm{m}/\mathrm{s},\eta =50$ mPa s, $\mathrm{Ca}=6.9\times {10}^{-4}$) investigated capillary numbers. The confocal microscopy time resolution for (a), (b), and (c) was 0.217, 0.530, and 0.109 s, respectively. (d) $W$ and (e) $A$ are linearly dependent on $h_0$ ($v\approx 15\mu \mathrm{m}/\mathrm{s},\eta =50$ mPa s, $\mathrm{Ca}=3.6\times {10}^{-5}$). (f) $W$ and (g) $A$ decrease with increasing $\mathrm{Ca}$ (a, b, and c refer to the film profiles at the corresponding $\mathrm{Ca}$).

Figure 6

Hydrodynamic flow of silicone oil meniscus $\eta =50$ mPa s advancing at $v\approx 15\mu \mathrm{m}/\mathrm{s}$ over a pre-existing oil film $h_0=11\mu \mathrm{m}$. (a) Illustration of flow in the oil based on confocal microscopy data collected at different regions in the film from several individual experiments. The film profile was captured from the reflection images in $xh$ plane (side-view). The horizontal velocity and vertical motion of the tracer particles were monitored in transmission (Fig. S10) [30] and fluorescence (Fig. 7) images in $xy$ plane (top-view) with a time resolution of 0.217 s. Blue and red arrows denote positive and negative horizontal velocity, respectively, of the tracer particles at the given positions. Length of the arrow tail indicates magnitude of the velocity measured at a position indicated by the center of the tail. The data was collected by setting the focal plane at the heights of 3.5, 5, and $10\mu \mathrm{m}$ above the glass substrate, indicated by the dashed lines. Horizontal zero position $x=0\mu \mathrm{m}$ was determined as a position of the meniscus interface at the height of $10\mu \mathrm{m}$. Numbers $1-7$ indicate the positions where switching of the flow directions were observed at the different heights. (b) Backflow over the primary minimum [between numbers 1 and 3 in (a)] and (c) backflow over the secondary minimum [between numbers 4 and 7 in (a)]. Inset in (b): illustration of the backflow transporting a tracer particle through the primary minimum.

Figure 7

Hydrodynamic flow at different heights in the silicone oil film. Oil viscosity $\eta =50$ mPa s, meniscus velocity $v\approx 15\mu \mathrm{m}/\mathrm{s}$, and initial film thickness $h_0=11\mu \mathrm{m}$. The coordinates of $1\mu \mathrm{m}$ polystyrene tracer microparticles in the oil film were monitored by confocal microscopy. The data was collected with the focal plane set at 10 and $5\mu \mathrm{m}$ above the glass substrate using the confocal microscope transmission channel. The data reveals two backflows in the film: (a), (c) over the secondary minimum and (b), (d) over the primary minimum in film thickness. (a), (b) Red and (c), (d) blue rectangles correspond to the data acquired at $\sim 10\pm 1\mu \mathrm{m}$ and $\sim 5\pm 1\mu \mathrm{m}$ heights in the film, respectively, using the confocal microscope fluorescent channel.