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Colour variation in drying paint films
Progress in Organic Coatings 136 (2019) 105173
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Progress in Organic Coatings journal homepage: www.elsevier.com/locate/porgcoat
Colour variation in drying paint films
T
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Marina Curak, Nazli Saranjam , Sanjeev Chandra Centre for Advanced Coatings and Technologies, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, M5S 3G8, Toronto, ON, Canada
A R T I C LE I N FO
A B S T R A C T
Keywords: Mass transfer Paint color Surface-tension driven flows Concentration gradient Slef-organizing patterns Paint pigments clustering
Color variations due to changes in paint film thickness and pigment content were studied experimentally. Three paints with differing concentration (0.5%, 2% and 4% by weight) of spherical blue pigments were applied with varying film thickness (310, 490, 730 μm) on stainless-steel substrates and dried in an oven while the paint surfaces were photographed. Weight loss due to solvent evaporation from the paint was recorded. The color of the dried paint films was measured. Surface tension driven convection was observed in drying paint films, which caused movement of pigment particles. An analytical model was used to predict solvent concentration gradients in the paint films and calculate Marangoni numbers, which determined the velocity of fluid motion. All motion stopped when the Marangoni number became small. Pigment particles tended to cluster around the edges of convection cells and produce changes in color, especially when the paint films were thin and the pigment fraction low. Increasing either the amount of pigment or the paint thickness made the paint color lighter, as a larger number of pigment particles increases reflection of light. Paints with high pigment concentration are less likely to see changes in color.
1. Introduction Automotive paint performs two different roles: protective, as a coating that shields a car body from abrasion and corrosion; and aesthetic, as an exterior finish that looks attractive. Paint color is very important to customers and is very tightly controlled by manufacturers. It is especially important that paint color be reproducible since different components of the same vehicle are frequently painted separately and only brought together during final assembly when color mismatches become evident. It is known that changes in spray and drying parameters during painting can lead to changes in color, though the exact mechanism by which this occurs is not well understood. In practice introducing a new paint color on an automotive assembly line requires extensive trial and error to determine the best conditions for paint application. Automotive paints are complex mixtures with several components including: resin, which is the main film forming component; solvent, which reduces the viscosity of the paint; pigments, which provide color; and other additives that may modify fluid properties, enhance corrosion protection and provide resistance to ultraviolet light [1]. Paints are typically sprayed onto automobile components using electrostatic rotating bell applicators and then dried in an oven where solvent evaporates from the paint film while the resin polymerizes to form a hard
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coating. Light incident upon a paint layer may be either transmitted, absorbed or reflected; since the resin is typically transparent, the location, density and orientation of color pigments or metallic flakes in the paint determine how light is reflected, and therefore its color [2]. Kirchner and Houweling [2] measured the orientation of metal flakes that had been added to paints by placing paint films under a microscope. They studied the effect of flake shape and size on orientation and determined that large flakes were much more parallel to the substrate than small flakes. Kirchner [3] conducted another study to determine why flat flakes oriented themselves in a uniform direction. One hypothesis tested was that as the solvent evaporates the paint film shrinks, aligning the flakes with the substrate. However, the paper concluded that this was not sufficient to explain the uniform flake orientation and it was likely that flows in the paint film are responsible for the motion of flakes and pigments. While a paint film is drying flows can be created in it due to the presence of surface tension gradients. The surface tension of paint depends on the concentration of solvent in it, and since evaporation is never perfectly uniform local solvent concentration variations on the paint surface create surface tension differences, driving solutocapillary flows as liquid moves from regions of low to high surface tension [4,5]. Flow cells become visible in the thin liquid film and ripples are created on its surface [4]. Eventually, as the solvent escapes and its
Corresponding author. E-mail address: [email protected] (N. Saranjam).
https://doi.org/10.1016/j.porgcoat.2019.06.019 Received 8 January 2019; Received in revised form 8 June 2019; Accepted 10 June 2019 Available online 30 August 2019 0300-9440/ © 2019 Published by Elsevier B.V.
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concentration becomes low, the cells disappear but if they are still present when the resin begins to harden the paint surface becomes uneven, which is known as the “orange peel” effect. Saranjam et al. [6] studied the formation of orange peel as paint samples with varying thickness were dried in an oven while the paint surface was photographed. The thicker the paint film the longer the duration for which cells exist and the greater the amplitude of the orange peel. This study was conducted to determine if surface tension driven flows in drying paint films have any effect on the distribution of pigments within it, and whether this movement can influence the color of the paint. Test were done with a clear paint in which spherical blue pigments were added. The concentration of pigment in the paint was varied from 0.5% to 2% and 4% by weight. Each paint was coated on stainless steel substrates with wet paint film thickness varied from 300 to 800 μm and dried in an oven. The surface of the paint samples was observed using a video camera and the velocity of pigment particles measured using particle imaging velocimetry. The color of the dried samples was measured to determine if there were any changes.
Fig. 1. Schematic diagram of the experimental apparatus.
standard deviation of ± 30 μm respectively. Each experiment was repeated 3 times for each set of conditions. Test samples were placed 20 s after coating inside a convection oven at an average temperature of 121 °C ± 1.5 °C. Fig. 1 shows a schematic of the experimental apparatus consisting of an convection oven made from an aluminum chamber with two flexible adhesive heating sheets, 152.4 mm long and 76.2 mm wide with a power of 180 W each (Model 35765K25, McMaster-Carr, Aurora, OH, USA), placed on opposing sides and secured with an adhesive (Model 74515A32, McMaster-Carr, Aurora, OH, USA). Each heating sheet was powered by a variable voltage power supply and controlled by a temperature controller connected to a thermocouple placed behind each heating sheet. An additional thermocouple was placed beside the sample in the oven to continuously monitor its temperature. There was no forced air velocity across the sample: heat and mass transfer were by natural convection alone. The exterior of the oven was covered with high-temperature rigid fiberglass insulation (Model 9350K4, McMaster-Carr, Aurora, OH, USA), to reduce heat loss. A glass window was provided on top of the oven through which the paint sample could be observed. The sample was photographed as it cured using a camera (Model PL-D7715CU-T, Pixelink, Ottawa, ON, Canada) with a resolution of 4608 × 3288 pixels where each pixel corresponded to a distance of 0.87 μm [7]. The sample was placed on the end of a vertical aluminium tube that passed through a hole in the bottom of the chamber and rested on an analytical balance (Model E01140, OHAUS Corporation, Parsipanny, NJ, USA) that recorded the change in mass every 60 s with a resolution of 0.1 mg. Color was defined using the CIELAB color space, an industry standard that attempts to approximate human perception. A particular color is represented as a point in three-dimensional space whose position is fixed by three coordinates: L, a and b. The lightness value L varies between the darkest black to the brightest white, a represents the variation from green to red, and b the variation from blue to yellow. Typically L is measured on a scale from 0 to 100, while a and b are on scales from −128 to +128. The overall change in color (ΔE) can be calculated by treating it as a vector in this space, so that by measuring the changes in each coordinate (ΔL, Δa and Δb) and combining them we can obtain the magnitude of change:
2. Experimental methodology Experiments were done using a model paint previously described by Saranjam [6] for which all the relevant fluid properties have been previously determined. The paint was composed of 85% resin and 15% butanol (Caledon Laboratory, Georgetown, Ontario, Canada). The resin was a mixture of 70% Cymel 1159 modified melamine-formaldehyde resin (Cytec, Woodland Park, NJ, USA) and 30% Paraloid AT-400 resin (DOW Chemicals, Midland MI, USA). The properties of the paint were measured to be: density:ρ =988 kg/m3; viscosity: μ =240 cP; surface tension: σ = 26 mN/m. Paint is a non-Newtonian liquid and shows shear thinning behavior during application. A thermogravimetric analysis was used to measure the total amount of butanol and it was determined [6] that the initial concentration Ci = 0.45. The surface tension of the resin alone was 27.5 mN/m and that of butanol 23.5 mN/m. The variation of surface tension and viscosity with solvent concentration have been measured and reported earlier [6]. Commercial paints frequently contain surface active additives that typically reduce surface tension and may suppress the effects of surface tension gradients. The objective of this study was to observe surface tension-driven flows and therefore no surfactants were added to the model paint. Commercially available spherical blue pigments (Sapphire Blue, Paint with Pearl, Denver, CO, USA) with a mean diameter of 26 μm and a range of 10–60 μm were added to the paint. The size was measured from photographs of the pigments taken under a microscope. These pigments are much larger than those typically used in commercial paints, but were selected so that they were easily visible during drying and their motion could be recorded with a video camera. Spherical pigments were selected so that paint color did not depend on their orientation, but only on concentration and distribution. Three different concentrations were used, 0.5%, 2%, and 4%. The concentrations were determined by putting a pre-determined amount of paint in a beaker and measuring the mass on a precision scale with 0.1 mg accuracy. Subsequently, pigments were weighed in another dish and incrementally added to the beaker with paint while monitoring the total mass to ensure accuracy. The paint and pigments were mixed with a glass stirring rod immediately prior to their being tested. No stabilizers were used for the pigments as these may affect surface tension. Circular reflective stainless-steel substrates, with a diameter of 50.8 mm and a surface roughness of 0.1 μm were coated with the test paint. The substrates were first cleaned with acetone to remove the oil residue off the substrate and then placed in a sample holder on a 1-D translation stage. Paint was deposited on the substrate using a syringe and the translation stage moved under a blade coater (Model Multicoater 411, Enrichsen GmbH & Co, Hemer, Germany) to spread the paint into a uniform film. Experiments were done with average wet paint film thickness of either 310 μm, 490 μm or 730 μm with a
ΔE = (ΔL2 + Δa2 + Δb2)0.5
(1)
After the paint samples were removed from the oven and cooled their color was measured using a Nix Color Pro Sensor (Nix Sensor Ltd, Hamilton, ON, Canada) that can be used to simulate varying lightings conditions and different observation angles [8]. The lighting was set to simulate daylight (D65° setting) and the color measured by a sensor that observed the surface through apertures having cone angles of either 2° or 10° (referred to as “observation angles”) which have been found to best correspond to human vision. 2
Progress in Organic Coatings 136 (2019) 105173
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Fig. 2. Surface driven flows during the drying of 310 μm thick paint films containing blue pigments with concentrations of (a) 0.5% (b) 2% (c) 4% by weight.
3. Results and discussion
evenly distributed. Even at this time the color of the paints is not completely uniform and there are clusters of pigments starting to appear. The movement of pigments is due to the appearance of Marangoni convection flows that are caused by surface tension gradients along the surface of the paint film that appear as the solvent evaporates. The surface tension of the paint increases as the amount of solvent in it is reduced. Random fluctuations in the air velocity and temperature above the surface of the drying paint layer are sufficient to create local variations in the evaporation rate of solvent. Non-uniform evaporation from the surface creates surface tension differences, creating flows from regions of low surface tension to those of high surface tension. As paint
Fig. 2 shows the surface of three different paints with pigment concentrations of (a) 0.5%, (b) 2%, and (c) 4% applied on stainless steel substrates with the same paint film thickness of 310 μm ± 30 μm, throughout the 30 min curing time in the oven maintained at a temperature of 121 °C ± 1.5 °C. Each frame shows a section of the paint surface that is 5.6 mm wide, and each row displays photographs taken of the three different paints at the same time during drying (t), measured from the instant that the paint samples were placed in the oven. The color of the paint appears darker in the earliest images (t = 0.5 min) as the concentration of pigment is increased and it is more
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Fig. 3. Particle Image Velocimetry (PIV) images showing velocity vectors (with magnitudes in the order of 10−5 m/s), moving towards the boundaries of the cells, at t = 1 min (a) entire image (b) zoomed in on one area.
moves away from a point on the surface where solvent concentration is high (and therefore surface tension is low) it is replenished by fresh paint drawn from within the film that has more solvent and consequently lower surface tension, sustaining convective motion in the form of cells where liquid from the edges of cells flows towards their centers or vice-versa. The cells can be circular, hexagonal or in the form of rolls depending on the thickness of the liquid film and its physical properties [5]. Schwarzenberger et al. [5] have described and classified different shapes of cells that have been observed during solutal Marangoni convection, driven by concentration differences in solutions containing two or more components. In the earliest frame (t = 0.5 min) of Fig. 3 pigments are slowly moving and have begun to organize themselves in hexagonal structures, categorized by Schwarzenberger et al. [5] as being quasi-stationary first-order rolling cells with flow from their centers towards their boundaries. Pigments move along with the liquid and tend to accumulate along cell boundaries and on the upper surface of the cells, making them clearly visible as lighter patches since the solid pigments reflect more light than the liquid does. At t = 2.67 min convection cells are no longer visible in paint with a pigment concentration of 0.5% (Fig. 3a) but appear larger in paints with higher pigment concentration (Fig. 3b and c). These larger cells are known as relaxation oscillations [5] and they exhibit pulsating behavior as neighboring cells competed with each other to grow larger, so that some expanded while others contracted (t = 2.67 and 3 min). Finally, after t = 4 min the rate of pulsations began to decrease, distinct cells began to disappear, and movement in the paint stopped. The magnitude of the average velocity of pigment particles in drying paint films was measured using an open source Particle Image Velocimetry (PIV) application through MATLAB (MathWorks, Natick, MA, USA) [9]. The velocity was calculated by measuring the distance between corresponding images of a particle in successive video frames and dividing by the elapsed time between them. Images of the paint were taken at a rate of 4 frames per second for the first 4 min and then 2 frames per minute until the sample was taken out of the oven, which was approximately after 30 min. The software conducted two passes, the first with an interrogation size of 64 pixels and a step of 32 pixels, the second pass was 32 pixels with a step size of 16. Reducing the interrogation area further produced negligible changes in the calculated velocity (˜ 10Ym/s) while significantly increasing the computational time. Fig. 3 shows a typical image of the pigment particles and associated velocity vectors at t=1 min for a paint film with 4% pigment and a thickness of 730 μm. An arithmetical average of all the velocity vectors in every image was taken to get a mean velocity at each instant during the curing process. Fig. 4 show the variation in average velocity magnitude for the three different paint layers with a thickness of 310 μm. The paint with the lowest amount of pigment (0.5%) had the lowest velocity, peaking at approximately 30 μm/s after 100 s. The paints with higher
Fig. 4. Average velocity variation with time in 310 μm thick paint films with pigment concentrations of 0.5%, 2% and 4% by weight.
concentrations had higher velocities, approximately 60 μm/s for the paint with 2% pigment and 65 μm/s for the 4% pigment paint. After approximately 2–3 min the velocity began to decrease sharply and after 5 min practically all motion ceased. Tests were repeated 3 times for a given set of conditions and the time at which the average velocity went to zero was repeatable within approximately ± 10%. Fig. 5 compares the average velocity magnitude of different thicknesses for the same paint with 4% pigment. The thicker the coating the greater the peak velocity and the longer the period of movement for the pigments, reflecting the increase in drying time of the paint with thickness. The duration during which surface tension driven convection occurs can be calculated from the variation of the Marangoni number (Ma), which is a dimensionless ratio of the surface tension forces driving flow to the viscous forces that restrain liquid motion. The Marangoni number is defined as [4,6]
Ma =
( )( ) L dσ dC
dC dx
μDv
2
(2)
The variation of surface tension with solvent concentration (dσ / dC ) has been measured for the model paint [6]. The viscosity of the paint ( μ ) and its thickness (L) are both known. The diffusion coefficient of solvent through the paint (Dv ) and the solvent concentration gradient (dC / dx ) have to be calculated using an analytical model of solvent diffusion in a paint layer [6] based on the one-dimensional equation for mass diffusion in a thin paint layer of thickness L [10]: 4
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Fig. 7. Mass transfer coefficient as a function of paint thickness for paints with pigment concentrations of 0.5%, 2% and 4% by weight.
with 0.5% pigment in it. The mass flux increases slightly for the first 2 min and is relatively independent of thickness. Then after 2–3 min the mass flux begins to decrease due to the exposed surface of the paint beginning to dry out and form a skin, which reduces evaporation. The thicker the paint layer the longer it took for the skin to form and the peak in mass flux was further delayed. The mass transfer coefficient was estimated by averaging the mass flux for the first 3 min and dividing it by the initial solvent concentration Ci = 0.45. Fig. 7 shows the calculated values of α for the different paints as a function of paint thickness. There was not a large change in the value of α, which had a mean value of 1.0 × 10−3 kg/m2/s with a variation of ± 0.2 × 10−3 kg/m2/s. These values were used in subsequent calculations. An analytical solution to Eq. (3) with the boundary conditions (4) and (5) was determined by Crank [10] (p. 60, 62). The dimensionless concentration of the solvent is [10].
Fig. 5. Average velocity variation with time in paint films with pigment concentrations of 4% by weight and thickness of 310, 490 and 730 μm.
∂C (x , t ) ∂2C (x , t ) = Dv , where 0 ≤ x ≤ L ∂t ∂x 2
(3)
The boundary conditions are that at the impervious substrate (x = 0) the mass flux is zero
∂C (0, t ) = 0 at x = 0 ∂x
(4)
Solvent escaping from the upper surface of the paint film ( x = L) is transferred to the surrounding atmosphere by convection. The mass flux (J), which is proportional to the concentration gradient in the liquid just below the free surface, is also assumed proportional to the concentration of solvent at the surface of the paint [11]
∂C (L, t ) J = −ρv Dv = α (C (L, t ) − C∞) at x = L ∂x
C (x , t ) − C∞ = Ci − C∞
x
∞
2
∑ (e−λn Fo ) n=1
2Bi cos(λn L ) (λn2 + Bi2 + Bi)cosλn
(6)
Where the eigenvalues λn are obtained from the equation
(5)
(7)
λn tanλn = Bi
where ρv is the density of the solvent vapor, α is a constant of proportionality and C (L, t ) is the concentration of solvent at the surface of the liquid paint film [12]. The concentration of solvent in the surrounding atmosphere (C∞) was assumed to be zero since the diffusivity of the solvent in air is several orders of magnitude greater than that in the paint [6,12] and it will rapidly be transported away from the test sample. The mass transfer coefficient, α, was calculated using values of J , the mass flux, calculated from the mass loss measurements during the curing process. Fig. 6 shows a typical set of measurements of J as a function of time for three different samples of varying thickness of paint
The Biot number is defined as
Bi =
αL Dv ρv
(8)
and the Fourier number as
Fo =
Dv t L2
(9)
Using Eq. (6) the ratio of the total amount of solvent that has evaporated (Mt ) after time t to the total amount of solvent within the paint sample (M∞) can be determined [10] (pg. 60).
Mt =1− M∞
∞
2
∑ (e−λn Fo ) n=1
(λn2
2Bi 2 + Bi2 + Bi) λn2
(10)
At short times Eq. (10) can be approximated by a much simpler equation [10]:
Mt 4 D t 0.5 = 0.5 ⎛ v2 ⎞ M∞ π ⎝ L ⎠
(11)
An average mass diffusivity can be determined by measuring Mt / M∞ as a function of time and selecting the value of Dv that gives best agreement between the measured variation and that predicted by Eq. (11). Fig. 8 shows both experimental measurement and analytical solution for the mass fraction evaporated during the 30 min drying period of a 0.5% pigment paint layer with 310 μm thickness. All the calculated values of Dv are summarized in Fig. 9, as a function of both film thickness and pigment concentration. Increasing film thickness
Fig. 6. Mass flux variation with time during the first five minutes of drying time for paint films with pigment concentrations of 4% by weight and thickness of 310, 490 and 730 μm. 5
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Fig. 8. Ratio of evaporated solvent mass to total solvent in the 0.5% paint film, experimental (dotted), theoretical (continuous) for a thickness of 310 μm.
Fig. 9. Average diffusion coefficient (Dv ) as a function of paint thickness for paints with pigment concentrations of 0.5%, 2% and 4% by weight.
produced an increase in average diffusivity because it takes a longer amount of for the paint to harden, after which the rate of solvent diffusion decreases. The 4% pigment showed an increased diffusivity at the highest film thickness. The higher the amount of pigment in a paint the lower the mass of solvent initially present if the film thickness is kept constant. This would result in an apparent increase of diffusivity in the model which did not account for the presence of the pigment. Solvent concentration distributions in the paint film during drying were calculated from Eqs. (6)–(9). Fig. 10 shows calculated profiles for 310 μm thick films of all three paints at 1, 8 and 30 min after the start of drying. The concentration difference ΔC across the film is initially large (Fig. 10, t = 1 min) as solvent is lost from the surface of the paint film (x/L = 1) while still remaining at its initial value near the substrate (x/ L = 0). Then as solvent diffuses out of the entire thickness of the paint ΔC decreases. By t = 30 min there is almost no solvent left in the entire
Fig. 11. Marangoni number variation with time for paints with a film thickness of (a) 310 μm, (b) 490 μm (c) 730 μm.
layer. The paint with 0.5% pigment, which had the largest amount of solvent in it, showed the slowest reduction in paint concentration. The Marangoni number was calculated using Eq. (2), where the initial film thickness was assumed to be constant, calculated values of Dv from Fig. 9 used, and the solvent concentration gradient (dC / dx ) was calculated from the slopes of curves such as those shown in Fig. 10 over the entire thickness of the paint, and was then multiplied by Ci and L [6]. Fig. 11 shows the variation of Marangoni numbers with time for different paints at thicknesses of (a) 310 μm, (b) 490 μm, (c) 730 μm. The Marangoni number first increases as solvent begins to evaporate and the concentration gradient across the paint film grows larger. Then, as the solvent concentration throughout the paint begins to decrease, the concentration gradient and Ma begins to decrease. Finally, as the solvent is almost completely depleted, Ma significantly has decreased. In all cases paints with a lower amount of pigments had higher Marangoni numbers than those with higher amounts of pigments. Additionally, the greater the film thickness, the higher the Marangoni
Fig. 10. Concentration profile of the solvent for 310 μm thick paint films 1, 8 and 30 min after the start of drying. 6
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Fig. 12. Different blue paint samples in natural light for 730 μm thick paint films with (a) 0.5% (b) 2% (c) 4% pigment concentration by weight.
paint films (< 100 μm) show a rapid decrease with time so that Marangoni cells, if they exist, may disappear within a few seconds. It was not possible to spread very thin films using a knife edge applicator and therefore additional tests were done using an electrostatic rotating bell spray to deposit ˜50 μm thick paint films on stainless steel substrates and dry them in an oven. No significant movement was seen in the paint, suggesting that either the value of Ma was too low to initiate movement or that movement stopped during the ˜1 min time required to transfer the samples from the spray booth to the oven. When paint samples were fully cured and the film had hardened, they were then placed in natural light and photographed. Fig. 12 shows images of samples of the three paints at thicknesses of 310 μm, 490 μm, and 730 μm. The darkness of the paint color increased both with the amount of pigment and the thickness of the paint film. Paint samples with the lowest amount of pigment (0.5%) were the most sensitive to the existence of Marangoni flows, since they showed regions where the bare substrate can be seen through The thickest paint layer (730 μm) shows the existence of Marangoni cells since the pigments clustered at
number. Both of these trends reflect the fact that the more solvent concentration there is in a paint film, the larger the concentration gradient within it. Increasing the paint thickness and reducing the pigment mass fraction both delayed the peak in the Ma curve since both of these increased the solvent diffusion time. The Marangoni number variation in Fig. 11 can be used to explain the surface tension driven flows seen in Fig. 2 and the variation in velocity seen in Fig. 5. Marangoni convection starts when the Marangoni number is sufficiently large, so that it is first visible in the paint with 0.5% pigment, which has the highest value of Ma. First order rolling cells are observed first, when the Marangoni number is relatively small, and then when the value of Ma increases after 2–3 min relaxed oscillation patterns are seen. At longer times (t > 5 min) the Marangoni number decreases and the cells start to disappear. At this time the paint has started to cure and its viscosity also increases so that the particle velocity drops to zero (Fig. 5). The Marangoni number declines sharply with paint film thickness since Ma is proportional to L2 (see Eq. (2)). Marangoni numbers for thin
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different paints were prepared containing pigments with a concentration of 0.5%, 2% and 4% by weight, and each was applied on stainlesssteel substrates using a knife-edge applicator to prepare films with thicknesses of approximately 310 μm, 490 μm and 730 μm. The coated samples were placed in an oven and the paint surfaces photographed during the curing process. The weight loss of the paint samples during drying was measured. Marangoni convection was observed in drying paint films due to surface tension gradients. This caused movement of pigment particles between the centers and edges of convection cells and their velocity was measured using PIV. The measured rate of solvent loss from the paint was used to develop a mathematical model to predict solvent concentration gradients in the paint films and calculate Marangoni numbers. The velocity of fluid motion increased with the magnitude of the Marangoni number and all motion stopped when the Marangoni number became small, which occurred when sufficient solvent had evaporated to make concentration gradients in the paint film negligible. The time during which convective flows occurred increased as the paint film became thicker as it took longer for solvent to evaporate. The position of the maximum velocity for larger film thicknesses, corresponds to when we see the relaxation oscillation patterns and advection is present. However, as the chaotic oscillation was not observed for thin films, due to faster curing/drying, the maximum velocity correlates to when maximum concentration gradient was reached by diffusion. Increasing the amount of pigment reduced the mass of solvent in a given volume of paint and therefore enhanced its apparent diffusivity. This resulted in lower values of Marangoni number as the pigment fraction increased. The movement of pigments due to Marangoni flows can result in changes in color. This is most acute when the paint films are thin (310 μm) and the pigment fraction is low (0.5% by mass). However, if paint thickness is very low (< 100 μm), the Marangoni number may be so low that there is no convective movement at all. Increasing both the amount of pigment or the paint thickness made the paints color lighter. When the pigment concentration is large and the paint films are thick there is much less change in color.
Fig. 13. Variation of the (a) overall colour change (ΔE) and (b) lightness/ darkness change (ΔL) of the blue samples with paint film thickness.
the boundaries of the cells. The cells can be seen in clearly in the samples with 0.5% and 2% pigment, which had the highest values of Marangoni number (see Fig. 12c). Since Ma was so high convection cells were still present when the paint cured, freezing the pigment particles in place. No cells are seen in the sample with 4% pigment since it had the lowest value of Ma and the convection cells had disappeared by the time the paint cured. The colors of the samples in Fig. 12 were read using the Nix Color Pro Sensor. Fig. 13a shows the overall color change (ΔE) calculated using Eq. (1) as a function of paint thickness, while Fig. 13b shows the change in the lightness/darkness scale (ΔL), which is easiest for the human eye to discern. The change recorded was the difference in color between the bare, unpainted surface, which was used as a reference, and the painted surfaces. The colors of the samples with the lowest amount of pigment were most sensitive to thickness: the color became brighter, so that ΔL became more negative (Fig. 13b) as film thickness was increased because of the greater amount of pigment visible through the depth of the paint layer, which increased the reflection of light. Consequently ΔE increased (Fig. 13a). Once the pigment fraction was above 2% further increases had little effect on color and no significant changes were observed. Samples with 4% pigment showed colors that were very close to those with 2% pigment, and both sets of samples showed only small changes with thickness. This indicates that if there is a sufficient concentration of pigments within the paint the colour saturates and does not change significantly with film thickness.
Acknowledgements The authors gratefully acknowledge funding and support for this work provided by the Natural Sciences and Engineering Research Council of Canada and Magna Exteriors. References [1] H. Streitberger, K. Dossel, Automotive Paints and Coatings, 1st ed., Wiley-VCH, Weinheim, Germany, 2008. [2] E. Kirchner, J. Houweling, Measuring flake orientation for metallic coatings, Prog. Org. Coat. 64 (2–3) (2009) 287–293. [3] E. Kirchner, Film shrinkage and flake orientation, Prog. Org. Coat. 65 (3) (2009) 333–336. [4] K. Schwarzenberger, T. Köllner, H. Linde, T. Boeck, S. Odenbach, K. Eckert, Pattern formation and mass transfer under stationary solutal marangoni instability, Adv. Colloid Interface Sci. 206 (2014) 344–371. [5] C. Hansen, P. Pierce, Cellular convection in polymer coatings-an assessment, Ind. Eng. Chem. Prod. Res. Dev. 12 (1) (1973) 67–70. [6] N. Saranjam, S. Chandra, J. Mostaghimi, H. Fan, J. Simmer, Orange peel formation due to surface tension-driven flows within drying paint films, J. Coat. Technol. Res. 13 (2016) 413–426. [7] PL-D7715CU-T Aptina MT9F002 Machine Vision Camera, Pixelink Industrial Cameras, A Navitar Company, 2017 [Online]. Available: http://pixelink.com/product/pl-d7715cu-taptinamt9f002/. (Accessed 14 February 2017). [8] Nix Pro Tech Specs, Nix Sensor Ltd., Hamilton, 2017 [Online]. Available: http:// www.ghinstruments.com/wp-content/uploads/2017/08/Nix-Pro-Tech-Specs-Digital_810-17.pdf. (Accessed 10 January 2017). [9] W. Thielicke, The Flapping Flight of Birds - Analysis and Application, Phd thesis Rijksuniversiteit Groningen, 2014. [10] J. Crank, The Mathematics of Diffusion, Oxford University Press, 1975. [11] H. Blandin, J. David, J. Vergnaud, J. Illien, M. Malizewicz, Modelling of drying of coatings: effect of the thickness, temperature and concentration of solvent, Prog. Org. Coat. 15 (2) (1987) 163–172. [12] L. Ion, J. Vergnaud, Process of drying a polymeric paint by diffusion-evaporation and shrinkage. Determination of the concentration-dependent diffusivity, Polym. Test. 14 (5) (1995) 479–487.
4. Conclusions An experimental study was conducted to determine the effect of paint film thickness and pigment content on variations in color. Three 8
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Colour variation in drying paint films
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Marina Curak, Nazli Saranjam , Sanjeev Chandra Centre for Advanced Coatings and Technologies, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, M5S 3G8, Toronto, ON, Canada
A R T I C LE I N FO
A B S T R A C T
Keywords: Mass transfer Paint color Surface-tension driven flows Concentration gradient Slef-organizing patterns Paint pigments clustering
Color variations due to changes in paint film thickness and pigment content were studied experimentally. Three paints with differing concentration (0.5%, 2% and 4% by weight) of spherical blue pigments were applied with varying film thickness (310, 490, 730 μm) on stainless-steel substrates and dried in an oven while the paint surfaces were photographed. Weight loss due to solvent evaporation from the paint was recorded. The color of the dried paint films was measured. Surface tension driven convection was observed in drying paint films, which caused movement of pigment particles. An analytical model was used to predict solvent concentration gradients in the paint films and calculate Marangoni numbers, which determined the velocity of fluid motion. All motion stopped when the Marangoni number became small. Pigment particles tended to cluster around the edges of convection cells and produce changes in color, especially when the paint films were thin and the pigment fraction low. Increasing either the amount of pigment or the paint thickness made the paint color lighter, as a larger number of pigment particles increases reflection of light. Paints with high pigment concentration are less likely to see changes in color.
1. Introduction Automotive paint performs two different roles: protective, as a coating that shields a car body from abrasion and corrosion; and aesthetic, as an exterior finish that looks attractive. Paint color is very important to customers and is very tightly controlled by manufacturers. It is especially important that paint color be reproducible since different components of the same vehicle are frequently painted separately and only brought together during final assembly when color mismatches become evident. It is known that changes in spray and drying parameters during painting can lead to changes in color, though the exact mechanism by which this occurs is not well understood. In practice introducing a new paint color on an automotive assembly line requires extensive trial and error to determine the best conditions for paint application. Automotive paints are complex mixtures with several components including: resin, which is the main film forming component; solvent, which reduces the viscosity of the paint; pigments, which provide color; and other additives that may modify fluid properties, enhance corrosion protection and provide resistance to ultraviolet light [1]. Paints are typically sprayed onto automobile components using electrostatic rotating bell applicators and then dried in an oven where solvent evaporates from the paint film while the resin polymerizes to form a hard
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coating. Light incident upon a paint layer may be either transmitted, absorbed or reflected; since the resin is typically transparent, the location, density and orientation of color pigments or metallic flakes in the paint determine how light is reflected, and therefore its color [2]. Kirchner and Houweling [2] measured the orientation of metal flakes that had been added to paints by placing paint films under a microscope. They studied the effect of flake shape and size on orientation and determined that large flakes were much more parallel to the substrate than small flakes. Kirchner [3] conducted another study to determine why flat flakes oriented themselves in a uniform direction. One hypothesis tested was that as the solvent evaporates the paint film shrinks, aligning the flakes with the substrate. However, the paper concluded that this was not sufficient to explain the uniform flake orientation and it was likely that flows in the paint film are responsible for the motion of flakes and pigments. While a paint film is drying flows can be created in it due to the presence of surface tension gradients. The surface tension of paint depends on the concentration of solvent in it, and since evaporation is never perfectly uniform local solvent concentration variations on the paint surface create surface tension differences, driving solutocapillary flows as liquid moves from regions of low to high surface tension [4,5]. Flow cells become visible in the thin liquid film and ripples are created on its surface [4]. Eventually, as the solvent escapes and its
Corresponding author. E-mail address: [email protected] (N. Saranjam).
https://doi.org/10.1016/j.porgcoat.2019.06.019 Received 8 January 2019; Received in revised form 8 June 2019; Accepted 10 June 2019 Available online 30 August 2019 0300-9440/ © 2019 Published by Elsevier B.V.
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concentration becomes low, the cells disappear but if they are still present when the resin begins to harden the paint surface becomes uneven, which is known as the “orange peel” effect. Saranjam et al. [6] studied the formation of orange peel as paint samples with varying thickness were dried in an oven while the paint surface was photographed. The thicker the paint film the longer the duration for which cells exist and the greater the amplitude of the orange peel. This study was conducted to determine if surface tension driven flows in drying paint films have any effect on the distribution of pigments within it, and whether this movement can influence the color of the paint. Test were done with a clear paint in which spherical blue pigments were added. The concentration of pigment in the paint was varied from 0.5% to 2% and 4% by weight. Each paint was coated on stainless steel substrates with wet paint film thickness varied from 300 to 800 μm and dried in an oven. The surface of the paint samples was observed using a video camera and the velocity of pigment particles measured using particle imaging velocimetry. The color of the dried samples was measured to determine if there were any changes.
Fig. 1. Schematic diagram of the experimental apparatus.
standard deviation of ± 30 μm respectively. Each experiment was repeated 3 times for each set of conditions. Test samples were placed 20 s after coating inside a convection oven at an average temperature of 121 °C ± 1.5 °C. Fig. 1 shows a schematic of the experimental apparatus consisting of an convection oven made from an aluminum chamber with two flexible adhesive heating sheets, 152.4 mm long and 76.2 mm wide with a power of 180 W each (Model 35765K25, McMaster-Carr, Aurora, OH, USA), placed on opposing sides and secured with an adhesive (Model 74515A32, McMaster-Carr, Aurora, OH, USA). Each heating sheet was powered by a variable voltage power supply and controlled by a temperature controller connected to a thermocouple placed behind each heating sheet. An additional thermocouple was placed beside the sample in the oven to continuously monitor its temperature. There was no forced air velocity across the sample: heat and mass transfer were by natural convection alone. The exterior of the oven was covered with high-temperature rigid fiberglass insulation (Model 9350K4, McMaster-Carr, Aurora, OH, USA), to reduce heat loss. A glass window was provided on top of the oven through which the paint sample could be observed. The sample was photographed as it cured using a camera (Model PL-D7715CU-T, Pixelink, Ottawa, ON, Canada) with a resolution of 4608 × 3288 pixels where each pixel corresponded to a distance of 0.87 μm [7]. The sample was placed on the end of a vertical aluminium tube that passed through a hole in the bottom of the chamber and rested on an analytical balance (Model E01140, OHAUS Corporation, Parsipanny, NJ, USA) that recorded the change in mass every 60 s with a resolution of 0.1 mg. Color was defined using the CIELAB color space, an industry standard that attempts to approximate human perception. A particular color is represented as a point in three-dimensional space whose position is fixed by three coordinates: L, a and b. The lightness value L varies between the darkest black to the brightest white, a represents the variation from green to red, and b the variation from blue to yellow. Typically L is measured on a scale from 0 to 100, while a and b are on scales from −128 to +128. The overall change in color (ΔE) can be calculated by treating it as a vector in this space, so that by measuring the changes in each coordinate (ΔL, Δa and Δb) and combining them we can obtain the magnitude of change:
2. Experimental methodology Experiments were done using a model paint previously described by Saranjam [6] for which all the relevant fluid properties have been previously determined. The paint was composed of 85% resin and 15% butanol (Caledon Laboratory, Georgetown, Ontario, Canada). The resin was a mixture of 70% Cymel 1159 modified melamine-formaldehyde resin (Cytec, Woodland Park, NJ, USA) and 30% Paraloid AT-400 resin (DOW Chemicals, Midland MI, USA). The properties of the paint were measured to be: density:ρ =988 kg/m3; viscosity: μ =240 cP; surface tension: σ = 26 mN/m. Paint is a non-Newtonian liquid and shows shear thinning behavior during application. A thermogravimetric analysis was used to measure the total amount of butanol and it was determined [6] that the initial concentration Ci = 0.45. The surface tension of the resin alone was 27.5 mN/m and that of butanol 23.5 mN/m. The variation of surface tension and viscosity with solvent concentration have been measured and reported earlier [6]. Commercial paints frequently contain surface active additives that typically reduce surface tension and may suppress the effects of surface tension gradients. The objective of this study was to observe surface tension-driven flows and therefore no surfactants were added to the model paint. Commercially available spherical blue pigments (Sapphire Blue, Paint with Pearl, Denver, CO, USA) with a mean diameter of 26 μm and a range of 10–60 μm were added to the paint. The size was measured from photographs of the pigments taken under a microscope. These pigments are much larger than those typically used in commercial paints, but were selected so that they were easily visible during drying and their motion could be recorded with a video camera. Spherical pigments were selected so that paint color did not depend on their orientation, but only on concentration and distribution. Three different concentrations were used, 0.5%, 2%, and 4%. The concentrations were determined by putting a pre-determined amount of paint in a beaker and measuring the mass on a precision scale with 0.1 mg accuracy. Subsequently, pigments were weighed in another dish and incrementally added to the beaker with paint while monitoring the total mass to ensure accuracy. The paint and pigments were mixed with a glass stirring rod immediately prior to their being tested. No stabilizers were used for the pigments as these may affect surface tension. Circular reflective stainless-steel substrates, with a diameter of 50.8 mm and a surface roughness of 0.1 μm were coated with the test paint. The substrates were first cleaned with acetone to remove the oil residue off the substrate and then placed in a sample holder on a 1-D translation stage. Paint was deposited on the substrate using a syringe and the translation stage moved under a blade coater (Model Multicoater 411, Enrichsen GmbH & Co, Hemer, Germany) to spread the paint into a uniform film. Experiments were done with average wet paint film thickness of either 310 μm, 490 μm or 730 μm with a
ΔE = (ΔL2 + Δa2 + Δb2)0.5
(1)
After the paint samples were removed from the oven and cooled their color was measured using a Nix Color Pro Sensor (Nix Sensor Ltd, Hamilton, ON, Canada) that can be used to simulate varying lightings conditions and different observation angles [8]. The lighting was set to simulate daylight (D65° setting) and the color measured by a sensor that observed the surface through apertures having cone angles of either 2° or 10° (referred to as “observation angles”) which have been found to best correspond to human vision. 2
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Fig. 2. Surface driven flows during the drying of 310 μm thick paint films containing blue pigments with concentrations of (a) 0.5% (b) 2% (c) 4% by weight.
3. Results and discussion
evenly distributed. Even at this time the color of the paints is not completely uniform and there are clusters of pigments starting to appear. The movement of pigments is due to the appearance of Marangoni convection flows that are caused by surface tension gradients along the surface of the paint film that appear as the solvent evaporates. The surface tension of the paint increases as the amount of solvent in it is reduced. Random fluctuations in the air velocity and temperature above the surface of the drying paint layer are sufficient to create local variations in the evaporation rate of solvent. Non-uniform evaporation from the surface creates surface tension differences, creating flows from regions of low surface tension to those of high surface tension. As paint
Fig. 2 shows the surface of three different paints with pigment concentrations of (a) 0.5%, (b) 2%, and (c) 4% applied on stainless steel substrates with the same paint film thickness of 310 μm ± 30 μm, throughout the 30 min curing time in the oven maintained at a temperature of 121 °C ± 1.5 °C. Each frame shows a section of the paint surface that is 5.6 mm wide, and each row displays photographs taken of the three different paints at the same time during drying (t), measured from the instant that the paint samples were placed in the oven. The color of the paint appears darker in the earliest images (t = 0.5 min) as the concentration of pigment is increased and it is more
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Fig. 3. Particle Image Velocimetry (PIV) images showing velocity vectors (with magnitudes in the order of 10−5 m/s), moving towards the boundaries of the cells, at t = 1 min (a) entire image (b) zoomed in on one area.
moves away from a point on the surface where solvent concentration is high (and therefore surface tension is low) it is replenished by fresh paint drawn from within the film that has more solvent and consequently lower surface tension, sustaining convective motion in the form of cells where liquid from the edges of cells flows towards their centers or vice-versa. The cells can be circular, hexagonal or in the form of rolls depending on the thickness of the liquid film and its physical properties [5]. Schwarzenberger et al. [5] have described and classified different shapes of cells that have been observed during solutal Marangoni convection, driven by concentration differences in solutions containing two or more components. In the earliest frame (t = 0.5 min) of Fig. 3 pigments are slowly moving and have begun to organize themselves in hexagonal structures, categorized by Schwarzenberger et al. [5] as being quasi-stationary first-order rolling cells with flow from their centers towards their boundaries. Pigments move along with the liquid and tend to accumulate along cell boundaries and on the upper surface of the cells, making them clearly visible as lighter patches since the solid pigments reflect more light than the liquid does. At t = 2.67 min convection cells are no longer visible in paint with a pigment concentration of 0.5% (Fig. 3a) but appear larger in paints with higher pigment concentration (Fig. 3b and c). These larger cells are known as relaxation oscillations [5] and they exhibit pulsating behavior as neighboring cells competed with each other to grow larger, so that some expanded while others contracted (t = 2.67 and 3 min). Finally, after t = 4 min the rate of pulsations began to decrease, distinct cells began to disappear, and movement in the paint stopped. The magnitude of the average velocity of pigment particles in drying paint films was measured using an open source Particle Image Velocimetry (PIV) application through MATLAB (MathWorks, Natick, MA, USA) [9]. The velocity was calculated by measuring the distance between corresponding images of a particle in successive video frames and dividing by the elapsed time between them. Images of the paint were taken at a rate of 4 frames per second for the first 4 min and then 2 frames per minute until the sample was taken out of the oven, which was approximately after 30 min. The software conducted two passes, the first with an interrogation size of 64 pixels and a step of 32 pixels, the second pass was 32 pixels with a step size of 16. Reducing the interrogation area further produced negligible changes in the calculated velocity (˜ 10Ym/s) while significantly increasing the computational time. Fig. 3 shows a typical image of the pigment particles and associated velocity vectors at t=1 min for a paint film with 4% pigment and a thickness of 730 μm. An arithmetical average of all the velocity vectors in every image was taken to get a mean velocity at each instant during the curing process. Fig. 4 show the variation in average velocity magnitude for the three different paint layers with a thickness of 310 μm. The paint with the lowest amount of pigment (0.5%) had the lowest velocity, peaking at approximately 30 μm/s after 100 s. The paints with higher
Fig. 4. Average velocity variation with time in 310 μm thick paint films with pigment concentrations of 0.5%, 2% and 4% by weight.
concentrations had higher velocities, approximately 60 μm/s for the paint with 2% pigment and 65 μm/s for the 4% pigment paint. After approximately 2–3 min the velocity began to decrease sharply and after 5 min practically all motion ceased. Tests were repeated 3 times for a given set of conditions and the time at which the average velocity went to zero was repeatable within approximately ± 10%. Fig. 5 compares the average velocity magnitude of different thicknesses for the same paint with 4% pigment. The thicker the coating the greater the peak velocity and the longer the period of movement for the pigments, reflecting the increase in drying time of the paint with thickness. The duration during which surface tension driven convection occurs can be calculated from the variation of the Marangoni number (Ma), which is a dimensionless ratio of the surface tension forces driving flow to the viscous forces that restrain liquid motion. The Marangoni number is defined as [4,6]
Ma =
( )( ) L dσ dC
dC dx
μDv
2
(2)
The variation of surface tension with solvent concentration (dσ / dC ) has been measured for the model paint [6]. The viscosity of the paint ( μ ) and its thickness (L) are both known. The diffusion coefficient of solvent through the paint (Dv ) and the solvent concentration gradient (dC / dx ) have to be calculated using an analytical model of solvent diffusion in a paint layer [6] based on the one-dimensional equation for mass diffusion in a thin paint layer of thickness L [10]: 4
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Fig. 7. Mass transfer coefficient as a function of paint thickness for paints with pigment concentrations of 0.5%, 2% and 4% by weight.
with 0.5% pigment in it. The mass flux increases slightly for the first 2 min and is relatively independent of thickness. Then after 2–3 min the mass flux begins to decrease due to the exposed surface of the paint beginning to dry out and form a skin, which reduces evaporation. The thicker the paint layer the longer it took for the skin to form and the peak in mass flux was further delayed. The mass transfer coefficient was estimated by averaging the mass flux for the first 3 min and dividing it by the initial solvent concentration Ci = 0.45. Fig. 7 shows the calculated values of α for the different paints as a function of paint thickness. There was not a large change in the value of α, which had a mean value of 1.0 × 10−3 kg/m2/s with a variation of ± 0.2 × 10−3 kg/m2/s. These values were used in subsequent calculations. An analytical solution to Eq. (3) with the boundary conditions (4) and (5) was determined by Crank [10] (p. 60, 62). The dimensionless concentration of the solvent is [10].
Fig. 5. Average velocity variation with time in paint films with pigment concentrations of 4% by weight and thickness of 310, 490 and 730 μm.
∂C (x , t ) ∂2C (x , t ) = Dv , where 0 ≤ x ≤ L ∂t ∂x 2
(3)
The boundary conditions are that at the impervious substrate (x = 0) the mass flux is zero
∂C (0, t ) = 0 at x = 0 ∂x
(4)
Solvent escaping from the upper surface of the paint film ( x = L) is transferred to the surrounding atmosphere by convection. The mass flux (J), which is proportional to the concentration gradient in the liquid just below the free surface, is also assumed proportional to the concentration of solvent at the surface of the paint [11]
∂C (L, t ) J = −ρv Dv = α (C (L, t ) − C∞) at x = L ∂x
C (x , t ) − C∞ = Ci − C∞
x
∞
2
∑ (e−λn Fo ) n=1
2Bi cos(λn L ) (λn2 + Bi2 + Bi)cosλn
(6)
Where the eigenvalues λn are obtained from the equation
(5)
(7)
λn tanλn = Bi
where ρv is the density of the solvent vapor, α is a constant of proportionality and C (L, t ) is the concentration of solvent at the surface of the liquid paint film [12]. The concentration of solvent in the surrounding atmosphere (C∞) was assumed to be zero since the diffusivity of the solvent in air is several orders of magnitude greater than that in the paint [6,12] and it will rapidly be transported away from the test sample. The mass transfer coefficient, α, was calculated using values of J , the mass flux, calculated from the mass loss measurements during the curing process. Fig. 6 shows a typical set of measurements of J as a function of time for three different samples of varying thickness of paint
The Biot number is defined as
Bi =
αL Dv ρv
(8)
and the Fourier number as
Fo =
Dv t L2
(9)
Using Eq. (6) the ratio of the total amount of solvent that has evaporated (Mt ) after time t to the total amount of solvent within the paint sample (M∞) can be determined [10] (pg. 60).
Mt =1− M∞
∞
2
∑ (e−λn Fo ) n=1
(λn2
2Bi 2 + Bi2 + Bi) λn2
(10)
At short times Eq. (10) can be approximated by a much simpler equation [10]:
Mt 4 D t 0.5 = 0.5 ⎛ v2 ⎞ M∞ π ⎝ L ⎠
(11)
An average mass diffusivity can be determined by measuring Mt / M∞ as a function of time and selecting the value of Dv that gives best agreement between the measured variation and that predicted by Eq. (11). Fig. 8 shows both experimental measurement and analytical solution for the mass fraction evaporated during the 30 min drying period of a 0.5% pigment paint layer with 310 μm thickness. All the calculated values of Dv are summarized in Fig. 9, as a function of both film thickness and pigment concentration. Increasing film thickness
Fig. 6. Mass flux variation with time during the first five minutes of drying time for paint films with pigment concentrations of 4% by weight and thickness of 310, 490 and 730 μm. 5
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Fig. 8. Ratio of evaporated solvent mass to total solvent in the 0.5% paint film, experimental (dotted), theoretical (continuous) for a thickness of 310 μm.
Fig. 9. Average diffusion coefficient (Dv ) as a function of paint thickness for paints with pigment concentrations of 0.5%, 2% and 4% by weight.
produced an increase in average diffusivity because it takes a longer amount of for the paint to harden, after which the rate of solvent diffusion decreases. The 4% pigment showed an increased diffusivity at the highest film thickness. The higher the amount of pigment in a paint the lower the mass of solvent initially present if the film thickness is kept constant. This would result in an apparent increase of diffusivity in the model which did not account for the presence of the pigment. Solvent concentration distributions in the paint film during drying were calculated from Eqs. (6)–(9). Fig. 10 shows calculated profiles for 310 μm thick films of all three paints at 1, 8 and 30 min after the start of drying. The concentration difference ΔC across the film is initially large (Fig. 10, t = 1 min) as solvent is lost from the surface of the paint film (x/L = 1) while still remaining at its initial value near the substrate (x/ L = 0). Then as solvent diffuses out of the entire thickness of the paint ΔC decreases. By t = 30 min there is almost no solvent left in the entire
Fig. 11. Marangoni number variation with time for paints with a film thickness of (a) 310 μm, (b) 490 μm (c) 730 μm.
layer. The paint with 0.5% pigment, which had the largest amount of solvent in it, showed the slowest reduction in paint concentration. The Marangoni number was calculated using Eq. (2), where the initial film thickness was assumed to be constant, calculated values of Dv from Fig. 9 used, and the solvent concentration gradient (dC / dx ) was calculated from the slopes of curves such as those shown in Fig. 10 over the entire thickness of the paint, and was then multiplied by Ci and L [6]. Fig. 11 shows the variation of Marangoni numbers with time for different paints at thicknesses of (a) 310 μm, (b) 490 μm, (c) 730 μm. The Marangoni number first increases as solvent begins to evaporate and the concentration gradient across the paint film grows larger. Then, as the solvent concentration throughout the paint begins to decrease, the concentration gradient and Ma begins to decrease. Finally, as the solvent is almost completely depleted, Ma significantly has decreased. In all cases paints with a lower amount of pigments had higher Marangoni numbers than those with higher amounts of pigments. Additionally, the greater the film thickness, the higher the Marangoni
Fig. 10. Concentration profile of the solvent for 310 μm thick paint films 1, 8 and 30 min after the start of drying. 6
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Fig. 12. Different blue paint samples in natural light for 730 μm thick paint films with (a) 0.5% (b) 2% (c) 4% pigment concentration by weight.
paint films (< 100 μm) show a rapid decrease with time so that Marangoni cells, if they exist, may disappear within a few seconds. It was not possible to spread very thin films using a knife edge applicator and therefore additional tests were done using an electrostatic rotating bell spray to deposit ˜50 μm thick paint films on stainless steel substrates and dry them in an oven. No significant movement was seen in the paint, suggesting that either the value of Ma was too low to initiate movement or that movement stopped during the ˜1 min time required to transfer the samples from the spray booth to the oven. When paint samples were fully cured and the film had hardened, they were then placed in natural light and photographed. Fig. 12 shows images of samples of the three paints at thicknesses of 310 μm, 490 μm, and 730 μm. The darkness of the paint color increased both with the amount of pigment and the thickness of the paint film. Paint samples with the lowest amount of pigment (0.5%) were the most sensitive to the existence of Marangoni flows, since they showed regions where the bare substrate can be seen through The thickest paint layer (730 μm) shows the existence of Marangoni cells since the pigments clustered at
number. Both of these trends reflect the fact that the more solvent concentration there is in a paint film, the larger the concentration gradient within it. Increasing the paint thickness and reducing the pigment mass fraction both delayed the peak in the Ma curve since both of these increased the solvent diffusion time. The Marangoni number variation in Fig. 11 can be used to explain the surface tension driven flows seen in Fig. 2 and the variation in velocity seen in Fig. 5. Marangoni convection starts when the Marangoni number is sufficiently large, so that it is first visible in the paint with 0.5% pigment, which has the highest value of Ma. First order rolling cells are observed first, when the Marangoni number is relatively small, and then when the value of Ma increases after 2–3 min relaxed oscillation patterns are seen. At longer times (t > 5 min) the Marangoni number decreases and the cells start to disappear. At this time the paint has started to cure and its viscosity also increases so that the particle velocity drops to zero (Fig. 5). The Marangoni number declines sharply with paint film thickness since Ma is proportional to L2 (see Eq. (2)). Marangoni numbers for thin
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different paints were prepared containing pigments with a concentration of 0.5%, 2% and 4% by weight, and each was applied on stainlesssteel substrates using a knife-edge applicator to prepare films with thicknesses of approximately 310 μm, 490 μm and 730 μm. The coated samples were placed in an oven and the paint surfaces photographed during the curing process. The weight loss of the paint samples during drying was measured. Marangoni convection was observed in drying paint films due to surface tension gradients. This caused movement of pigment particles between the centers and edges of convection cells and their velocity was measured using PIV. The measured rate of solvent loss from the paint was used to develop a mathematical model to predict solvent concentration gradients in the paint films and calculate Marangoni numbers. The velocity of fluid motion increased with the magnitude of the Marangoni number and all motion stopped when the Marangoni number became small, which occurred when sufficient solvent had evaporated to make concentration gradients in the paint film negligible. The time during which convective flows occurred increased as the paint film became thicker as it took longer for solvent to evaporate. The position of the maximum velocity for larger film thicknesses, corresponds to when we see the relaxation oscillation patterns and advection is present. However, as the chaotic oscillation was not observed for thin films, due to faster curing/drying, the maximum velocity correlates to when maximum concentration gradient was reached by diffusion. Increasing the amount of pigment reduced the mass of solvent in a given volume of paint and therefore enhanced its apparent diffusivity. This resulted in lower values of Marangoni number as the pigment fraction increased. The movement of pigments due to Marangoni flows can result in changes in color. This is most acute when the paint films are thin (310 μm) and the pigment fraction is low (0.5% by mass). However, if paint thickness is very low (< 100 μm), the Marangoni number may be so low that there is no convective movement at all. Increasing both the amount of pigment or the paint thickness made the paints color lighter. When the pigment concentration is large and the paint films are thick there is much less change in color.
Fig. 13. Variation of the (a) overall colour change (ΔE) and (b) lightness/ darkness change (ΔL) of the blue samples with paint film thickness.
the boundaries of the cells. The cells can be seen in clearly in the samples with 0.5% and 2% pigment, which had the highest values of Marangoni number (see Fig. 12c). Since Ma was so high convection cells were still present when the paint cured, freezing the pigment particles in place. No cells are seen in the sample with 4% pigment since it had the lowest value of Ma and the convection cells had disappeared by the time the paint cured. The colors of the samples in Fig. 12 were read using the Nix Color Pro Sensor. Fig. 13a shows the overall color change (ΔE) calculated using Eq. (1) as a function of paint thickness, while Fig. 13b shows the change in the lightness/darkness scale (ΔL), which is easiest for the human eye to discern. The change recorded was the difference in color between the bare, unpainted surface, which was used as a reference, and the painted surfaces. The colors of the samples with the lowest amount of pigment were most sensitive to thickness: the color became brighter, so that ΔL became more negative (Fig. 13b) as film thickness was increased because of the greater amount of pigment visible through the depth of the paint layer, which increased the reflection of light. Consequently ΔE increased (Fig. 13a). Once the pigment fraction was above 2% further increases had little effect on color and no significant changes were observed. Samples with 4% pigment showed colors that were very close to those with 2% pigment, and both sets of samples showed only small changes with thickness. This indicates that if there is a sufficient concentration of pigments within the paint the colour saturates and does not change significantly with film thickness.
Acknowledgements The authors gratefully acknowledge funding and support for this work provided by the Natural Sciences and Engineering Research Council of Canada and Magna Exteriors. References [1] H. Streitberger, K. Dossel, Automotive Paints and Coatings, 1st ed., Wiley-VCH, Weinheim, Germany, 2008. [2] E. Kirchner, J. Houweling, Measuring flake orientation for metallic coatings, Prog. Org. Coat. 64 (2–3) (2009) 287–293. [3] E. Kirchner, Film shrinkage and flake orientation, Prog. Org. Coat. 65 (3) (2009) 333–336. [4] K. Schwarzenberger, T. Köllner, H. Linde, T. Boeck, S. Odenbach, K. Eckert, Pattern formation and mass transfer under stationary solutal marangoni instability, Adv. Colloid Interface Sci. 206 (2014) 344–371. [5] C. Hansen, P. Pierce, Cellular convection in polymer coatings-an assessment, Ind. Eng. Chem. Prod. Res. Dev. 12 (1) (1973) 67–70. [6] N. Saranjam, S. Chandra, J. Mostaghimi, H. Fan, J. Simmer, Orange peel formation due to surface tension-driven flows within drying paint films, J. Coat. Technol. Res. 13 (2016) 413–426. [7] PL-D7715CU-T Aptina MT9F002 Machine Vision Camera, Pixelink Industrial Cameras, A Navitar Company, 2017 [Online]. Available: http://pixelink.com/product/pl-d7715cu-taptinamt9f002/. (Accessed 14 February 2017). [8] Nix Pro Tech Specs, Nix Sensor Ltd., Hamilton, 2017 [Online]. Available: http:// www.ghinstruments.com/wp-content/uploads/2017/08/Nix-Pro-Tech-Specs-Digital_810-17.pdf. (Accessed 10 January 2017). [9] W. Thielicke, The Flapping Flight of Birds - Analysis and Application, Phd thesis Rijksuniversiteit Groningen, 2014. [10] J. Crank, The Mathematics of Diffusion, Oxford University Press, 1975. [11] H. Blandin, J. David, J. Vergnaud, J. Illien, M. Malizewicz, Modelling of drying of coatings: effect of the thickness, temperature and concentration of solvent, Prog. Org. Coat. 15 (2) (1987) 163–172. [12] L. Ion, J. Vergnaud, Process of drying a polymeric paint by diffusion-evaporation and shrinkage. Determination of the concentration-dependent diffusivity, Polym. Test. 14 (5) (1995) 479–487.
4. Conclusions An experimental study was conducted to determine the effect of paint film thickness and pigment content on variations in color. Three 8