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 wave-like 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-suctioninduced backflows occur. M ax P la nc k In st itu te fo r P ol ym er R es ea rc h – Au th or ’s M an us cr ip t


I. Introduction
Controlling the wetting properties and film formation are of utmost importance in many fields of technology including coating and printing applications [1][2][3][4], assembly of colloidal particles [5], lubrication of surfaces and bearings [6], oil recovery [7], flotation to recycle and enrich minerals [8], and fabrication of self-cleaning or water repellent surfaces [9][10][11][12][13][14][15][16].These processes are dynamicand often greatly influenced by menisci, i.e. a curved liquid interface that forms when a liquid meets a solid or another, immiscible liquid [17].Liquid films also are important in many biological systems.Instructive examples are a human eye [18,19] where the tear film on cornea is stabilized by menisci at the eye lids or Nepenthes pitcher plants [20] where the prey capture mechanism is based on aquaplaning of insects at the slippery peristome.Dynamic wetting of one liquid over a solid supported thin film of another, immiscible liquid is still hardly explored [21].This lack of knowledge is due to missing experimental techniques which are able to discriminate between different liquids or provide the required time and spatial resolution.Wetting over liquid films has become increasingly important due to the innovation of lubricant-infused slippery surfaces [22][23][24][25][26][27][28][29] a new class of functional materials inspired by the pitcher plant [22,29].Liquid drops slide on a solid supported lubricant film at very low tilt angles, typically even below 3° [23,28].Schellenberger et al. [25] showed that in equilibrium, the meniscus around a drop on a lubricant-infused surface can reach the length of ~3 mm.So far, flow dynamics within menisci and the film region ahead of moving drops remain unknown.
Here, we investigate water front advancing over a thin, pre-existing film of silicone oil on a smooth glass surface.At the liquid contact line the oil is elevated to a meniscus (Fig. 1 and Max Planck Institute for Polymer Research -Author's Manuscript Fig. S1a).The meniscus is pushed forward by the advancing water front.We apply laser scanning confocal microscopy to image the shape of all liquid interfaces.Surprisingly, the meniscus is not monotonous but shows wave-like profile with local minima and maxima.We quantify the spatial and temporal variation of the Laplace pressure in the oil.We quantify the local pressure gradient driven backflows in the meniscus and the film by adding 1 µm diameter polystyrene tracer particles to the oil.This capillary-suction-induced flow in the meniscus is universal and can last even for days.Due to the design of our setup, the shape of the meniscus is not disturbed by gravity.This allows us to investigate low capillary numbers.
We analyze the shape of the liquid interface using the lubrication approximation, balancing viscous and capillary forces.The theory cannot predict the film profile for  =    ⁄ < 6×10 -4 , as no single wavelength can be defined.Here,  is the viscosity of the oil,  the velocity of the meniscus, and  the oil-air surface tension.

II. Results
We first observe a situation where a 0.5 µL water drop is placed on a smooth glass substrate coated with a film ℎ 0 ≈ 10 µm of silicone oil (polydimethylsiloxane, PDMS,  = 50 mPa s,  = 21 mN/m), Fig. 1a,b.The silicone oil forms a wetting ridge, i.e. a concave curved annular meniscus, around the drop.Adjacent to the meniscus the film is depleted and a local minimum film thickness ℎ  ≈ 1 µm forms before the film reaches its initial thickness ℎ 0 ≈ 10 µm far away from the meniscus.
The depletion zone forms because negative Laplace pressure in the meniscus initiates a pressure-gradient-driven capillary suction of oil from the flat film region.Due to the concave curvature of the oil surface, the pressure inside the meniscus is lower than in the flat film To demonstrate that capillary suction is a generic phenomenon we placed a piece of glass (Fig. 1c) or a silica sphere (25 µm diameter, Fig. S3) into the film and observed the flow in the oil.Right after placing the glass edge into the film, the oil is drawn towards the vertical wall and forms a meniscus.A circulative convection was observed in the meniscus around the glass (Video S4), similar to the meniscus around the water drop.The film depletion adjacent to the meniscus continues for as long as there is a pressure difference between the meniscus and the film region.Balancing the pressure difference can take several hoursor even days as shown with the meniscus around the piece of glass in Fig. 1c depending on the geometry of the system and viscosity of the liquid (Supplemental Material, Fig. S4 and Fig. S5).check that such a steady state exists, we recorded the film profile at different positions, and accordingly at different times, in the flow cell (Fig. 2a).Within the experimental error, the film profile remained unchanged (Experimental Section).When stopping movement of the meniscus the maximum in film thickness ℎ  disappeared while the minimum ℎ  remained for at least 60 min (Fig. 4).From now on, we call the local minimum ℎ  and the maximum ℎ  ahead of the meniscus (Fig. 5a) a "primary minimum" and a "primary maximum", respectively, since there exist another, less prominent "secondary minimum" and "secondary maximum" advancing in the front (Fig. 5a, inset).The lower curvature of the liquid interface causes lower pressure drop and capillary suction: ∆ over the primary and secondary minima ≈ -132 Pa and ≈ -36 Pa, respectively (Fig. 3).The lateral distance between the secondary minimum and maximum, i.e.
the width of half-wavelength W, appears to be similar to that of the primary minimum and maximum ≈ 400 µm.However, the amplitude A, i.e. the height difference between the minimum and the maximum is much smaller, ~1 µm.
To distinguish the effect of viscous forces, , with respect to capillary forces, , on the film profile, we measured the half-wavelength and amplitude between the primary minimum and maximum at varying  (3.9×10 -6 ≤  ≤ 6.9×10 -4 , Fig. 5a-c) and initial film thickness ℎ 0 .
Both W and A increase linearly with ℎ 0 (Fig. 5d,e).When increasing the velocity of the meniscus from ~15 µm/s to ~290 µm/s both W and A decrease (Fig. S8).The reason is that ℎ  has no time to evolve when the water front moves fast.Particularly, at  < 10 -4 , where the capillary forces become increasingly important with respect to the viscous stresses, there is a threshold where both W and A start to increase greatly with decreasing  (Fig. 5f,g).
We compared the dynamic menisci ahead of moving water front (Fig. S1a) to those in dipcoating when a solid plate is withdrawn from or driven back into a liquid bath (Fig. S1b, dipcoating; Fig. S1c, "reverse dip-coating").There the receding meniscus leaves behind a socalled "LLD" film [1,30] of thickness ℎ 0 , firstly analyzed by Landau and Levich [31] and Derjaguin [32].The flow in the film region is determined by the interplay of viscous forces and capillarity, and is described within the lubrication approximation [3,[31][32][33][34][35][36] assuming small curvature of the liquid-air interface and  ≪ 1. Dynamic menisci were further investigated in a capillary tube by Bretherton [37].

Max Planck Institute for Polymer Research -Author's Manuscript
reverse dip-coating, a balance of the viscous and capillary forces within the fluid layer yield the thin-film equation for the scaled film thickness  = ℎ/ℎ 0 : Here,  is a characteristic scale  = /, with  = ℎ 0 ( . The sign for the velocity of the meniscus is taken negative corresponding to a "reverse dip-coating scenario".Strictly the only formal requirement for validity of the above lubrication approximation is  ≪ 1.For small variations in the film thickness (() = 1+() with () ≪ 1), equation ( 1) has the 0 th order solution with a constant  to be determined.In this classic case, the film profile exhibits regular waves of constant half-wavelength  = 2/√3.
Our measurements show that only the case with the largest capillary number  = 6.9×10 -4   ( = 50 mPa s,  = 270 µm/s) exhibits such regular waves (Fig. 5c).In all other cases, the wavelength is not constant along .Additionally, with decreasing  the experimental halfwavelength W measured between the first minimum and first maximum becomes smaller than the Landau-Levich half-wavelength .
profile in the case of the largest capillary number  = 6.9×10 -4 .Fitting the experimental data with equation (2) yields a good match (Fig. 5c).The fit was performed in Mathematica with The model within the Landau-Levich-Bretherton framework predicts a constant spacing between the minima and maxima for all .Notably, a decreasing/increasing spacing occurs with decreasing capillary number.Experimentally, for  = 3.6×10 -5 (Fig. 5a) the spacing between the primary minimum and maximum was about 40% less than spacing between the maximum and the secondary minimum.When the velocity of the meniscus is reduced to zero ( = 0), the characteristic half-wavelength W/ℎ 0 should go → ∞, in agreement with our data, Fig. 5f.Our setup rules out that gravitational drainage could cause the discrepancy between theoretical predictions and experimental observations [35] as the flow cell was horizontally aligned.
To find the reason for the discrepancy between theory and experiments for  < 6×10 -4 we measured local flow in the oil film by imaging movement of the tracer particles (Figs.6a, 7, S10).In front of the minima in film thickness (Fig. 6b for the primary minimum and Fig. 6c for the secondary minimum) the tracer particles have a positive velocity with respect to the flow direction of the meniscus.Notably, when the minima are approaching the particles, the flow slows down before the particles experience a negative velocity when sucked through the Inset in (b): illustration of the backflow transporting a tracer particle through the primary minimum.
We identified 7 positions at different heights in the oil film, labelled 1-7 in Fig. 6a, where the flow direction switched.These "turning points" are associated with the two backflows.Before changing the flow direction, the oil has lower positive velocity close to the solid (no-slip condition at the solid-liquid interface) as compared to the liquid-air interface (negligible friction).Therefore, the backflows start earlier and are longer at the heights of 3.5 and 5 µm as compared to the height at 10 µm (Fig. 6a, Fig. 7 and Supplemental Material, Table SI).
After entering the meniscus, the flow turns back to positive and starts to follow the motion of the meniscus.This hints that the strong backflows within the liquid film cause the discrepancy between theory and experiments.The capillary suction discussed here was observed for different thicknesses of the film (Fig. S4) and viscosities of the liquid (Fig. S5).It is expected to have broad implications in technology.One example is the common problem of inhomogeneous formation of coating films -also known as the "orange peel effect"in painting, lacquering, and other thin-film coating applications [38].Small microscale defects can cause considerably large variation in film thickness even at mm-wide areas (Fig. S3).The capillary suction and film depletion should also be apparent in a standard dip-coating process (Fig. S1b).
Getting back to the pitcher plant and lubricant-infused slippery surfaces; when a 0.

III. Conclusions
In summary, we investigate the wetting dynamics of one liquid (water) front advancing over a micrometer-thick film of another immiscible liquid (silicone oil).Fiji open-source platform for image analysis [39].The curved oil film profiles were analyzed from sequentially recorded confocal microscopy images with a house-made Fiji macro, which was designed to distinguish the oil-air interface from changes in pixel intensity of the microscopy images.
From the quantitative data extracted from the confocal microscopy videos, the halfwavelength (W) and amplitude (A) were determined using at least 3 individual flow profiles to Max Planck Institute for Polymer Research -Author's Manuscript position were calculated knowing the elapsed time, the distance covered by the backflow, and the velocity of the advancing meniscus (Table SI): where    is the time at which the meniscus passed the backflow start position,    is the time at which the backflow started, and  is the velocity of the oil meniscus.
The position where the backflow ends in relation to the position of the oil meniscus is given by where   is the duration and   is the distance covered by the backflow.
To further verify the positions of the backflows with respect to the oil film curvature, we compared the reflection channel microscopy information from the oil−air interface, where the changes in the height of the film were detected, with the transmission channel information, where dynamics of the tracer particles were detected.
, where  1 and  2 are the radii describing the meniscus curvature (Fig.1b, Supplemental Material).This equals to the hydrostatic pressure in water at a depth of ~8 mm.In order to visualize the flow in the meniscus, we added polystyrene tracer particles to the silicone oil (Video S1).The capillary flow follows the oil-air interface.Here, viscous drag is negligible and the capillary flow strongest.Liquid flows up the meniscus until it turns downwards to compensate the meniscus growth at the perimeter (Fig.1b, Fig.S2, Video S2, Video S3).

FIG. 1 .
FIG. 1. Silicone oil meniscus and the oil film around a water drop or a piece of glass on a

FIG. 4 .
FIG. 4. Silicone oil meniscus η = 50 mPa s at rest in the flow cell.When stopping movement FIG. 5. Characterization of advancing silicone oil meniscus and the oil film profile in the flow

FIG. 7 .
FIG. 7. Hydrodynamic flow at different heights in the silicone oil film.Oil viscosity η = 50 5 µL water drop surrounded by open air slides on a thin silicone oil film (η = 50 mPa s, ℎ 0 ≈ 8 µm) on a PDMS modified glass slide [24] (Experimental Section)consistent with the observations in the flow cella minimum and a maximum in film thickness are formed ahead of the annular wetting ridge surrounding the drop.Inclination of the substrate by 4° caused a downward motion of the drop at a velocity of ~70 µm/s.Here, the minimum and maximum in film thickness became ~3 µm and ~10 µm, respectively (Video S8).
The novel experimental setup with confocal microscopy and tracer microparticles within the liquid provides information of the shape of the liquid surface and of the flow within the micrometer-thick oil film.A negative Laplace pressure in the liquid meniscus leads to capillary suction and as a consequence a local thinning of the liquid film ahead of the advancing meniscus.The lubrication approximation theory within Landau-Levich-Bretherton framework can describe the dynamic film profile for  of the order of 6×10 -4 .It cannot predict the film profile at lower  where strong capillary-suction-induced backflows occur.Capillary forces can initiate strong pressure dropsand thus significantly change the flow and profile of thin liquid filmsaround solid particles, walls, or drops of immiscible liquids.IV.Experimental SectionMaterials: Silicone oils were purchased from Sigma-Aldrich (Germany).The flow in thin oil films was investigated at varying capillary numbers () with different flow velocities and viscosities of the oils (η = 5 mPa s, γ = 18.1 ± 0.2 mN/m; η = 10 mPa s, γ = 18.9 ± 0.3 mN/m; η = 50 mPa s, γ = 20.9 ± 0.5 mN/m; η = 500 mPa s, γ = 22.7 ± 0.2 mN/m).If not otherwise mentioned, the silicone oil with η = 50 mPa s was used.Interfacial tension between the oil and water,   , is 38.9 ± 0.3 mN/m.Hydrophobic fluorescent dye, Coumarin 6 with the concentration of 50 µg/g, was used to label the silicone oil.Prior to the experiments, the dyed oil was sonicated for 2 h and filtered through a 0.22 µm syringe filter to remove possible aggregates of the dye.To monitor flow inside the oil film, 1 µm diameter polystyrene tracer particles were added to the oil at a concentration of 10 µg/g.Water drops (de-ionized MilliQ existing liquid films of silicone oils were labeled with a hydrophilic fluorescent dye, N,N′-(2,6-diisopropylphenyl)-1,6,7,12-tetra(1-methylpyridinium-3-yloxy)-perylene-3,4,9,10tetracarboxylic acid diimide tetra-methane-sulfonate (WS-PDI), with a concentration of 10 µg/g.With the used concentrations, the effect of dyes on the surface tension of the silicone oil and water, or the interfacial tension between the oil and water, was negligible and remained within the experimental error of 0.5 mN/m.Surface and interfacial tensions: Surface tensions of the liquids were measured using the Wilhelmy plate method with DCAT 11 -tensiometer (DataPhysics Instruments GmbH, Germany).Interfacial tensions between the liquids were measured by DataPhysics OCA 35 instrument using the pendant drop method (DataPhysics Instruments GmbH, Germany).Confocal microscopy: Inverted laser scanning confocal microscope (LSCM, Leica TCS SP8 SMD, Leica Microsystems GmbH, Germany) was used to investigate the profile and hydrodynamics of the silicone oil menisci and the oil films.The confocal microscope was equipped with a water immersion objective (40× magnification) with horizontal and vertical resolution of ~500 nm and ~1 µm, respectively.Argon laser lines 458 nm and 476 nm were used for reflection at interfaces and for excitation of Coumarin 6 dye, respectively.DPSS laser line 561 nm was used to excite WS-PDI dye.Five individual detectors with freely adjustable spectral ranges allow simultaneous measurement of emitted light from the dyes (emission peak at 488 nm for Coumarin 6 and at 609 nm for WS-PDI), reflected light from the interfaces, and transmitted light through the sample.Meniscus around a drop, a solid sphere, and a glass piece: To investigate the evolution of the oil meniscus outside the flow cell in open air around a water drop, in front of a piece of glass, or around silica particles having a diameter of 25 µm (AkzoNobel, Kromasil, Sweden), we deposited 1 µL of silicone oil, η = 50 mPa s or η = 5 mPa s, on the glass substrate and spincoated the sample at 1000 rpm or 200 rpm, respectively, for 60 s.This resulted in a smooth film of oil with thickness ~8-10 µm.With silicone oil η = 50 mPa s we achieved a thick film of ~100 µm (Fig.S4) by letting a 1 µL drop of the oil spontaneously spread on the glass substrate.Monitoring hydrodynamics within the oil meniscus was started immediately after placing the water drop, the piece of glass, or the silica particles on the oil film and focusing at the area of interest, typically within 1-2 minutes.Flow cell: Commercial flow cells, sticky-Slide VI 0.4 from ibidi (Germany), were used to investigate the dynamic menisci under well-defined conditions in horizontal plane.The flow cells (length = 17 mm; width = 3.8 mm; height = 0.5 mm) are made of high optical quality plastic, are closed from the top, and can be attached to the substrate by a self-adhesive underside.Microscope coverslip glass with a thickness of 170 µm (Thermo Fisher Scientific, Germany), cleaned with ethanol, rinsed with MilliQ water, and dried under a nitrogen flow, was used as a substrate.The glass substrate was firmly attached to the flow cell and ~0.5 µL of silicone oil was deposited in the flow cell from the inlet.The film thickness was controlled by adjusting the tilting angle: ~60° tilt angle yielded a film thickness ℎ 0 ≈ 11 µm along the center line of the flow channel.After the film formation, an inlet tube for water flow was connected to the flow cell.A pressure generated while connecting the tube punctured the oil plug at the outlet of the flow cell.During the experiments the oil film was under atmospheric pressure.Water flow was driven into the flow cell by a peristaltic pump (Reglo Analog MS-4/8, Ismatec, Germany) connected to a poly(vinyl chloride) tube with inner diameter of 0.13 mm.This tube was further connected to a wider tube with inner diameter of 1.37 mm to eliminate possible velocity fluctuations originating from the pump.Velocity of the oil meniscus in the flow cell was determined for each individual experiment by direct confocal microscopy observation, i.e. the length the meniscus advanced was divided by the elapsed time.Water drop sliding on a slippery surface: To investigate a meniscus around a sliding water drop on a silicone oil coated slippery surface, the glass substrate was treated following a simple procedure that results in a nm-thick hydrophobic PDMS brush coating[24].Briefly, the glass was first cleaned with ethanol and water and dried under nitrogen flow.5 µL of silicone oil η = 50 mPa s was deposited on the glass after which the sample was heated on a hot plate at 300°C for ~3 min.After the heat treatment, the sample was rinsed with tetrahydrofuran and water. 1 µL drop of silicone oil  = 50 mPa s was spin-coated on the surface at 1000 rpm for 60 s to achieve a smooth film of the oil with thickness of 8 µm.The sample was placed on the confocal microscope sample holder at a tilt angle of 4°.A 0.5 µL water drop was then placed on the inclined surface where it was imaged when sliding downwards.Data analysis: Profile of the oil menisci and films were investigated by capturing the film profiles at xh-plane (side-view) at the center line of the flow cell and by monitoring dynamics of the polystyrene tracer particles within the oil at xy-plane (top-view) at different heights in the film by confocal microscopy.Image processing and data analysis was carried out using