# Simultaneous Determination of Droplet Size, pH Value and Concentration to Evaluate the Aging Behavior of Metalworking Fluids

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## Abstract

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_{a}and effective scattering coefficients µ’

_{s}. Droplet size was determined via dynamic light scattering (DLS) measurements. Droplet size showed non-linear dependence on MWF concentration and pH, but the nitrite concentration had no significant effect. pH and MWF concentration showed a strong synergistic effect, which indicates that MWF aging is a rather complex process. The observed effects were similar for the DLS and the µ’

_{s}values, which shows the comparability of the methodologies. The correlations of the methods were R

^{2}

_{c}= 0.928 and R

^{2}

_{P}= 0.927, as calculated by a partial least squares regression (PLS-R) model. Furthermore, using µ

_{a}, it was possible to generate a predictive PLS-R model for MWF concentration (R

^{2}

_{c}= 0.890, R

^{2}

_{P}= 0.924). Simultaneous determination of the pH based on the µ’

_{s}is possible with good accuracy (R²

_{c}= 0.803, R²

_{P}= 0.732). With prior knowledge of the MWF concentration using the µ

_{a}-PLS-R model, the predictive capability of the µ’

_{s}-PLS-R model for pH was refined (10 wt%: R²

_{c}= 0.998, R²

_{p}= 0.997). This highlights the relevance of the combined measurement of µ

_{a}and µ’

_{s}. Recognizing the synergistic nature of the effects of MWF concentration and pH on the droplet size is an important prerequisite for extending the service life of an MWF in the metalworking industry. The presented method can be applied as an in-process analytical tool that allows one to compensate for ageing effects during use of the MWF by taking appropriate corrective measures, such as pH correction or adjustment of concentration.

## 1. Introduction

_{s}. The comparability of μ’

_{s}and DLS measurements was demonstrated by partial least squares regression (PLS-R). μ’

_{s}and the absorption coefficient μ

_{a}were directly measured simultaneously by a newly developed instrument (SphereSpectro 150H, Gigahertz Optik GmbH) [24,27]. Since the instrument allows the parallel measurement of μ

_{a}, the MWF concentration was spectrally checked using a PLS-R model. In addition to the droplet size, the determination of the pH based on the µ’

_{s}was also performed.

## 2. Materials and Methods

#### 2.1. Chemicals

#### 2.2. Sample Preparation

#### 2.3. Response Surface Model

_{s}at 650 nm acted as response variables. The factor level limits were determined both by preliminary experiments considering MWF concentrations typically used in the industry [28]. In industrial practice, MWF emulsions outside of pH 8.5–9.5 are usually discarded. The nitrite concentration followed local German safety regulations according to TRGS611 [29]. For MWF emulsions without inhibitor, the upper limit is 20 mg/mL, whereas for MWF emulsions with inhibitor it is 80 mg/mL [30]. For the experimental design, this range was slightly extended to allow accurate interpolations and to allow observing small effects. An overview over the factor settings is given in Table 1.

#### 2.4. Determination of the Effective Scattering Coefficient μ’_{s} and the Absorption Coefficient μ_{a}

_{a}and µ’

_{s}were measured using a spectrophotometer (SphereSpectro 150H, Gigahertz Optik GmbH, Türkenfeld, Germany). The instrument was equipped with an integrating sphere (150 mm), a tungsten lamp, a mirror based optical setup for optical beam handling (different beams) and an array-spectroradiometer based detector system (Silicium, Si) and indium gallium arsenide (InGaAs detectors). The spectral range was set to 400–800 nm with a spectral resolution of 1 nm. A maximum integration time of 5 s was selected for the measurements in the absorbance and scattering modes. The samples were filled into a spectrometer-specific quartz cuvette with an optical path length of 3.6 mm (Figure 1d). For the calculation of µ

_{a}and µ’

_{s}the reflectance and transmittance of a sample are required. Preliminary experiments had shown the suitability of water as an approximation for the MWF emulsions. Therefore, its Sellmeier coefficients were applied [31]. After signal compensation with the calibration standard, the corresponding coefficient value pair was taken from a reference table provided by the instrument manufacturer [32] in which Monte Carlo simulation-based values were collected. The measurements were performed over a period of three days. The time at which a certain measurement was performed was included in the RSM as a block factor in order to account for systematic effects introduced by the actual sequence in measurements. For the determination of factor effects, the values of µ’

_{s}recorded at 650 nm were used as the response variable.

#### 2.5. Dynamic Light Scattering for Hydrodynamic Radius Determination

_{water}= 1.333 and n

_{MWFconcentrate}= 1.45.

#### 2.6. Multivariate Data Analysis

_{s}and µ

_{a}, a wavelength range of 400–800 nm was used.

_{a}as independent variables. The correlation of Z-average and µ’

_{s}was calculated with µ’

_{s}as the independent variable and Z-average as the dependent variable. The number of factors for each PLS-R model was optimized for a high coefficient of determination (R

^{2}) and a low root mean square error of calibration (RMSEC) and prediction (RMSEP). This approach was applied to both the calibration and validation model for each method. A spectral range of 400–800 nm was selected.

## 3. Results and Discussion

#### 3.1. Response Surface Model

_{s}were identified and quantified using response surface methodology. The data are collected in Table 2.

_{s}value from the spectrum. µ’

_{s}at 650 nm was found to be suitable for evaluating the RSM, as it described the variance within the samples sufficiently. It was located near the center of the visible spectrum, and therefore far enough away from the strongly scattering samples at the lower end and the weakly scattering samples at the upper end of the investigated spectral range.

_{MWF}for the Z-average model was included to comply with the requirement of preservation of the model hierarchy, which means that all factors that are involved in a second-order interaction must be included in the model regardless whether they are statistically significant by themselves or not [35] (p. 213). The characteristics of both models are shown in Table 3.

^{2}

_{µ’s}= 0.9891 and R

^{2}

_{Z}

_{−a}

_{verage}=0.9557). The values for R

^{2}

_{adjusted}of 0.9858 and 0.9438 for µ’

_{s}and z-average, respectively, indicate that no overfitting of the data was present and the number of model terms used in the response surface models was appropriate in relation to the number of experiments performed [20,36]. According to the R

^{2}

_{predicted}, both models allowed robust and accurate predictions of the response values within the examined experimental space (R

^{2}

_{µ’s}= 0.9727 and R

^{2}

_{Z}

_{−}

_{average}= 0.9212). The pure error of design was 0.01 for both models, indicating good predictive power of the models within the experimental space studied.

_{s}. In the case of µ’

_{s}, this general effect of pH was much less pronounced at lower MWF concentrations (synergy effect; at the lowest concentrations of MWF, there was even no effect of pH at all on µ’

_{s}). MWF emulsions are designed to be stable in the alkaline range. They are stabilized by an emulsifier, which allows the formation of spherical droplets, and in turn, a minimum contact area between MWF and water [28]. Lowering the pH simulates a form of emulsion aging (biofouling): During regular operation, microorganisms grow on the walls of the storage tanks despite applied biocides. It is known that these microorganisms can metabolize components of the MWF and as a result will lower the pH in the course of their metabolism [37]. With decreasing pH, the negative charges on the emulsifier become neutralized by H

^{+}. This, in turn, reduces the repulsive electrostatic interaction forces between the droplets and their coagulation is favored. However, with less active emulsifier, still the same quantity of MWF has to be emulsified, leading to larger droplet sizes. This behavior is non-linear for µ’

_{s}at 650 nm, as indicated by the negative B² term. The increase in light scattering is more pronounced at lower pHs.

_{s}. It is only included in the Z-average model to preserve model hierarchy.

_{s}value increases. This means that at higher MWF concentrations, generally more droplets form [38]. This increases the number of light scattering events and is consistent with the definition of µ’

_{s}as the reciprocal of the average distance light travels between two scattering events [24]. With more droplets present, the mean free path length between them will become increasingly smaller. The Z-average model has a positive non-linear effect term A², reflecting that an increase in droplet size is disproportionally more pronounced as the MWF concentration increases.

_{s}at 650 nm and Z-average. The similarity of the influences on both response variables demonstrates the comparability of the two measurement methods. MVA, especially PCA and PLS-R, of the µ’

_{s}and µ

_{a}-spectra, was performed to support the results. Using multivariate statistics allows, in contrast to the response surface methodology applied in RSM, the simultaneous consideration of all wavelength-dependent µ’

_{s}values and deriving a more comprehensive quantitative regression model.

#### 3.2. Multivariate Data Analysis

#### 3.2.1. Correlation of µ’_{s} and Z-Average by PLS-R

_{s}-spectra as input variables and Z-average as the response variable was used to assess the correlation between the two response variables. Three factors were sufficient for building the model, since they explained 93% of the total variance in the dataset, and additions of more factors did not significantly improve model quality. The PLS-R model of µ’

_{s}resulted in high R

^{2}and low RMSEC and RMSEP values for the calibration and validation models. Only small differences were observed between the calibration (R²

_{c}= 0.938, RMSEC = 10.1 nm) and validation (R²

_{P}= 0.927, RMSEP = 10.1 nm) model.

_{s}and the Z-average was demonstrated. As a result, spectroscopic measurement of µ’

_{s}enables the accurate determination and prediction of a quantitative measure for the droplet size.

#### 3.2.2. Effects of pH and MWF Concentration on µ_{a}- and µ’_{s}-Spectra as Revealed by PCA

_{a}- (Figure 5) and µ’

_{s}-spectra (Figure 6) over the whole range of the visible spectrum from 400 to 800 nm. In Figure 5a the scores values of PC-1 (93.5%) are plotted against those for PC-2 (5.6%) for the µ

_{a}-spectra.

_{a}are represented mainly by changes in the spectral region between 400 and 500 nm.

_{a}-based PCA model are displayed in Figure 5b. The highest influence of PC-1 is shown in the spectral range between 400 and 500 nm. For PC-2, the influence of the variables increases continuously with increasing wavelengths.

^{2}against F-residuals (Figure 5c). In Figure 5d the µ

_{a}-spectra are given, and the different samples are colored according to their MWF concentrations: 5 wt% (black), 10 wt% (green) and 15 wt% (red). Higher µ

_{a}values occur in the short-wavelength range. With increasing MWF concentration, µ

_{a}increases until 500 nm. This can also be seen in the loadings of PC-1. As a consequence, the variations in the MWF concentration dominate the information carried by the µ

_{a}-spectra. This allowed deriving predictive models for the MWF concentration based on µ

_{a}.

_{s}. Both PCs together explain nearly 100% of the total variance within the dataset. The influence of the pH was correlated with PC-1 and PC-2. Samples with different pHs appear as separate clusters along the PC-2 axis. pHs 9.5 (red), 9.0 (green) and 8.5 (black) are separated from one another. pHs 9.5 and 9.0 are grouped above-average on PC-1 and PC-2, respectively. pH 8.5 is divided into three groups based on the effect of STD 2 and STD 6 and is positioned almost completely below-average for PC-1. This is attributed to the strong non-linear behavior of the droplet size and hence µ’

_{s}as a function of pH. These experiments were affected by the interaction between pH and MWF concentration, and thus show high variance in the pH 8.5 data, as also indicated by the RSM.

_{s}-based PCA model are displayed in Figure 6b. The loading values of PC-1 are negative, and the ones < 475 nm of PC-2 are positive. Their trajectories are mirrored with main influences of both PCs in the area <475 nm. The influence plot with Hotelling’s T

^{2}against F-residuals shows the strong influences of STD 2 and STD 6 on the model, according to the RSM (Figure 6c). In Figure 6d the µ’

_{s}-spectra are illustrated and colored according the pHs 8.5 (black), 9.0 (green) and 9.5 (red). Higher µ’

_{s}values occur in the short-wavelength range. With decreasing pH, µ’

_{s}generally increases, and the decrease in µ’

_{s}from the short- to long-wavelength range becomes more pronounced.

_{s}and caused the response surface to be non-linear with respect to the factor pH. The protonation of the emulsifier in combination with the high MWF concentration enhanced the coagulation of the droplets.

_{s}[39] (136f), [40] (p 361).

^{4}) is reflected by the steep ascent of PC-2 loadings, the flatter profile in the PC-1 loadings corresponds to the less wavelength-dependent Mie scattering. With higher pHs, and thus more stable emulsions and smaller droplets, the ratio of Mie scattering is lower (above-average PC-1 scores), and the ratio of Rayleigh scattering increases (above-average PC-2 scores). In particular, this effect was observed for the increased µ’

_{s}at wavelengths >500 nm as an offset in samples STD 2 and STD 6.

_{s}-spectra. This allowed deriving a mathematical model that accurately predicts the pH.

#### 3.2.3. Determination of MWF Concentration Based on µ_{a}

_{a}scores based on the MWF concentrations, quantitative prediction modelling of MWF concentration was performed using PLS-R. The actual MWF concentrations derived from the settings according to Table 2 were used as responses. Three factors were selected for the model generation. The PLS-R model of µ

_{a}is characterized by a high R

^{2}(R²

_{c}= 0.890, R

^{2}

_{p}= 0.924) and low RMSEC = 1.174 wt%; and RMSEP = 0.975 wt% for the calibration and validation models.

_{a}are still considered suitable for the determination of the MWF concentration in a wide concentration range.

#### 3.2.4. Determination of pH Based on µ’_{s}

_{s}scores based on the pH, a prediction of pHs was attempted by PLS-R. Three factors were selected for the model. The interaction between pHs and MWF concentration led to slightly less satisfactory model statistics for pH prediction in the PLS-R model (R²

_{c}= 0.803, RMSEC = 0.157, R²

_{P}= 0.732, RMSEP = 0.183).

_{s}-PCA model, the scores of PC-1 and PC-2 were used to perform quadratic discriminant analysis (QDA). The confusion matrix resulting from this model is listed in Table 5. The confusion matrix describes the performance of the classification model based on the QDA. The model had an overall accuracy of 99.0%, which means that the model can correctly classify µ’

_{s}-spectra according to pHs. The highlighted diagonal describes how many spectra were predicted by the model as true. Only one spectrum of a mixture with a pH of 8.5 was predicted falsely to have a pH of 9.0. An average sensitivity of 98.6%, a specificity of 99.3%, a false positive rate of 0.7% and a precision of 99.3% were calculated based on the confusion matrix terminology.

_{a}is possible. This allowed us to create a successive approach to accurately characterize the MWF emulsion, in which the MWF concentration is first determined by µ

_{a}and then the pH is predicted using the PLS-R model of µ’

_{s}to the corresponding MWF concentration. When a PLS-R three factor model (Appendix A Figure A1) was implemented using only the data from a defined MWF concentration, 10 wt% in this case, a strong regression model for pH was obtained with R²

_{c}= 0.998 and R²

_{p}= 0.997, and very minor calibration and validation errors of RMSEC = 0.011 and RMSEP = 0.013, respectively.

## 4. Conclusions

_{s}at 650 nm and Z-average values obtained from DLS measurements were used as response variables. No statistically significant effect was observed for the factor “nitrite concentration.” The MWF concentration and pH showed statistically significant and non-linear effects on droplet size and µ’

_{s}. In particular, the second-order interaction effect between concentration and pH revealed that aging of MWF emulsions depends in a rather complex (i.e., synergistic and non-linear) way on the two factors. With decreasing pH, the droplet size and µ’

_{s}at 650 nm increase, with the effect being stronger at higher MWF concentrations. The correlation of µ’

_{s}-spectra and Z-average was demonstrated by PLS-R models: R²

_{P}= 0.927. This illustrates the suitability of µ’

_{s}as an alternative measurement method of droplet size and MWF emulsion aging.

_{s}-spectra, QDA classification by pH was possible with 99% overall accuracy. A quantitative PLS-R prediction with an error of 0.18 and R²

_{P}= 0.733 was obtained. The simultaneous measurement of µ

_{a}allows the prediction of MWF concentration with R²

_{P}= 0.924 and an error RMSEP = 0.97 wt%. The presented method of concurrent measurement of µ’

_{s}and µ

_{a}thus allows the simultaneous determination and quantification of the droplet size, MWF concentration and pH. In combination with the causal model based on the statistically significant factor effect terms, the current condition of a MWF emulsion could, in principle, be monitored in real-time by means of online sensors.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

µ’_{s} | effective scattering coefficient |

µ_{a} | absorption coefficient |

λ | wavelength |

ANOVA | analysis of variance |

C_{MWF} | metalworking fluid concentration |

C_{Nitrite} | nitrite concentration |

d | diameter |

DLS | dynamic light scattering |

FCD | face-centered central composite design |

i. e. | id est |

InGaAs | indium gallium arsenide |

mm | millimeter |

MWF | metallworking fluids |

nm | nanometer |

n_{MWFconcentrate} | refractive index of metalworking fluid concentrate |

n_{water} | refractive index of water |

PC | principal component |

PCA | principal component analysis |

PI | prediction interval |

PLS-R | partial least squares regression |

QDA | quadratic discriminant analysis |

R^{2} | coefficient of determination |

R²_{c} | coefficient of determination for calibration |

R²_{p} | coefficient of determination for prediction |

RMSEC | root mean square error of calibration |

RMSEP | root mean square error of prediction |

RSM | response surface model |

s | second |

Si | silicium |

STD | standard order |

SVD | singular value decomposition |

Val | validation point |

wt% | weight percent |

## Appendix A. Determination of pH Based on µ’_{s} −10 wt%

_{s}-spectra at 10 wt% MWF concentration as input variables and pHs as response variables was calculated. Three factors were selected for the model generation. The PLS-R model of µ’

_{s}is characterized by a high R

^{2}(R²

_{c}= 0.998, R²

_{p}= 0.997) and low RMSEC = 0.011 and RMSEP = 0.013 values for the calibration and validation models.

**Figure A1.**PLS-R with three factors for pHs at 10% MWF concentration values on µ’

_{s}-spectra. The regression coefficients of the three-factor model are shown in (

**a**). Predicted vs. reference of pHs for calibration (green) and validation (red) are displayed in (

**b**).

## References

- Spasiano, D.; Petrella, A.; Lacedra, V. Chemical Destabilization of Fresh and Spent Cutting Oil Emulsions: Differences between an Ecofriendly and Two Commercial Synthetic Lubricants. Sustainability
**2020**, 12, 5697. [Google Scholar] [CrossRef] - Sułek, M.W.; Bąk-Sowińska, A.; Przepiórka, J. Ecological Cutting Fluids. Materials
**2020**, 13, 5812. [Google Scholar] [CrossRef] - Benedicto, E.; Rubio, E.M.; Carou, D.; Santacruz, C. The Role of Surfactant Structure on the Development of a Sustainable and Effective Cutting Fluid for Machining Titanium Alloys. Metals
**2020**, 10, 1388. [Google Scholar] [CrossRef] - Deutsches Institut für Normung e.V. Schmierstoffe Bearbeitungsmedien für die Umformung und Zerspanung von Werkstoffen: Begriffe; Beuth Verlag: Berlin, Germany, 2013. [Google Scholar]
- Herrmann, C.; Madanchi, N.; Winter, M.; Ohlschlager, G.; Greßmann, A.; Zettl, E.; Schwengers, K.; Lange, U. Ökologische und Ökonomische Bewertung des Ressourcenaufwands: Wassermischbare Kühlschmierstoffe. 2017. Available online: https://www.ressource-deutschland.de/fileadmin/user_upload/downloads/studien/Studie_Kuehlschmierstoffe_barrierefrei.pdf (accessed on 21 November 2021).
- Brinksmeier, E.; Meyer, D.; Huesmann-Cordes, A.G.; Herrmann, C. Metalworking fluids—Mechanisms and performance. CIRP Ann.
**2015**, 64, 605–628. [Google Scholar] [CrossRef][Green Version] - Verein Deutscher Ingenieure e.V. Pflege von Kühlschmierstoffen für Spanende und Umformende Fertigungsverfahren: Maßnahmen zur Qualitätserhaltung, Prozessverbesserung, Abfall- und Abwasserverminderung; Beuth Verlag: Berlin, Germany, 2014. [Google Scholar]
- Grossi, M.; Riccò, B. An automatic titration system for oil concentration measurement in metalworking fluids. Measurement
**2017**, 97, 8–14. [Google Scholar] [CrossRef] - Kiefer, J.; Seidel, B.; Meyer, D. Optical Spectroscopy for Analysis and Monitoring of Metalworking Fluids. Appl. Spectrosc.
**2018**, 72, 1790–1797. [Google Scholar] [CrossRef] [PubMed] - Seidel, B.; Meyer, D. Investigation of the Influence of Aging on the Lubricity of Metalworking Fluids by Means of Design of Experiment. Lubricants
**2019**, 7, 94. [Google Scholar] [CrossRef][Green Version] - Assenhaimer, C.; Domingos, A.S.; Glasse, B.; Fritsching, U.; Guardani, R. Long-term monitoring of metalworking fluid emulsion aging using a spectroscopic sensor. Can. J. Chem. Eng.
**2017**, 95, 2341–2349. [Google Scholar] [CrossRef] - Assenhaimer, C.; Machado, L.J.; Glasse, B.; Fritsching, U.; Guardani, R. Use of a spectroscopic sensor to monitor droplet size distribution in emulsions using neural networks. Can. J. Chem. Eng.
**2014**, 92, 318–323. [Google Scholar] [CrossRef] - Glasse, B.; Assenhaimer, C.; Guardani, R.; Fritsching, U. Turbidimetry for the stability evaluation of emulsions used in machining industry. Can. J. Chem. Eng.
**2014**, 92, 324–329. [Google Scholar] [CrossRef] - Glasse, B.; Fritsching, U.; Koch, T.; de Paiva, J.L.; Guardani, R. Turbidimetric Spectroscopy for the Evaluation of Metalworking Fluids Stability. Tribol. Trans.
**2012**, 55, 237–244. [Google Scholar] [CrossRef] - Menniti, A.; Rajagopalan, K.; Kramer, T.A.; Clark, M.M. An evaluation of the colloidal stability of metal working fluid. J. Colloid Interface Sci.
**2005**, 284, 477–488. [Google Scholar] [CrossRef] [PubMed] - Deluhery, J.; Rajagopalan, N. A turbidimetric method for the rapid evaluation of MWF emulsion stability. Colloids Surf. A Physicochem. Eng. Asp.
**2005**, 256, 145–149. [Google Scholar] [CrossRef] - Matos, M.; Lobo, A.; Benito, J.M.; Coca, J.; Pazos, C. Extending the Useful Life of Metalworking Fluids in a Copper Wire Drawing Industry by Monitoring Their Functional Properties. Tribol. Trans.
**2012**, 55, 685–692. [Google Scholar] [CrossRef] - Assenhaimer, C. Evaluation of Emulsion Destabilization by Light Scattering Applied to Metalworking Fluids. Ph.D. Thesis, Universidade de São Paulo, São Paulo, Brazil, 2015. [Google Scholar]
- Ulrich, C.; Dan, L.; Mårtensson, P.; Kluftinger, A.; Gawronski, M.; Björefors, F. Evaluation of industrial cutting fluids using electrochemical impedance spectroscopy and multivariate data analysis. Talanta
**2012**, 97, 468–472. [Google Scholar] [CrossRef] - Seidl, R.; Weiss, S.; Kessler, R.W.; Kessler, W.; Zikulnig-Rusch, E.M.; Kandelbauer, A. Prediction of Residual Curing Capacity of Melamine-Formaldehyde Resins at an Early Stage of Synthesis by In-Line FTIR Spectroscopy. Polymers
**2021**, 13, 2541. [Google Scholar] [CrossRef] [PubMed] - Englert, T.; Stiedl, J.; Green, S.; Jacob, T.; Chassé, T.; Rebner, K. Quantifying flux residues after soldering on technical copper using ultraviolet visible (UV–Vis) spectroscopy and multivariate analysis. Microelectron. Reliab.
**2021**, 125, 114367. [Google Scholar] [CrossRef] - Steinbach, J.C.; Schneider, M.; Hauler, O.; Lorenz, G.; Rebner, K.; Kandelbauer, A. A Process Analytical Concept for In-Line FTIR Monitoring of Polysiloxane Formation. Polymers
**2020**, 12, 2473. [Google Scholar] [CrossRef] [PubMed] - Ulitzsch, S.; Bäuerle, T.; Stefanakis, M.; Brecht, M.; Chassé, T.; Lorenz, G.; Kandelbauer, A. Synthesis of an Addition-Crosslinkable, Silicon-Modified Polyolefin via Reactive Extrusion Monitored by In-Line Raman Spectroscopy. Polymers
**2021**, 13, 1246. [Google Scholar] [CrossRef] [PubMed] - Foschum, F.; Bergmann, F.; Kienle, A. Precise determination of the optical properties of turbid media using an optimized integrating sphere and advanced Monte Carlo simulations. Part 1: Theory. Appl. Opt.
**2020**, 59, 3203–3215. [Google Scholar] [CrossRef] [PubMed] - Grossi, M.; Riccò, B. Oil Concentration Measurement in Metalworking Fluids by Optical Spectroscopy. In Proceedings of the 18th International Trade Dair of Material & Energy Recovery and Sustainable Development, Rimini, Italy, 5–8 November 2014. [Google Scholar]
- Glasse, B.; Assenhaimer, C.; Guardani, R.; Fritsching, U. Analysis of the Stability of Metal Working Fluid Emulsions by Turbidity Spectra. Chem. Eng. Technol.
**2013**, 36, 1202–1208. [Google Scholar] [CrossRef] - Bergmann, F.; Foschum, F.; Zuber, R.; Kienle, A. Precise determination of the optical properties of turbid media using an optimized integrating sphere and advanced Monte Carlo simulations. Part 2: Experiments. Appl. Opt.
**2020**, 59, 3216–3226. [Google Scholar] [CrossRef] [PubMed] - Benito, J.M.; Cambiella, A.; Lobo, A.; Gutiérrez, G.; Coca, J.; Pazos, C. Formulation, characterization and treatment of metalworking oil-in-water emulsions. Clean Technol. Environ. Policy
**2010**, 12, 31–41. [Google Scholar] [CrossRef] - Bundesanstalt für Arbeitsschutz und Arbeitsmedizin. Verwendungsbeschränkungen für Wassermischbare bzw. Wassergemischte Kühlschmierstoffe, bei deren Einsatz N-Nitrosamine Auftreten Können; Beuth Verlag: Berlin, Germany, 2007. [Google Scholar]
- Deutsche Gesetzliche Unfallversicherung. Inhibitoren der Nitrosaminbildung: Wirksamkeitsnachweis, Praktikables Maßnahmenkonzept nach TRGS 611, 2016 (FB HM-045). Available online: https://www.dguv.de/medien/fb-holzundmetall/publikationen-dokumente/infoblaetter/infobl_deutsch/045_inhibitoren_trgs611.pdf (accessed on 3 December 2021).
- Daimon, M.; Masumura, A. Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region. Appl. Opt.
**2007**, 46, 3811–3820. [Google Scholar] [CrossRef] - Berghof Gigahertz-Optik. Material Determination with Spherespectro 150H: For Scattering Samples. Available online: https://www.gigahertz-optik.com/assets/Uploads/SphereSpectro150H_DINA4_EN_Brochure.pdf (accessed on 21 November 2021).
- Stefanakis, M.; Lorenz, A.; Bartsch, J.W.; Bassler, M.C.; Wagner, A.; Brecht, M.; Pagenstecher, A.; Schittenhelm, J.; Boldrini, B.; Hakelberg, S.; et al. Formalin Fixation as Tissue Preprocessing for Multimodal Optical Spectroscopy Using the Example of Human Brain Tumour Cross Sections: Supplementary Material. J. Spectrosc.
**2021**, 2021, 5598309. [Google Scholar] [CrossRef] - Bassler, M.C.; Stefanakis, M.; Sequeira, I.; Ostertag, E.; Wagner, A.; Bartsch, J.W.; Roeßler, M.; Mandic, R.; Reddmann, E.F.; Lorenz, A.; et al. Comparison of Whiskbroom and Pushbroom darkfield elastic light scattering spectroscopic imaging for head and neck cancer identification in a mouse model. Anal. Bioanal. Chem.
**2021**, 2021, 7363–7383. [Google Scholar] [CrossRef] [PubMed] - Montgomery, D.C. Design and Analysis of Experiments, 8th ed.; John Wiley & Sons Inc.: Hoboken, NJ, USA, 2013; ISBN 978-1118-14692-7. [Google Scholar]
- Ulitzsch, S.; Bäuerle, T.; Chassé, T.; Lorenz, G.; Kandelbauer, A. Optimizing the Process Efficiency of Reactive Extrusion in the Synthesis of Vinyltrimethoxysilane-Grafted Ethylene-Octene-Copolymer (EOC-g-VTMS) by Response Surface Methodology. Polymers
**2020**, 12, 2798. [Google Scholar] [CrossRef] [PubMed] - Rabenstein, A.; Koch, T.; Remesch, M.; Brinksmeier, E.; Kuever, J. Microbial degradation of water miscible metal working fluids. Int. Biodeterior. Biodegrad.
**2009**, 63, 1023–1029. [Google Scholar] [CrossRef] - Deutsches Institut für Normung e.V. Prüfung von Metallbearbeitungsflüssigkeiten—Bestimmung des pH-Wertes von Wassergemischten Metallbearbeitungsflüssigkeiten; Beuth Verlag: Berlin, Germany, 2013. [Google Scholar]
- Bohren, C.F.; Huffman, D.R. Absorption and Scattering of Light by Small Particles; Wiley: New York, NY, USA, 1998; ISBN 0-471-29340-7. [Google Scholar]
- Petty, G.W. A First Course in Atmospheric Radiation, 2nd ed.; Sundog Publications: Madison, WI, USA, 2006; ISBN 978-0-9729033-1-8. [Google Scholar]

**Figure 1.**Illustration of sample preparation and the factor level settings according to the response surface methodology. (

**a**) Preparation of the desired MWF concentrations and control by refractometry. (

**b**) Factor level settings of pH and nitrite concentrations. (

**c**) Schematic representation of the examined experimental space. (

**d**) Photograph of a typical sample in a quartz cuvette (10 wt% MWF concentration).

**Figure 2.**Response surface plots of the models: (

**a**) µ’

_{s}and (

**b**) Z-average. Circles indicate design points. Response values increase from blue to red surface color.

**Figure 3.**Interaction plot of AB interaction for (

**a)**µ’

_{s}and (

**b**) Z-average. Red triangles indicate responses measured at high pHs. Black squares indicate measured response at low pHs. Green circles indicate measured response at medium pH. Dashed lines indicate 95% confidential intervals.

**Figure 4.**PLS-R with three factors for correlation of µ’

_{s}and Z-average. The regression coefficients of the three-factor model are shown in (

**a**). Predicted vs. reference of Z-average for calibration (green) and validation (red) are displayed in (

**b**).

**Figure 5.**PCA and spectra of µ

_{a}. (

**a**) Scores plot with MWF concentration 5 wt% (black circle), 10 wt% (green triangle) and 15 wt% (red square) for PC-1 against PC-2. (

**b**) Corresponding loadings PC-1 (black) and PC-2 (red). (

**c**) Influence plot Hotelling’s T

^{2}versus F-residuals for PC-2. (

**d**) µ’

_{s}-spectra of MWF concentration 5 wt% (black), 10 wt% (green) and 15 wt% (red).

**Figure 6.**PCA and spectra of µ’

_{s}. (

**a**) Scores plot with pH 8.5 (black circle), pH 9.0 (green triangle) and pH 9.5 (red square) for PC-1 against PC-2. (

**b**) Corresponding loadings PC-1 (black) and PC-2 (red). (

**c**) Influence plot Hotelling’s T

^{2}versus F-residuals for PC-2. (

**d**) µ’

_{s}-spectra of pH 8.5 (black), pH 9.0 (green) and pH 9.5 (red).

**Figure 7.**PLS-R with three factors for MWF concentration based on µ

_{a}-spectra. The regression coefficients of the three-factor model are shown in (

**a**). Predicted vs. reference of MWF concentration for calibration (green) and validation (red) are displayed in (

**b**).

**Figure 8.**PLS-R with three factors for pHs based on µ’

_{s}-spectra. The regression coefficients of the three-factor model are shown in (

**a**). Predicted vs. reference of pHs for calibration (green) and validation (red) are displayed in (

**b**).

Factor | Name | Unit | −1 | 0 | +1 |
---|---|---|---|---|---|

A | MWF concentration | % | 5 | 10 | 15 |

B | pH | pH | 8.5 | 9.0 | 9.5 |

C | Nitrite concentration | mg∙L^{−1} | 0 | 50 | 100 |

**Table 2.**Experiments conducted according to the face-centered central composite design (FCD), sorted by standard order (STD) according to the Yates nomenclature. The order in which the measurements were actually performed is also given. The factor level settings of each experimental run are given along with the corresponding response values.

Factor Level Settings | Response Values | |||||
---|---|---|---|---|---|---|

STD | Run | A | B | C | ||

C_{MWF} | pH Value | C_{Nitrite} | µ’_{s} | Z-Average | ||

/wt% | /mg∙L^{−1} | /mm^{−1} | /nm | |||

1 | 14 | 5 | 8.5 | 0 | 0.538 | 128.1 |

2 | 15 | 15 | 8.5 | 0 | 2.303 | 193.0 |

3 | 20 | 5 | 9.5 | 0 | 0.129 | 66.4 |

4 | 10 | 15 | 9.5 | 0 | 0.112 | 53.3 |

5 | 9 | 5 | 8.5 | 100 | 0.606 | 126.6 |

6 | 13 | 15 | 8.5 | 100 | 1.932 | 185.3 |

7 | 8 | 5 | 9.5 | 100 | 0.124 | 73.5 |

8 | 3 | 15 | 9.5 | 100 | 0.116 | 57.3 |

9 | 1 | 5 | 9 | 50 | 0.393 | 107.8 |

10 | 17 | 15 | 9 | 50 | 0.504 | 82.0 |

11 | 7 | 10 | 8.5 | 50 | 0.910 | 110.7 |

12 | 2 | 10 | 9.5 | 50 | 0.100 | 52.0 |

13 | 11 | 10 | 9 | 0 | 0.451 | 79.3 |

14 | 6 | 10 | 9 | 100 | 0.434 | 81.8 |

15 | 16 | 10 | 9 | 50 | 0.472 | 83.3 |

16 | 19 | 10 | 9 | 50 | 0.458 | 82.7 |

17 | 4 | 10 | 9 | 50 | 0.489 | 81.9 |

18 | 5 | 10 | 9 | 50 | 0.460 | 80.6 |

19 | 18 | 10 | 9 | 50 | 0.462 | 81.4 |

20 | 12 | 10 | 9 | 50 | 0.472 | 94.9 |

Val1 | 21 | 11.2 | 8.8 | 0 | 0.757 | 85.2 |

Val2 | 22 | 13.8 | 8.7 | 0 | 1.040 | 118.4 |

µ‘_{s} | Z-Average | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Source | Sum of Squares | df | Mean Square | F-Value | p-Value | Source | Sum of Squares | df | Mean Square | F-Value | p-Value |

Model | 2.70 | 4 | 0.6749 | 390.28 | <0.0001 | Model | 0.43 | 4 | 0.1087 | 80.84 | <0.0001 |

A-c_{MWF} | 0.13 | 1 | 0.13 | 76.54 | <0.0001 | A-c_{MWF} | 0.00 | 1 | 0.00 | 0.03 | 0.8578 |

B-pH | 2.31 | 1 | 2.31 | 1335.02 | <0.0001 | B-pH | 0.37 | 1 | 0.37 | 273.73 | <0.0001 |

AB | 0.19 | 1 | 0.19 | 109.32 | <0.0001 | AB | 0.04 | 1 | 0.04 | 27.76 | <0.0001 |

B² | 0.07 | 1 | 0.07 | 40.24 | <0.0001 | A² | 0.03 | 1 | 0.03 | 21.84 | 0.0003 |

Residual | 0.03 | 15 | 0.0017 | - | - | Residual | 0.02 | 15 | 0.0013 | - | - |

Lack of fit | 0.02 | 4 | 0.0050 | 8.93 | 0.002 | Lack of fit | 0.01 | 4 | 0.0036 | 7.03 | 0.005 |

Pure error | 0.01 | 11 | 0.0006 | - | - | Pure error | 0.01 | 11 | 0.0005 | - | - |

Cor total | 2.73 | 19 | - | - | - | Cor total | 0.4549 | 19 | - | - | - |

**Table 4.**Actual vs. predicted values (with low and high 95% prediction interval (PI) with alpha = 0.05) and corresponding residuals for the validation points Val1 and Val2.

STD | µ’_{s} | Z-Average | |
---|---|---|---|

Val1 | Predicted Value (±95%PI) | 0.762 (0.601–0.995) | 100.3 (82.7–120.9) |

Actual Value | 0.757 | 85.2 | |

Residual | −0.005 | −15.1 | |

Val2 | Predicted Value (±95%PI) | 1.176 (0.919–1.491) | 134.8 (110.4–163.5) |

Actual Value | 1.040 | 118.4 | |

Residual | −0.136 | −16.4 |

Actual | 8.5 | 9.0 | 9.5 | |
---|---|---|---|---|

Predicted | ||||

8.5 | 24 | 0 | 0 | |

9.0 | 1 | 50 | 0 | |

9.5 | 0 | 0 | 25 |

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**MDPI and ACS Style**

Wahrendorff, P.; Stefanakis, M.; Steinbach, J.C.; Allnoch, D.; Zuber, R.; Kapfhammer, R.; Brecht, M.; Kandelbauer, A.; Rebner, K.
Simultaneous Determination of Droplet Size, pH Value and Concentration to Evaluate the Aging Behavior of Metalworking Fluids. *Sensors* **2021**, *21*, 8299.
https://doi.org/10.3390/s21248299

**AMA Style**

Wahrendorff P, Stefanakis M, Steinbach JC, Allnoch D, Zuber R, Kapfhammer R, Brecht M, Kandelbauer A, Rebner K.
Simultaneous Determination of Droplet Size, pH Value and Concentration to Evaluate the Aging Behavior of Metalworking Fluids. *Sensors*. 2021; 21(24):8299.
https://doi.org/10.3390/s21248299

**Chicago/Turabian Style**

Wahrendorff, Patrick, Mona Stefanakis, Julia C. Steinbach, Dominik Allnoch, Ralf Zuber, Ralf Kapfhammer, Marc Brecht, Andreas Kandelbauer, and Karsten Rebner.
2021. "Simultaneous Determination of Droplet Size, pH Value and Concentration to Evaluate the Aging Behavior of Metalworking Fluids" *Sensors* 21, no. 24: 8299.
https://doi.org/10.3390/s21248299