## Rheological model for paint properties

##### Abstract

The feasibility of predicting paint properties directly from the raw material formulation as well as
the rheological data is investigated in this study. Although extensive work has been carried out on
the prediction of paint properties in terms of the raw material data, very little research has been
carried out on the prediction of paint properties in terms of the rheological data. Little is known
about the relationship between fundamental rheological properties and real-world performance.
The paint under investigation consists of fourteen raw materials. These raw materials interact in a
very complex manner to produce certain desired paint properties. Evaluation of these interactions
in terms of constitutive equations is almost impossible and the relationships between paint
properties, raw materials and rheology can only be modelled in a statistical way. Linear
relationships are investigated with linear parameter estimation techniques such as multiple linear
regression. However, it has been found that many of these relationships are non-linear and that
linear modelling techniques are no longer applicable for certain situations, e.g. at very high
concentrations of specific raw materials. Non-linear techniques such as neural networks are used
in these situations.
The relationship between the raw materials, paint properties and rheology are evaluated using the
following three models:
· MODEL 1: The relationship between rheology and raw materials
· MODEL 2: The relationship between paint properties and raw materials
· MODEL 3: The relationship between paint properties and rheology
MODEL 1 makes use of techniques such as principal component analysis and preliminary
modelling to respectively reduce redundancy and to capture as much data as possible. MODELS
2 and 3 make use of linear screening techniques in order to identify relevant raw materials and
paint properties.
The validity of every model is checked to ensure that predictions and interpretations are unbiased
and efficient. MODEL 1 revealed that emulsion, extender particles, pigment, water, organic
pigment and solvent are the six most important raw materials affecting the rheology of the specific
paint. The rheology curves that are predicted most accurately by means of multiple linear
regression are the “Amplitude Sweep” (AS), “3-Interval-Thixotropy-Test” (3-ITT) and the “Flow
Curve” (FC). Non-linear rheological behaviour is encountered at high pigment volume
concentrations (PVC) and volume solids (VS), due to the strong dependency of the rheology of
the paint on these properties. It has been shown that neural networks perform better than multiple
linear regression in predicting the rheological behaviour of these paint samples for which the raw
materials vary by more than 20% from the standard formulation. On average, neural networks improve predictability of the rheological parameters of these samples by 54%. The largest
improvement in predictability is made on the rheological variable “Extra Low Frequency” value
(CXLF), where multiple linear regression resulted in relative errors of 59%, while neural networks
resulted in errors of only 5%. Other predictions of rheology curves where neural networks have
shown a major improvement on predictability are the “Time Sweep” (TS) – 68% increase in
accuracy and “Low Shear” curve (LS) – 63% increase in accuracy. The smallest increase that the
neural network had on the predictability of a rheology curve, was a 33% increase in accuracy of
the “Amplitude Sweep” (AS) predictions.
Multiple linear regression models of MODEL 2 predict the critical paint properties of Opacity,
Gloss, Krebs Viscosity and Dry Film Thickness with relative errors smaller than 10%. It has been
shown that 90% of all new predictions fall within the allowable error margin set by the paint
manufacturer. Paint properties that can be predicted with an expected error of between 10% and
20% are Dry and Wet Burnish, Open Time and Water Permeability. Paint properties that are
predicted the most inaccurately by MLR, that results in errors larger than 20% are Dirt Pick-Up
and Sagging. Non-linear techniques such as neural networks are used to predict the paint
properties of these paint samples for which the raw materials vary by more than 20% from the
standard formulation. The neural networks show a major improvement on the predictability of the
paint properties for those paint samples that vary more than 20% from the standard formulation.
On average, neural networks improve predictability of the paint properties by 47%. The largest
improvement in predictability is made on the Wet Burnish20 prediction, where multiple linear
regression resulted in relative errors of 66%, while neural networks resulted in errors of only 0.6%.
Other paint property predictions where neural networks have shown a major improvement on
predictability of 80% or more in accuracy are Gloss – 80% increase in accuracy and Dry Film
Thickness – 81% increase in accuracy. The smallest increase that the neural network had on the
predictability of a paint property, was a 33% increase in accuracy of the Sag predictions. MODEL
2 makes it possible for the paint manufacturer to test tolerances around certain paint properties
during manufacturing.
Rheology is still a very under-utilised tool for explaining certain paint properties. MODEL 3
quantified the correlation between fundamental rheological properties and real world performance
of a paint. It has been shown that rheological measurements can be used accurately to predict
certain critical paint properties such as Opacity, Krebs Viscosity, Dry Film Thickness and Gloss
within the allowable error margin given by the paint manufacturer. Multiple linear regression
models predict the paint properties of Opacity, Krebs Viscosity and Dry Film Thickness with
relative errors smaller than 10%, with rheology as input to the model. A neural network of MODEL
3 was developed to predict the paint properties of those paint samples that vary more than 20%
from the standard formulation, by using rheology data as input to the model. The neural networks
perform better than multiple linear regression in predicting the paint properties of these paint
samples. On average, neural networks that use rheology data as input, predict the paint
properties 49% more accurate than equivalent multiple linear regression models. The greatest improvement in model predictability is for Water Permeability - 73% increase in accuracy and
Gloss - 70% increase in accuracy....