Rupture of thin liquid films sprayed on solid surfaces

Abstract

An experimental study was done to observe the formation of thin films by spraying liquid onto a solid surface and to determine the conditions under which the films would rupture or remain stable. Water, or water mixed with 20–70 % by weight of glycerin, was sprayed for varying lengths of time onto a circular, 165-mm-diameter plate made of either Plexiglas, steel, or Parafilm-M and the motion of the liquid recorded using a high-speed camera. Water films ruptured immediately after the impact near the center of the surface. Then, if the film thickness was greater than a critical value, the water flooded back and the hole closed; otherwise, the hole remained in the water layer. The critical film thickness increases linearly with advancing liquid–solid contact angle. Increasing liquid viscosity by adding glycerin had little effect on critical film thickness, but inhibited spreading of the liquid and suppressed initial rupture of the liquid layer. A surface energy model was used to predict the variation of critical film thickness with surface wettability.

1 Introduction

Thin liquid films are frequently applied by spraying liquid onto a solid surface in applications such as spray painting, spray coating, or application of pesticides. In all of these, it is important that the liquid film remains stable until the liquid can dry or cure. If spray parameters are not chosen properly, or the substrate is not suitably prepared, the liquid film can rupture, leaving holes in the coating. Previous studies have shown that several factors can affect the rupture of a liquid film on a solid surface (Taylor and Michael 1973; Sharma and Ruckenstein 1989; Mulji and Chandra 2010; Dhiman and Chandra 2008; Dhiman and Chandra 2010), including the liquid–solid contact angle and surface roughness.

Padday (1970) experimentally measured film thicknesses of various liquids on solids and concluded that the critical thickness, below which a hole would form in the liquid layer, increased with liquid–solid contact angle. In a study of an infinite film, Taylor and Michael (1973) found that a critical hole size exists above which, at a given film thickness, the hole would enlarge spontaneously and below which it would close and derived an expression for a film thickness that is unconditionally stable. Sharma and Ruckenstein (1989) compared the total energy of a film with a hole to one without and, by calculating the energy change associated with the formation of a hole, calculated the critical film thickness in terms of contact angle and hole size.

Kheshgi and Scriven (1991) examined the mechanism of dewetting using a hydrodynamic analysis that considered the disjoining pressure, due to molecular scale forces between the substrate and liquid, as well as local disturbances such as surface tension gradients. They showed that if a film thins to 1 μm due to any disturbance, it will rupture due to disjoining pressure. Redon et al. (1991) found that the rate of growth of a hole in a film is constant and independent of the hole size or film thickness and is very sensitive to the receding contact angle.

Mulji and Chandra (2010) studied the rupture of liquid films as they are drained to lower thicknesses on different substrates. They showed by thermodynamic stability analysis that roughness promotes film stability and not dewetting and that a hole formed due to air entrapment would recover if the film is relatively thick and the contact angle was either small or large. Dhiman and Chandra (2008, 2010) studied the rupture of radially spreading films created by impacting jets and droplets. Expressions were developed for a critical Reynolds number based on impacting jet or droplet velocity and diameter, beyond which film rupture is likely to occur.

This study was conducted to observe the rupture of liquid films formed by a spray impacting on a solid surface. The critical film thickness was measured for different liquid–solid contact angles and viscosity. The liquids sprayed were deionized water and aqueous glycerin solutions with varying concentration to obtain a wide range of viscosities. The substrates used were Plexiglas, mirror-polished steel, and Parafilm–M^®, a hydrophobic polymer film available for general laboratory use which was spread on a Plexiglas substrate.

2 Experimental method

Figure 1 shows a schematic diagram of the experimental setup used. A tank full of water was connected to a centrifugal pump (Model PA411-50MT, The Berns Corporation, USA) that passed the water through stainless steel and plastic tubing toward a solenoid valve (Model 8262G232, Asco Valves, USA). A partially open metering valve (Model B-1RS6, Whitey Metering Valves, USA) was used to manually control the flow upstream of the nozzle. This valve and a pressure regulator (Model 26A, Watts Regulator Co., USA) maintained a closed loop for fluid flow and ensured no backflow into the pump. The solenoid valve was normally closed, and a pulse generator driving a transistor switch was used to open the valve for a precise amount of time. When the valve was opened, water passed through a stainless-steel, full-cone, general-purpose spray nozzle (Model 1/4G-316SS6.5, Spraying Systems Co., USA) for a preset duration. The spray was typically switched on for durations from 1.10 to 4.00 s, and the volume flow rate of water from the nozzle was 1.88 L/min. The average flux of water impacting the substrate was 1.04 kg/m²s.

Fig. 1

Schematic of experimental setup used for water and aqueous glycerin sprays

Target substrates were disks 184 mm in diameter, which in experiments were clamped down by a stainless-steel, threaded ring leaving an exposed surface with diameter D = 165 mm. The different substrates were Plexiglas, mirror-polished steel, and Parafilm–M, a flexible hydrophobic, plastic film that was carefully spread over a Plexiglas substrate without stretching it. The ring holding the disks in place provided a 10-mm-high lip around their edges, which confined the liquid being sprayed onto the surface and prevented it flowing off the sides. In the absence of this ring, water sprayed onto the surface drains off and never forms a continuous film. More viscous liquids, such as the 65 wt% glycerin in water solutions, stayed on the surface and often did not contact the ring before their motion was arrested.

The liquid pressure upstream of the nozzle was maintained at 50 kPa during spraying, for which the spray had a cone angle of 45°. A simple calculation showed that to ensure complete coverage of the 165-mm-diameter substrate, the nozzle had to be located at least 200 mm directly above the center of the substrate. In experiments the nozzle was positioned at a height of 215 mm so that the spray extended a little before the edge of the substrate. Tests with the nozzle placed further away, at a height of 299 mm, showed no significant change in the results, except that the spray mass flux was lower and it took longer to deposit the same volume of liquid. We did not do any tests with the nozzle closer than 215 mm, since this led to partial coverage of the substrate and also enhanced splashing in which droplets impacted the surface and rebounded off.

A high-speed video camera (Model FastCam Ultima APX, Photron, Japan) was used with a halogen light source to capture the dynamics of the liquid film immediately after spraying. The camera was operated at 6,000 frames per second (fps) with an exposure time of 167 μs for videos showing the whole substrate and at 10,000 fps with an exposure time of 100 μs for close-up videos to show details of film breakup.

The volume of water sprayed on a surface was measured by carefully withdrawing it through a hypodermic needle into a graduated syringe. Dividing the volume of liquid by the area of the substrate gave an average liquid film thickness. Each measurement was repeated at least five times for a given set of conditions and an average film thickness reported.

Tests were done using deionized water and water–glycerin mixtures with the weight fraction of glycerin varying from 20 to 70 %. Properties of each mixture are shown in Table 1. The density (ρ) and kinematic viscosity (ν) of water–glycerin mixtures were taken from online data published by Dow Chemical (2010a, b). The liquid–gas interfacial tension (surface tension, σ) was calculated using an empirical formula derived by Khossravi and Connors (1993) for glycerin solutions at 25 °C.

Table 1 Properties of tested liquids at 25 °C (% are for glycerin solutions by weight)

Equilibrium, advancing, and receding contact angles were measured on each substrate. The equilibrium contact angle (θ) measurements were made with an 8-μl-volume sessile droplet. About 30 s after gently dispensing a droplet on a substrate, a high-resolution camera captured images of it at rest. To measure advancing contact angles (θ _A ), a syringe pump was used to dispense a liquid droplet (about 5 mm in diameter) on the substrate with the needle remaining inside the droplet. While the droplet was still growing and the liquid–solid contact was advancing, a high-resolution video camera was used to capture the motion of the advancing line. For receding contact angles (θ _R ), the syringe was used to suck liquid back until the solid–liquid contact line began to recede. All images were then exported to image analysis software (ImageJ, National Institute of Health, USA) from which the contact angles were measured. Each contact angle for each substrate was measured five to ten times at different locations. All surfaces were smooth, with average roughness varying from 20 to 40 nm. Previous experiments (Mulji and Chandra 2010) have shown that the roughness has to be several orders of magnitude greater than this to affect film rupture.

Table 2 lists the contact angles of liquids measured on the substrates used. As expected, Parafilm was the most hydrophobic substrate, with Plexiglas and mirror steel relatively hydrophilic. Plexiglas was not used for experiments with glycerin solutions. The measured contact angles are repeatable within ±3° on steel and Plexiglas and ±2° on Parafilm-M.

Table 2 Contact angles on different substrates used

3 Results and discussion

Figure 2 shows a sequence of high-speed images of a water film on a mirror-polished steel surface, immediately after the spray was turned off. The time at which each image was taken is indicated, with t = 0 ms corresponding to the spray being shut off. In the first frame (t = 100 ms), the water was still flowing outward, where it hit the raised edge of the ring holding the substrate down, and then flowed back toward the center. The liquid was filled with bubbles created by air entrained by impacting droplets. The water film became thinnest near the center of the substrate, directly under the spray nozzle, and at t = 150 ms a small hole was seen in the water film through which the bare substrate was exposed. Two more holes formed in the film at t = 250 ms. After that the water started to close back over the holes, and at t = 350 ms they had become much smaller and had completely closed by t = 385 ms. There were still many air bubbles in the water, but they gradually burst through the surface and disappeared. It took several seconds for all the bubbles to disappear from the water.

Fig. 2

Water film dynamics on a polished steel surface immediately after spraying. Time t = 0 corresponds to the spray being turned off. A hole can be seen in the film at t = 150 ms; all holes are completely closed by t = 425 ms

As the duration for which the water spray was turned on was increased, and the thickness of the water film (h) on the surface became greater, holes created in the film closed more rapidly. Once the water layer exceeded a critical thickness (h _c ), all holes in the water layer closed spontaneously by the time the film reached equilibrium. Figure 3 shows close-up images of a sprayed water film on the three different substrates for film thickness just below critical (h < h _c ), for which a hole remained in the film even in the final state. Each column shows successive stages of the water film at the center of the substrate, directly under the nozzle axis. The time t = 0 ms corresponds to the spray being turned off. At t = 100 ms, a thin water film completely covered the Plexiglas substrate (Fig. 3a), while three holes had started to grow in the water layer on the steel plate (Fig. 3b). On the Parafilm-M surface (Fig. 3c), the hole was so large that its edges are not visible, lying outside the field of view of the camera. The droplets created by the breakup of the water layer are visible, beaded up on the hydrophobic surface. At t = 125 ms the film on Plexiglas showed the first sign of rupture, while the holes on the steel plate had grown significantly larger. At t = 200 ms, the holes in the films on Plexiglas and steel continued to grow and merge with each, while the hole in the film on Parafilm-M started to recover with the edge of the advancing water film visible. By t = 400 ms all the holes had started to close as the water film rebounded off the edge of the rim enclosing the substrates and the holes became progressively smaller. The final frame in each sequence shows the equilibrium state on each surface, at times of roughly 4 s. All the films had holes in them, which did not close completely. Bubbles due to droplet impact can be seen in all instances and were roughly the same size on all substrates. With time, most burst through the surface.

Fig. 3

Water film dynamics immediately after spraying on three different substrates: a Plexiglas, b steel, and c Parafilm. Time t = 0 corresponds to the spray being turned off. Holes can be seen in the film at t = 100 ms and do not recover

Figure 4 shows close-up images of sprayed water films on the three different substrates for film thickness just greater than critical (h > h _c ), in which all holes closed at equilibrium. The images show similar dynamics to those shown in Fig. 3. However, in this case the film recovered completely and all holes had closed at t = 540, 450, and 850 ms for Plexiglas, steel, and Parafilm-M, respectively. Again, bubbles can be seen in most images, and they disappear with time.

Fig. 4

Water film dynamics immediately after spraying on three different substrates: a Plexiglas, b steel, and c Parafilm-M. Time t = 0 corresponds to the spray being turned off. Holes can be seen in the film at t = 100 and are completely closed by t = 550–940 ms

For all experiments with water, dewetting (film rupture and creation of dry patches) occurred at or close to the center of the substrate, while the just-sprayed liquid was still moving toward the rim confining the liquid to the surface. If rupture occurred in more than one location, the dry patches grew and combined into one or two larger regions. Then, water rebounded off the wall surrounding the edges of the substrate and flowed back to the center of the substrate, which was dry. If the volume of sprayed water was sufficient, so that the average film thickness was greater than h _c , then that rebounding water closed the hole and reestablished an unbroken film. If the average film thickness was less than h _c , the hole did not close and the film did not recover. The critical film thickness was defined as being the minimum necessary to heal the film after the initial formation of holes in it.

The manner in which the water film on the substrate first ruptured differed for each substrate. The Plexiglas surfaces typically showed a small breakup region at the center of the substrate (Fig. 3, t = 125 ms). The steel surface showed simultaneous dewetting at several locations. The center of the Parafilm surface, even at the earliest stages (see Fig. 3, t = 100 ms), had a large dewetted area with small droplets scattered in it. The ease with which films ruptured on the three surfaces corresponded to the receding contact angle of water on them (see Table 2), which were 18°, 28°, and 80° for the steel, Plexiglas, and Parafilm surfaces, respectively. A smaller θ _R hinders retraction of the water film and makes it harder to dewet the surface.

Figure 5 shows the average critical thicknesses (h _C ), calculated by measuring the minimum volume of liquid necessary for the film to just recover and dividing by the surface area of the substrate, as a function of both equilibrium and advancing contact angles. There appears to be a linear relation between the advancing contact angle and the critical film thickness. The larger the θ _A is, the more resistance there is to the water film flooding back and closing the hole, and therefore, the critical film thickness increases with contact angle. The values of critical height were relatively insensitive to the mass flux or droplet impact velocity: changing the height of the spray nozzle above the test surface from 215 to 299 mm had negligible effect on the critical thickness values.

Fig. 5

Variation of sprayed water film critical thickness with contact angle. Filled circle: equilibrium, filled square: advancing

The critical thickness necessary to prevent a thin liquid layer on a solid surface from rupturing can be calculated using a thermodynamic stability analysis developed by Sharma and Ruckenstein (1989). They calculated the total energy of a liquid film both with and without a hole of a given diameter in it: The configuration with lower energy was assumed to be the stable one. The surface energy of a thin liquid layer with surface area A, lying on top of a solid surface, is as follows:

$$ F_{\text{film}} = (\gamma_{ \lg } + \gamma_{\text{sl}} )A $$

(1)

If the film has a hole with radius r ₁ at the lower surface and r ₂ on the upper surface in contact with air (see Fig. 6), its energy becomes:

$$ F_{\text{hole}} = \gamma_{ \lg } \left( {A - \pi r_{2}^{2} } \right) + \gamma_{\text{sl}} \left( {A - \pi r_{1}^{2} } \right) + S\gamma_{ \lg } + \pi r_{1}^{2} \gamma_{\text{sg}} , $$

(2)

where S is the area of the liquid meniscus lying between r ₁ and r ₂. The presence of the hole changes the energy of the system by:

$$ \Updelta F = F_{\text{hole}} - F_{\text{film}} = - \pi r_{2}^{2} \gamma_{\lg } + \pi r_{1}^{2} (\gamma_{sg} - \gamma_{{s\text{l} }} ) + S\gamma_{\lg } . $$

(3)

Young’s equation gives a relation between the contact angle and surface tensions:

$$ \gamma_{\text{sg}} - \gamma_{\text{sl}} = \gamma_{ \lg } \cos \theta , $$

(4)

Using this, the free energy change is as follows:

$$ \Updelta F = \gamma_{\lg } \left( {S - \pi r_{2}^{2} + \pi r_{1}^{2} \cos \theta } \right) $$

(5)

Fig. 6

Shape of liquid meniscus around a hole in a liquid film

If ΔF < 0, the presence of a hole reduces the energy of the film so that it will grow larger and the film will rupture, whereas if ΔF > 0, the hole increases system energy and it will close, leaving the film intact. A large value of S in Eq. (5) promotes film stability. Sharma and Ruckenstein (1989) solved the Young–Laplace equation of capillarity to find the surface area of the liquid meniscus S as a function of the contact angle θ and the ratio of the film thickness to hole radius, h/r ₁.

Dhiman and Chandra (2008) used the analysis of Sharma and Ruckenstein (1989) to calculate the critical value of h/r ₁ above which the film is stable (ΔF > 0) as a function of advancing contact angle. Their results are shown in Fig. 7. Both high and low contact angles produce a meniscus with large surface area when a hole is created in the liquid film. The large surface energy associated with this exposed area will inhibit further expansion of the hole, making it close. In contrast, intermediate contact angles (θ–90^o) produce a meniscus with small surface area, rendering such a hole energetically favorable and making it grow. The most unstable film is on a surface with contact angle 118°, for which h/r ₁ = 0.69.

Fig. 7

Variation of the ratio of critical film thickness, h _C , to hole radius, r ₁ , with contact angle, θ, for a stable film. h _C /r ₁ is maximum (=0.69) at θ = 118° (adapted from Reference Dhiman and Chandra (2008)

In our experiments, 80° < θ _A  < 110°, over which range h/r ₁ increased almost linearly with θ _A (see Fig. 5), which agreed with the theoretically predicted trend (see Fig. 7). We can use the analysis to estimate the minimum size of the hole that created film rupture, for example, reading from Fig. 5 for the steel surface, when θ _A  = 90° h _C  = 2.6 mm. Fig. 7 gives h _C /r ₁  = 0.65 for θ _A  = 90° so that r ₁ = 4.0 mm: It would take the formation of at least a 4.0-mm-radius hole in the film for rupture to occur. Mulji and Chandra (2010) have shown that bubbles bursting through the water film can create holes that expand and create ruptures. Measurements from photographs showed that bubbles in the water film typically ranged from 0.3 to 0.8 mm. However, the model assumed that the water was quiescent and the film thickness was uniform; the outward motion of the liquid probably assisted film rupture by causing local thinning of the film directly under the nozzle. If the film thinned to approximately 0.3 mm, assuming h _C /r ₁  = 0.65 implies that a 1-mm-diameter hole would be sufficient to rupture it.

The stability analysis does not show any effect of fluid viscosity; Eq. (5) includes only surface tension and contact angle. The healing of the rupture in the liquid film occurs when the spray has been shut off and the characteristic flow velocity is that of the liquid along the edge of the closing hole which can be measured from the images in Fig. 4 to be of the order of V = 0.1 m/s. The corresponding capillary number (Ca = μV/σ) is of the order 10⁻³. Since Ca ≪ 1, the flow is driven by capillary forces, and we would expect viscous forces not to be important.

Experiments were done with water–glycerin mixture sprays to test whether fluid viscosity had any effect on film stability. Figure 8 shows high-speed, close-up images of a sprayed 20 % glycerin solution film on both steel and Parafilm substrates, for the cases of film thickness just above and just below the critical thickness, showing films that just ruptured and just recovered. Time t = 0 corresponds to the spray being turned off. The dynamics are similar to those of the water films shown in Figs. 3 and 4. At t = 200 ms, many bubbles due to impact can be seen in the films on steel and Parafilm-M, appearing as bright spots on the steel surface. At t = 300 ms, expanding holes can be seen in all films. At t = 450 ms the holes started to contract as the liquid film rebounded off the walls surrounding the substrate. The holes continued to contract, and for the case of h > h _c , they completely closed over at t = 450 and 600 ms for steel and Parafilm-M, respectively, whereas for h < h _c the holes did not recover. Bubbles can be seen in all images, and with time they burst through the surface.

Fig. 8

Aqueous 20 wt% glycerin film dynamics after the spray was turned off. Holes can be seen in the film at t = 200 ms for both steel and Parafilm-M. For recovered films, holes are completely closed by t = 450 ms for steel and t = 600 ms for Parafilm-M

Increasing the viscosity of the sprayed liquid, by increasing the concentration of glycerin in it, suppressed the initial breakup of the film immediately after it was sprayed. The 20 % glycerin solution, with a kinematic viscosity 1.7 times that of water, did not rupture at multiple locations like pure water (see Fig. 3) when sprayed on steel, but only at the center where the spray impacted. The higher viscosity inhibited coalescence of bubbles and movement of the liquid, so that it was more difficult for a hole to form that was sufficiently large to trigger rupture of the film. Even on Parafilm-M, where a water film ruptured almost immediately (see Fig. 3), it took at least 200 ms for a hole to be visible (see Fig. 8). Fewer droplets were seen inside this dry patch for a 20 or 40 % glycerin film than for water.

At higher glycerin concentrations, where viscosity increased significantly, there was no breakup at the center of the film when sprayed on steel, and we could not therefore measure a critical thickness. It is likely that the viscous liquid did not thin sufficiently at the center for bubbles to puncture it and create a hole. Figure 9 shows high-speed images of the entire steel substrate after spraying with a 65 % glycerin solution. In this case a dry patch was first visible near the edge of the substrate (see t = 400 ms) as the liquid film recoiled from the edge of the substrate, but no rupture was seen near the center of the substrate. The highly viscous liquid failed to spread sufficiently to cover the entire substrate.

Fig. 9

Aqueous 65 wt% glycerin film dynamics on a steel substrate after the spray was turned off at time t = 0. No central rupture was observed in the film

When glycerin–water mixtures were sprayed on Parafilm-M, a hole always formed initially at the center of the substrate. Figure 10 shows close-up images of a film of 65 % glycerin solution sprayed on Parafilm-M. The dynamics are similar to those seen earlier for 20 % glycerin on Parafilm-M (Fig. 7). Holes start to form at t = 100 ms and continue to expand until t = 220 ms. At t = 300 ms, the liquid starts rebounding and holes start to close. If h > h _c , the hole closes completely by t = 850 ms.

Fig. 10

Aqueous 65 wt% glycerin film dynamics on a Parafilm-M substrate after spray was turned off. Holes can be seen in the film at t = 100 ms

The liquid moved slowly due to high viscosity, and fewer and smaller bubbles were observed than in water films. Bubble diameters were measured at around 0.1–0.5 mm for aqueous glycerin sprays, compared to 0.3 to 0.8 mm in water. Increasing viscosity had relatively little effect on the critical film thickness, and for a Parafilm substrate we measured h _C  = 3.8 ± 0.2 mm for all glycerin mass fractions between 20 and 70 %. The addition of glycerin in this range of concentrations increased viscosity by an order of magnitude (Table 1), while having a relatively small effect on surface tension and contact angle (Table 2). The critical thickness was close to that of pure water on Parafilm, h _c  = 4.3 mm. This finding is in accord with the model of Eq. (5), which predicts that the critical thickness is independent of viscosity. Viscosity has only a weak effect, in that it inhibits the initial nucleation of bubbles and holes in the film, and therefore increasing viscosity by even an order of magnitude only slightly decreases the critical film thickness.

4 Conclusions

A thin water film sprayed onto a surface typically ruptured near the center of the substrate, directly under the nozzle. The growth of the initial rupture became more rapid as the receding liquid–solid contact angle increased. If the volume of water sprayed was sufficient for the film thickness to exceed a critical thickness (h _c ), the liquid rewet the surface after it ruptured and the hole closed. If the film thickness was less than h _c , the hole remained. The value of the critical thickness increased linearly with advancing liquid–solid contact angle for the surfaces tested, whose advancing contact angle varied from 80° to 110°.

Air entrapped by impacting droplets in the spray led to the formation of a large number of bubbles in the water film with diameters that varied typically from 0.3 to 0.8 mm. The bubbles gradually broke through the water surface and disappeared. A model based on comparing the energy of an intact liquid film to one with a hole in it was used to predict the critical hole size. It is likely that local thinning of the film at the point of spray impact allowed air bubbles to act as initiation points for film rupture.

Dissolving up to 70 wt% glycerin in water increased the viscosity of the liquid sprayed by an order of magnitude while making only small changes to surface tension and density. High viscosity inhibited initial breakup of the liquid film: For impact on a steel surface, there was no hole formed at the center of the surface. Increased liquid viscosity diminished thinning of the liquid film and made air bubbles too small to create a sufficiently large hole. However, dewetting of the surface occurred near the edge of the substrate because the viscous liquid could not flow sufficiently to entirely cover the surface. On the most hydrophobic surface, Parafilm-M, there was film rupture for even the highest-viscosity liquid. The critical thickness did not vary very much with viscosity, showing that it depends mostly on the wettability of the substrate, as predicted by the surface energy model.