58 TESTING
was applied across the shear rate range of 0.1 - 1000 s-1
Upon loading, a logarithmic shear rate ramp , with five points per decade across
five minutes. The obtained data was analysed using a non-linear least squares regression in the Haake Rheowin software to extract the rheological parameters. This analysis was performed across the shear rate range of 0.1-100 s-1
the subsequent flow experiments. Two specific shear rates of 4.83 and 20.7 s-1
which is reflective of were then
selected to compare the viscosities outputted from both in-line and off-line methodologies.
Extracting rheological parameters To predict the viscosity at the required shear rates using supervised machine learning, a two- layer feed-forward neural network architecture was selected. The inputs to the neural network include 34 velocity data points from the ERR sensor and the differential pressure across the sensor. Such inputs are acquired over approximately
30 seconds to ensure that dynamic changes in the process can be captured. The output layer consists of a single neuron and a linear transfer function to output a predict a viscosity. For each shear rate, an independent model
was applied with the target data a viscosity obtained from off-line rotational rheometry. Across all materials, the viscosity was seen to vary by up to three orders of magnitude and therefore to ensure that the measurement sensitivity is retained when the viscosity is small, two models were trained for each shear rate. Due to the importance of rheology
measurements in processing, it is important to obtain a high level of accuracy and thus Bayesian regularisation was selected as the training algorithm. This training was performed in the MatLab machine learning toolbox, with the data split into 75% training and 25% test to verify the performance of the algorithm.
Results The rheological properties of a fluid strongly influence the shape of the velocity profiles in laminar pipe flow due to a shear rate response of the fluid. The displayed velocity profiles were obtained using the method outlined by Machin et al.2
, which utilised a parametric fitting of ERR
data to a power law rheological model. From this approach, it is evident that
the velocity profiles of shampoo (Figure 3d) observed increased blunting, when compared to the hand dish wash (Figure 3b) due to the increase in shear thinning behaviour. This is reflected in the rheology data obtained from off-line measurements, in Figures 3a and 3c. To capture the increased complexity of the fluid structure, a machine learning algorithm was developed to act determine the viscosity at the chosen shear rates. The prediction of in-line viscosity was seen to mirror that of the off-line rheometer. When considering low viscosity fluids, at , the correlation coefficients between
4.83 s-1
the measured and predicted viscosity were 0.999, 0.998 and 0.999 for the training, test and complete datasets, respectively. Such high
PERSONAL CARE November 2021 A 1400 1200 1000 800 600 400 200 200 400 600 800 1000 Viscosity (mPas)-Offline 1200 1400
--- y=x ■ Hand dish wash 1 ■ Hand dish wash 2 ■ Fabric wash 1 ■ Fabric wash 2
B
18000 16000 14000 12000 10000 8000 6000 4000 2000 0
--- y=x ■ Shampoo 1 ■ Shampoo 2 ■ Body wash ■ Conditioner
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 Viscosity (mPas)-Offline
Figure 4: Comparison of ERR & offline rheology measurements at 4.83 s-1: a) low viscosity products; b) higher viscosity products8
correlation is also reflected in Figure 4 and in the corresponding root-mean squared errors (RMSEs) of 2.50 mPa s, 30.6 mPa and 11.87 mPa. This ensures that the application of artificial neural networks to ERR provides a highly accurate prediction of in-line viscosity. The high performance has been attained
using a relatively small dataset and is likely to be improved further, with the performance of algorithms trained using Bayesian regularisation enhanced monotonically with increasing size of the dataset, as discussed by Neal.9
The
ability of the high viscosity model to predict viscosity was also seen to have high correlation with correlation coefficients of 0.999, 0.997 and 0.999 obtained for the training, test and complete dataset, respectively. To predict rheological behaviour, the
viscosity of the system must be predicted at multiple shear rates and hence a second shear rate of 20.7 s-1
was selected. As the shear rate
was increased, a minor decrease in the viscosity prediction error was observed. The RMSE for the low-viscosity fluid model was seen to reduce from 30.6 mPa to 21.8 mPa. Similarly, the RMSE in the high-viscosity model decreased by 59%, with ERR able to accurately predict the viscosity at multiple shear rates and ultimately rheological properties of a wide range of complex industrial fluids. The RMSE error obtained for all test data conditions is below the desired error for an in-line rheology measurement ensuring high in-plant applicability.
Conclusion This study has demonstrated that ERR measurements can accurately predict in- line rheological properties across a range of industrial personal and home care products. AI algorithms can also extend the capability of ERR to capture complex fluid behaviours often observed in industrial fluids, such as shear-banding and wall depletion. This greatly enhances the in-plant applicability of the technique.
The application of AI algorithms to ERR
has the potential to elevate rheometry from a critical, off-line control tool, to one which can
control and optimise processes in real-time. This novel technology has been shown
to provide accurate measurements of a key functional product quality in the production line in real time, and could result in huge savings, shorter lead times and better quality control for manufacturers of liquid personal care products. Ensuring rheology is correct is key to product quality and effectiveness and adoption of this technology could overcome some of the key constraints of traditional methods. Further details of this study are forthcoming.10
References 1. Barnes HA, Hutton JF, Walters K. An introduction to rheology. 3rd ed. Amsterdam: Elsevier. 2001
2. Machin T D, Wei K, Greenwood RW; Simmons MJH. In-pipe rheology & mixing characterisation using electrical resistance sensing. Chemical Engineering Science. 2018; 187
3. Paul E, Atiemo-Obeng V, Kresta S. Handbook of industrial mixing: Science & practice. Wiley-Interscience: New York. 2004
4. Wang M, Mann R, Dickin FJ. A large- scale tomographic sensing system for mixing processes. IWISP 1996 Conference Proceedings
5. Knirsch M, Dos Santos C, De Oliveira Soares Vicente A; Vessoni Penna, Ohmic C. Heating. A Review. Trends Food Sci. 2010. 21(9); 436–441
6. Papoulis A. The Fourier integral & its applications. McGraw-Hill: New York. 1996; 244-253
7. Incropera F, De Witt D; Bergman TL, Lavine A. Fundamentals of heat & mass transfer. 6th Ed. John Wiley and Sons: New York. 2007
8. Wang, M. Industrial tomography: Systems & applications. Elsevier. 2002
9. Neal, R. Bayesian learning for neural networks. Springer: New York, 1996
10. Hoyle BS, Machin TD, Mohamad-Saleh J. Machine learning process information from tomography data, in Wang M. (ed). Industrial tomography: Systems & applications. Elsevier, 2022
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Viscosity (mPas)-ERR +AI
Viscosity (mPas)-ERR +AI
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