Journal of Coatings Technology and Research

, Volume 16, Issue 2, pp 263–305 | Cite as

Applied rheology and architectural coating performance

  • Richard R. EleyEmail author
Review article


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.


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

List of symbols


Fluidity integral


Total fluidity integral


Total film fluidity


Total film fluidity including effect of striation wavelength


Shear strain (dimensionless); surface tension


Oscillatory strain amplitude

\( \dot{\gamma } \)

Shear rate, rate of strain, s −1 = dγ/dt


Phase-angle difference of stress and strain maxima in oscillatory deformation


Hencky extensional strain, dimensionless = ln(L/L0)

\( \dot{\varepsilon } \)

Hencky extensional strain rate, s−1 = /dt


Coefficient of viscosity = σ/\( \dot{\gamma } \)


Viscosity as a function of time

\( \eta \text{(}\dot{\varepsilon }\text{)} \)

Viscosity as a function of Hencky extensional strain rate


Viscosity as a function of shear stress


Viscosity at the shear stress of brushing


Liquid-phase viscosity


Plastic viscosity (Bingham model)


Casson model “infinite-shear viscosity”


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

\( \dot{\theta } \)

Roller angular velocity (time derivative of angular rotation)


Wavelength of coating surface striations


Ratio of circumference of a circle to its diameter




Floc (aggregate) density


Liquid density


Density of particle


Shear stress


Shear stress of coating application


Shear stress driving leveling


Shear stress driving sagging


Particle shear stress exerted on the surrounding fluid


Yield stress


Angular frequency or velocity (= 2πf) (rad s−1)


Area of shear face


Contact area of brush or roller with the substrate


Surface area of a particle


Associative thickener


Capillary number


Brownian diffusion coefficient, diffusivity


Hydrodynamically equivalent spherical floc diameter


Diffusion-limited aggregation


Diffusion-limited cluster aggregation




Finite element analysis


Force applied to paint applicator device


Brush or roller drag force


Force of gravity


Shear modulus


Complex shear modulus


Storage modulus: energy stored per unit volume per cycle of deformation


Loss modulus: energy dissipated per unit volume per cycle of deformation


Consistency parameter in power-law constitutive model


Brush stroke length; length dimension


Capillary length


Microfibrous cellulose


Poise, CGS unit of viscosity


Pascal-second, SI unit of viscosity


Particle radius


Reaction-limited aggregation


Absolute temperature, °Κ


Characteristic time for instability growth


Velocity, volume


Floc sedimentation velocity


Relative velocity of a roller and substrate


Brush width


Work of brushing


Amplitude of coating surface striations


Time-zero amplitude of coating surface striations


Final amplitude of coating surface striations


Particle diameter


Base of natural logarithms = 2.718


Frequency, Hertz (Hz, cycles per second)


Gravitational acceleration 980.17 cm/s2

h, h0

Film thickness


Liquid filament length


Thickness of the lubrication layer


Coating thickness as a function of time


Number of particles in an aggregate


Boltzmann constant, 1.381 × 10−16 erg per degree Kelvin




Power-law exponent


Roller radius


Time in seconds, s


Time for a particle to diffuse a distance R, one half its diameter


Velocity of particle diffusion


Velocity of particle sedimentation


Coordinate parallel to substrate


Coordinate normal to substrate



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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Copyright information

© American Coatings Association 2019

Authors and Affiliations

  1. 1.Senior Scientist (retired)Akzo Nobel CoatingsStrongsvilleUSA
  2. 2.Formerly Adjunct Professor, Department of Mechanical EngineeringUniversity of DelawareNewarkUSA

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