Bubble Clustering in Drying Paint Films - Industrial & Engineering

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BUBBLE CLUSTERING IN DRYING PAINT FILMS Nazli Saranjam, and Sanjeev Chandra Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b03313 • Publication Date (Web): 28 Nov 2016 Downloaded from http://pubs.acs.org on November 30, 2016

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BUBBLE CLUSTERING IN DRYING PAINT FILMS N. Saranjam, S. Chandra Department of Mechanical and Industrial Engineering University of Toronto Toronto, Ontario, Canada

ABSTRACT Paint films with uniform thicknesses (~1 mm) were applied on glass substrates using a model paint consisting of a resin dissolved in butanol. Small air bubbles were introduced into the liquid and test samples cured in a natural convection oven. Bubbles in paint grew larger as the evaporating solvent diffused into them. Photographs of the liquid film surfaces were taken during drying and the distance between bubbles measured. Bubbles were observed to move towards each other and form clusters. When a vertical surface was introduced into the liquid film bubbles moved towards the surface if the liquid-solid contact angle θ < 90°, but moved away if θ>90°. A floating bubble or hydrophilic surface creates an upward curving liquid meniscus near itself so that neighbouring bubbles experience buoyancy forces that drive them up the rising liquid surface. A hydrophobic surface creates a downwards-curving meniscus, so that bubbles move away from it. Bubble motion was modeled using an analysis of the shape of liquid meniscus and buoyancy forces acting on floating bubbles.

KEY WORDS: paint drying, bubble clustering, bubble growth

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INTRODUCTION The final step in the manufacture of many industrial components is the application of paint or some similar polymer coating. Paint, which is typically a polymer dissolved in a solvent, is sprayed on automotive body panels and then baked in an oven where the solvent evaporates while the polymer cross-links and cures, forming a hard layer. The paint enhances the appearance of the car and prevents corrosion of metal components. A polyurethane topcoat is usually applied on furniture and cabinetry to seal and protect the wood. In all of these applications it is very important to achieve a smooth, unbroken coating that shields the substrate from exposure to moisture, sunlight or atmospheric pollution. When paint is sprayed on a surface a large number of air bubbles may be entrained by impacting droplets and trapped in the deposited layer 1. This is a well-known problem and several “de-foaming agents” are commercially available, which are typically surfactants that are added to water-based paints to reduce surface tension and allow bubbles to burst through the paint layer and escape 2. In the automotive industry it is standard practice to wait for 5-10 minutes, a period known as the “flash-off” time, to allow paint bubbles to disappear before components are placed in a heated oven to cure. When we form a thin layer of a liquid mixture in which one component is much more volatile than the others, local concentration variations develop on the evaporating surface. Since paint surface tension increases when the amount of solvent in it is depleted, there is a flow from regions of low concentration to those of high concentration, a phenomenon known as solute-driven Marangoni convection. If there persist sufficiently large concentration difference, a self-sustaining flow is established consisting of recirculation zones within polygonal cells 3. Bubbles smaller than the size of these cells are


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transported along with the liquid and those that are carried to the surface of the paint burst through and disappear. Any bubbles remaining in the paint after it is placed in an oven become trapped since a viscous skin forms on the surface of the paint film as the solvent dries 3. The remaining solvent diffuses into the bubbles, making them grow rapidly so that some may become large enough to burst through the surface, leaving blisters and pinholes in the paint surface. Bubbles in dried paints are frequently observed to group together, creating regions that appear cloudy in clear-coat paints 4. Bubble clusters are often observed to be concentrated in corners where two surfaces meet at an angle. A number of experimental and analytical studies have previously been carried out on thermocapillary flow and its effect on bubble motion

5 6 7 8.

Experiments show that a sufficiently

large temperature gradient in a vertical column of liquid can counteract the buoyancy force and hold a bubble stationary 5. The presence of concentration gradients was found to affect convective flows around a bubble 9 10. The growth of vapour bubbles in a liquid of infinite extent has been studied by many researchers

11 12

bubbles in drying paint layers. Bragg

13

, but there are very few studies

3

on the growth of

used sheets of uniform sized bubbles as a model to

visualize the imperfections found in crystal and polycrystal lattices. Nicolson

14

developed a

model to estimate the potential energy of two similar bubbles floating next to each other. Shi and Argon 15 extend this model to obtain the attractive force between two bubbles of different radii and evaluate the energies of bubble clusters. Srinivasarao et al.

16

described the formation of

three-dimensional arrays of air bubbles in a polymer film because of evaporative cooling and thermocapillary flows. Kralchevsky and Nagayama 17 have given a comprehensive review of the emergence of structures in particles subject to capillary forces.



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This study was undertaken to observe the growth and movement of bubbles in a paint layer and to determine the mechanisms that control bubble transport. In particular, we wanted to understand why bubbles cluster together and why they are concentrated near corners. Bubbles were introduced into uniform paint layers applied on glass substrates to simulate industrial applications where bubbles might be entrapped during the spraying process. Relatively thick (1 mm) paint films were applied on the test surfaces, which allowed large bubbles to grow that were easy to observe and photograph. Thick paint layers have large volume to surface ratios, increasing the time required for curing and giving a longer time to study bubble dynamics. Painted surfaces were dried in an oven and bubble growth and movement photographed. Measurements were made of the spacing between bubble and analytical models developed to predict the speed with which bubbles approached each other. Tests were also done with glycerin, which had viscosity values similar to paint but did not cure and harden.

EXPERIMENTAL SYSTEM A model paint formulation was developed for experiments to have viscosity, surface tension, and curing temperature similar to that of a commercial clear coat 18. The model paint consisted of 85 wt% resin and 15 wt% solvent (normal butanol, Caledon Laboratory Chemicals, ON, Canada). The resin composition contains 70 wt% butylated melamine P/W formaldehyde (CYMEL® 1159 Resin, CYTEC, NJ, USA) and 30 wt% hydroxyl-functional thermosetting acrylic (PARALOIDTM AT400 Resin, DOW Chemicals, PA, USA). The properties of the paint at room temperature were: density (ρ) 988 kg/m3, viscosity 240 cP, and surface tension 26 mN/m. The resin also contained butanol and small amounts of methyl n-amyl ketone solvent, so a thermogravimetric analysis instrument (Model SDT Q600, TA Instruments, New Castle, USA)


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was used to determine the total solvent content of the model paint. Paint samples, weighing less than 15 mg, were heated with a 10°C/min ramp from room temperature to 250°C. This heating cycle was repeated after cooling the sample to ensure evaporation of all the volatiles and the results showed approximately 45% solvent content in the model paint composition. The initial concentration of butanol in the model paint, Ci, used in calculations was 0.45. Some experiments were done with glycerin (Caledon Laboratory Chemicals, ON, Canada) that had high viscosity similar to that of the paint but did not harden. The properties of glycerol were: density (ρ) 1261 kg/m3, viscosity 1300 cP, and surface tension 63.4 mN/m. Heat-resistant borosilicate glass substrates (Model 8477K78, Mc-MASTER-CARR, USA), 63.5 mm in diameter with 3.2 mm thickness, were used as test surfaces. They were cleaned with acetone to remove dust particles and any oil or silicon residue. Paint was deposited on the substrates using a syringe and the substrate manually tilted to allow paint to spread on the substrate and completely coat it. Glass petri dishes, 63 mm in diameter, were used to contain larger volumes of liquid such as glycerin and glycerin-butanol to study the motion of bubble for longer periods of time. To create air bubbles within the paint prior to spreading it on test substrates glass vials (66011-085, VWR International, USA) were filled three quarters full with paint and shaken to introduce small amounts of air into the liquid. Coated substrates were placed inside a metal chamber (with less than 15 seconds delay after applying the coating) that was used as a convection oven to cure paint samples (see Figure 1). A 750 W band heater (Model HB-5075/240V, OMEGA Engineering, Quebec, Canada) regulated by a bench-top temperature controller (Model MCS-2110K-R, OMEGA Engineering, Quebec, Canada) was placed inside the chamber, surrounding the substrate, and used to elevate the temperature of the air to up to 200°C. Air circulation in the chamber was kept at minimum with a



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velocity less than 2 m/s at the inlet to the metal chamber to help carry the fumes out to the exhaust fume hood and maintain only natural convection in the vicinity of the drying sample. The heater surrounding the test surface minimized any direct forced convection flows over the paint. Substrates were placed on a support rod that passed through the bottom of the chamber and rested on an analytical balance (Model E01140, OHAUS Corporation, Parsipanny, USA) which recorded their weight with a resolution of 0.1 mg every 60 s. The chamber had a glass top through which the substrate could be viewed and still images with 1280 x 1024 pixels resolution of the paint surface were taken at 2 seconds intervals using a camera system (Model SensiCam Optikon PCO, Cooke Corporation, Germany). Pictures of liquid layers with growing bubbles were analyzed using the threshold function in image analysis software (ImageJ, National Institute of Health) to count the number of bubbles in each image, the cross-sectional area of each bubble, the location of individual bubbles, and the distance between bubbles as they formed clusters.

RESULTS AND DISCUSSION Figure 2 shows bubble growth and movement in a 1 mm thick paint curing at a temperature of 120 ± 5°C. The paint was placed in a circular glass disc whose edges are visible around the boundaries of the images in Figure 2. Small bubbles were introduced in the paint by stirring it before spreading it on the glass surface. As curing progressed the bubbles grew larger as solvent diffused into them (see t=4.1 min). The largest concentration of bubbles was around the edges of the glass disc where air, trapped when the liquid was spreading on the surface, acted as nucleation sites. Bubble growth was relatively slow at first, but then grew faster (t > 11.2 min). Some of the bubbles disappeared as they burst through the surface of the paint film, but most of them survived and grew larger. Bubbles in the paint film began to form clusters, moving towards


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each other. Two circles, 10 mm and 13 mm in diameter respectively, are superimposed in Figure 2 on the images for t ≥ 15.7 min, to identify groups of bubbles that grouped together. The bubbles accelerated as the distance between them diminished which is an indication of the attraction force increasing as bubbles get closer. The growth rate of individual bubbles was determined by measuring bubble diameters from photographs. Figure 3 shows the variation of bubble radius as a function of time for bubbles in paint films curing at three different temperatures (100°C, 120°C and 140°C). Bubble growth was initially slow and then increased very rapidly. The transition occurred at approximately t = 6 min at a temperature of 140°C and came progressively later as the paint curing temperature was reduced. As the paint dries butanol evaporated from it, with the lowest concentration on the surface of the paint film. The depletion of solvent leads to the face of the paint exposed to the air drying out first and forming a solid skin that acts as a barrier to further escape of volatiles. The solvent trapped in the paint is forced into the bubbles, making them grow rapidly. Increasing the curing temperature hastens the formation of the skin, making the transition to faster growth happen sooner. The rate at which solvent is depleted can be determined by weighing the paint sample as it dries. Figure 4 shows the solvent mass loss (Mt) from a paint sample curing at 120°C, normalized by the total mass of solvent (M∞) in it. For comparison similar data is shown for a sample with a 1 mm thick layer of a 70% glycerin30% butanol mixture, which had similar viscosity and density as the paint but did not harden or form a skin while drying. At short times (t < 5 min) the evaporation rate of butanol was similar in both samples, which corresponded to the period of slow bubble growth (see Figure 3). After that time the rate of solvent depletion was slower for the paint, showing the effect of curing and the formation of a surface skin. At t = 30 min over



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90% of the solvent had diffused out of the glycerin-butanol solution (see Figure 4) whereas less than 60% had escaped from the paint. The initial variation of the bubble surface area was linear and could be predicted quite well by classical bubble growth theory 3. Small bubbles in a thin paint film are transported by Marangoni flows that occur due to variation in the solvent concentration, which produces surface tension gradients 19. If there are sufficiently large concentration differences across or along the surface, a self-sustaining flow is created in the form of recirculating flows within polygonal cells. Bubbles smaller than the size of these cells, are transported along with the liquid and tend to accumulate near the stagnation point of the vortex inside a recirculating flow 3. This type of flow continues to bring the bubbles to the surface where they escape 1. However, once a skin forms on the paint surface the bubbles can no longer escape, but are trapped in the film. This is due to a thin liquid sheet being formed at the liquid-air interface where bubbles are resting. This liquid sheet has to rupture before the bubbles can escape the paint layer, but the higher the viscosity, the longer the time taken for the paint film to drain and

rupture 20 21 22. After this time the movement of the bubbles is no longer

governed by the Marangoni flows but by buoyancy forces created due to the surface of the paint film being distorted by bubbles protruding through it 14. A bubble that projects above the liquid surface creates an upward sloping liquid meniscus around itself, causing the bubbles in its vicinity to experience a net upward force due to buoyancy (see Figure 5). Since bubbles are constrained at the free surface they move along the meniscus until they touch each other, further increasing the distortion in their vicinity

24

. The larger a group of bubbles the greater the

buoyancy force created around it, so bubble movement accelerates until all have been drawn into clusters in the paint film.


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The length scale over which the meniscus is curved may be estimated from the capillary length: =

(1)

For the properties of paint this length was estimated to be approximately 2 mm, which appears to be a reasonable estimate of the distance over which bubbles were drawn to neighbouring bubbles to form clusters. In Figure 2 two circles are drawn on images corresponding to t>15.7 min, with radius 5 and 6.5 mm respectively, to show two regions in which clusters formed. The capillary length therefore gives a reasonable order-of-magnitude estimate of the range over which bubbles are attracted towards one another. Clustering of bubbles occurs not only in paint but can be observed in other types of liquids with long-lived bubbles trapped at the interface. Figure 6 shows a sequence of images of an approximately 5 mm deep pool of glycerin at room temperature. Bubble were mixed with glycerin by agitating the container and depositing the content in a 63 mm diameter glass petri dish. The sample was immediately placed under the camera and still images were taken every 2 seconds. Bubbles were distributed randomly in the film at t = 0 min, but the smaller bubbles were attracted to the largest bubble (approximately 1 mm in diameter) indicated by the dashed circle in less than 4 minutes. The capillary length for glycerin calculated from Eqn. 1 is approximately Lc = 2.2 mm. The white circles drawn in Figure 6 are 5 mm in diameter and show how bubbles confined within this area were attracted to each other. Since the glycerin did not solidify many of the bubbles were able to burst through the surface and disappeared. Eventually



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two main clusters were formed on the surface at t = 10 min. After sufficiently long times (approximately 30 min), these islands of bubbles also migrated to the wall of the container. The presence of a wall deforms the interface just as a bubble does, with the direction of the interfacial curvature depending on the liquid-solid contact angle (θ) (see Figure 7). If the surface is hydrophilic, so that θ < 90°, the liquid meniscus rises upwards near the wall (Figure 7a). Bubbles experience an upwards buoyancy force and move toward the highest point of elevation of the liquid surface. Viewed from above it appears that the bubble is moving towards the surface. Alternately, if the surface is hydrophobic with θ > 90, the liquid meniscus rises upwards away from the solid wall and bubbles should move away from the surface (Figure 7b). To test this hypothesis paint in a glass container was agitated to entrap bubbles and 32 ml of the liquid was deposited on a 63.5 mm diameter glass substrate (Model 8477K78, Mc-MASTERCARR, USA) to create an approximately 1 mm deep layer. A PTFE ring (Model 9559K62, McMASTER-CARR, USA) with an inside diameter of 19 mm, outside diameter of 22 mm, and thickness of 1.8 mm, was immediately positioned on the surface that was then placed in an oven at 120 ± 5°C. Photographs of bubble motion and growth were taken at 2 s interval. Paint wets PTFE (θ ≈ 50°) so that the meniscus formed by a paint layer is concave upwards. Bubbles are therefore expected to move towards the solid surface as shown in Figure 7a. Figure 8 illustrates the behaviour of bubbles as the paint layer was cured. At t=0 the bubbles were scattered across the paint surface, moving freely due to surface tension-driven flows resulting from evaporation of solvent and concentration gradient. Bubbles in the neighbourhood of others experience a net upward buoyancy force, move closer to each other and start to form clusters as seen at t=13.5 min. At the same time small air bubbles trapped on the surface of the solid ring when it was immersed in the liquid act as nucleation sites. Solvent evaporating from the paint


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fills the paint bubbles, making them grow rapidly. The formation of a skin on the surface of the paint layer inhibits solvent from leaving the surface and also traps bubbles in the paint layer so that they cannot escape. The increasing viscosity of the paint also slows down the motion of bubbles. By

t = 20.3 min there are a large number of bubbles attached to the surface of the

ring surrounded by several bubble clusters. The rheology of paint during curing is extremely complex and it is not only viscoelastic but is also non-linear. The viscosity initially decreases due to shear heating and thermal effects, but as curing proceeds, it changes from a viscous liquid to an elastic gel and the viscosity approaches a theoretical infinity. This time is defined as the gel point when the resin does not possess favourable properties for flow and contains both soluble and insoluble materials

23

. As the

reaction proceeds, the amount of gel increases at the expense of the soluble material and the curing system reaches the vitrification point. An isothermal time-temperature transformation cure diagram (TTT), which is specific to a particular material, provides a framework for understanding the cure process of thermosetting materials, but this is beyond the scope of this study. On Curing, gelation occurs and retards macroscopic flow, however, at the vitrification point, the material transforms from a rubbery to a glassy state and even chemical reaction can proceed at a very low diffusion-controlled rate until complete curing

25 26

. Due to concentration

gradient across paint film thickness, the rheology also varies depth wise and as solidification is fastest at the interface where solvent depletion is most pronounced, bubbles become trapped underneath the rubbery surface but continue to move under the influence of buoyancy forces. The time scale for vitrification and complete curing is much larger than when the bubble clusters were observed to form (t > 1 hr). Past the vitrification point, all motion stops and a very high



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shear stress is needed for bubbles to continue to move at the expense of plastically deforming the paint.

Glycerin does not wet PTFE very well (σ= 64 mN/m, θ ≈ 100°) so that the meniscus formed is convex upwards. Bubbles should therefore move away from the wall as seen in Figure 7b. To confirm this hypothesis bubbles were introduced in glycerin by agitating the liquid in a glass container and depositing the contents in a 63 mm glass petri dish in which a PTFE ring (Model 92150A163, Mc-MASTER-CARR, USA) with an inside diameter of 10 mm, outside diameter of 15.8 mm, and thickness of 1.5 mm, was placed and time-lapse photos taken every 2 seconds. Figure 9 shows a sequence of images of bubbles confined within the inner wall of a PTFE ring in an approximately 5 mm deep film of glycerin at room temperature.

Time t=0 s

corresponds to less than 10 seconds after the ring was placed on the surface. The bubbles were distributed randomly throughout the liquid, but after only 20 seconds, buoyancy forces drove the bubbles towards the highest point of the curved surface, which was at the center of the ring (see t=3 min). Since the film did not solidify in this case bubbles continued to escape from the free surface until at t=9.5 min the majority of bubbles had disappeared.

The dynamics of floating bubbles To estimate the typical distance between bubbles as a function of time, following Nicolson’s 14

approximation, we first consider an isolated bubble of radius R at rest on the surface of a fluid.

The bubble creates a meniscus around itself that forms an angle θ with the level liquid surface


Page 25 of 36

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(see Figure 10). The bubble radius R can be non-dimensionalized using the capillary length Lc to give a dimensionless radius =

In our experiments, α can be calculated at each time step using the bubble radius and appropriate capillary length. The liquid contacts the sphere at a radius b and the angle between the liquid meniscus and bubble surface is ψ. If Z is the height of the liquid surface in the neighbourhood of a bubble and r distance from the vertical axis, we can introduce the dimensionless variables =

, = ,

=

The angle and the dimensionless length β can be related by examining the right-angled triangle formed by the side with length b and hypotenuse R in Figure 10: tan = Nicolson

14

1 −

(2)

solved the Laplace equation to derive the shape of the free liquid surface around a

bubble and calculate the variation of Z with radial distance r, assuming that the capillary pressure balanced the hydrostatic pressure difference over the height of the meniscus. If the slope between the cap of the bubble and the remainder of the liquid meniscus is assumed to be continuous at the ring where the liquid touches the bubble surface (where δ=β), we obtain the equation 14: = − = tan 4 −


(3)


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Page 26 of 36

The height to which the bubble rises above the level liquid surface is determined by equating the upward buoyancy force it experiences (due to the mass of liquid displaced by the submerged bubble volume) to the downward component of the surface tension acting on the circular contact line with radius b. Solving these equations, Nicolson

14

tabulated values of β (the radius of the

liquid meniscus around the bubble) as a function of α (the dimensionless bubble radius), which are shown in Figure 11. Using the slope of the interface at the ring of contact

= tan , Vella and Mahadevan 24

found the following expression: tan sin = "#

(4)

Where B ≡ R2/ Lc2 is the Bond number that represents the ratio of gravity to surface tension forces. Eqn. (4) is valid for B

Bubble Clustering in Drying Paint Films - Industrial & Engineering

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