# Applied rheology and architectural coating performance

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## Abstract

Paint rheology is understood to play a vital role in both product performance and customer acceptance. Consequently, the ability to formulate paints having the necessary flow properties is essential for paint technologists. Experienced formulators have said that as much as half the cost of new product development can be consumed in getting the rheology right. In fact, the quality-control viscosity measurement devices in everyday use in the development laboratory are of little help in this endeavor. Among other shortcomings, most such instruments apply shear stresses which are far from those involved in important coating flow processes. The rheological properties required for a successful coating must be defined with due regard to the prevailing conditions of stress involved in application and film formation. This requires that measurements should be taken over a wide range of shear stress and timescales. The task for the applied rheologist is to bridge rheology and technology, but it is often unclear how to connect rheological data with the “real-world” performance of paints, due to the complexity of coating flows. This review in part discusses the use of controlled-stress rheometry to characterize coatings, and presents ways of applying the results effectively to the analysis of paint flow. The methodology is fundamental but not unduly time-consuming, since the objective is to provide sound yet timely guidance to formulators. Thirteen commercial semigloss latex paints were analyzed rheologically to develop correlations to paint performance. Using the method of shear stress mapping, key regions of the non-equilibrium flow curve are identified for the control of paint flow processes. With this approach, simple but strong correlations were obtained of paint flow metrics to viscosity chosen at the relevant stresses. The fact of high correlation means one can expect that an appropriate viscosity adjustment will correspondingly improve performance. It is argued that shear stress, not shear rate, is the correct independent variable both for experimentation and for the graphical presentation and analysis of viscosity data. The yield stress parameter, particle flocculation, and sedimentation are also discussed, and an oscillatory shear method of direct measurement of yield stress is described.

## Keywords

Coating rheology Flow curve Controlled-stress rheometry Experimental rheology Yield stress Leveling Sag Particle settling Flocculation Sedimentation Microstructure## List of symbols

- Φ
Fluidity integral

- Φ(∞)
Total fluidity integral

- Ψ(∞)
Total film fluidity

- Ψ′(∞)
Total film fluidity including effect of striation wavelength

*γ*Shear strain (dimensionless); surface tension

*γ*_{0}Oscillatory strain amplitude

- \( \dot{\gamma } \)
Shear rate, rate of strain, s

^{−1}=*d*γ/*dt**δ*Phase-angle difference of stress and strain maxima in oscillatory deformation

*ε*Hencky extensional strain, dimensionless = ln(

*L*/*L*_{0})- \( \dot{\varepsilon } \)
Hencky extensional strain rate, s

^{−1}=*dε*/*dt**η*Coefficient of viscosity =

*σ*/\( \dot{\gamma } \)*η*(*t*)Viscosity as a function of time

- \( \eta \text{(}\dot{\varepsilon }\text{)} \)
Viscosity as a function of Hencky extensional strain rate

*η*(*σ*)Viscosity as a function of shear stress

*η*_{b}Viscosity at the shear stress of brushing

*η*_{l}Liquid-phase viscosity

*η*_{pl}Plastic viscosity (Bingham model)

*η*_{∞}Casson model “infinite-shear viscosity”

*θ*Angle of rotation of paint roller; angle of inclination to the vertical

- \( \dot{\theta } \)
Roller angular velocity (time derivative of angular rotation)

*λ*Wavelength of coating surface striations

*π*Ratio of circumference of a circle to its diameter

*ρ*Density

*ρ*_{f}Floc (aggregate) density

*ρ*_{l}Liquid density

*ρ*_{p}Density of particle

*σ*Shear stress

*σ*_{app}Shear stress of coating application

*σ*_{lev}Shear stress driving leveling

*σ*_{sag}Shear stress driving sagging

*σ*_{p}Particle shear stress exerted on the surrounding fluid

*σ*_{y}Yield stress

*ω*Angular frequency or velocity (= 2

*πf*) (rad s^{−1})*A*Area of shear face

*A*_{c}Contact area of brush or roller with the substrate

*A*_{p}Surface area of a particle

- AT
Associative thickener

*Ca*Capillary number

*D*Brownian diffusion coefficient, diffusivity

*D*_{f}Hydrodynamically equivalent spherical floc diameter

- DLA
Diffusion-limited aggregation

- DLCA
Diffusion-limited cluster aggregation

*F*Force

- FEA
Finite element analysis

*F*_{app}Force applied to paint applicator device

*F*_{d}Brush or roller drag force

*F*_{g}Force of gravity

*G*Shear modulus

*G**Complex shear modulus

*G*′Storage modulus: energy stored per unit volume per cycle of deformation

*G*″Loss modulus: energy dissipated per unit volume per cycle of deformation

*K*Consistency parameter in power-law constitutive model

*L*Brush stroke length; length dimension

*L*_{c}Capillary length

- MFC
Microfibrous cellulose

- P
Poise, CGS unit of viscosity

- Pa·s
Pascal-second, SI unit of viscosity

*R*Particle radius

- RLA
Reaction-limited aggregation

*T*Absolute temperature, °Κ

*T*_{c}Characteristic time for instability growth

*V*Velocity, volume

*V*_{f}Floc sedimentation velocity

*V*_{r}Relative velocity of a roller and substrate

*W*Brush width

*W*_{b}Work of brushing

*a*Amplitude of coating surface striations

*a*_{0}Time-zero amplitude of coating surface striations

*a*_{∞}Final amplitude of coating surface striations

*d*Particle diameter

*e*Base of natural logarithms = 2.718

*f*Frequency, Hertz (Hz, cycles per second)

*g*Gravitational acceleration 980.17 cm/s

^{2}*h*,*h*_{0}Film thickness

*h*_{f}Liquid filament length

*h*_{l}Thickness of the lubrication layer

*h*(*t*)Coating thickness as a function of time

*k*Number of particles in an aggregate

*k*_{B}Boltzmann constant, 1.381 × 10

^{−16}erg per degree Kelvin*l*Length

*n*Power-law exponent

*r*Roller radius

*t*Time in seconds, s

*t*_{R}Time for a particle to diffuse a distance

*R*, one half its diameter*v*_{diff}Velocity of particle diffusion

*v*_{sed}Velocity of particle sedimentation

*x*Coordinate parallel to substrate

*y*Coordinate normal to substrate

## Notes

### Acknowledgments

The author is indebted to Prof. Leonard W. Schwartz and Prof. R. Valery Roy, Department of Mechanical Engineering, University of Delaware, from whom in a long and fruitful association he acquired a working knowledge of fluid mechanics, vital to understanding coating flows. The author gratefully thanks Dr. David E. Weidner, for his generous and expert consultation. Ms. Kimberly Hennigan and Ms. Natalie Homann, who performed the majority of the experimentation herein, are acknowledged with gratitude. The author also wishes to thank Dr. Ted Provder for encouraging the writing of this paper. Original experimental data presented herein were previously released for publication by permission of ICI Paints North America.

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