# Feasibility Study for a Chemical Process Particle Size Characterization System for Explosive Environments Using Low Laser Power

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Approximation and Curve Fitting

_{1}to x

_{n}is multiplied by the coefficient matrix and is equated with the associated matrix B of the Y-values.

^{T}is multiplied by matrix A and matrix B to matrix C and D, respectively as shown in Equation (2).

_{i}and the corresponding approximation points $\widehat{\mathrm{y}}$ averaged over the number of measuring points n.

_{p}to I

_{q}, in which the slope of the two curves have the same sign, while the other area is composed of the remaining intervals I

_{r}to I

_{s}where the slopes have opposite sign. For each of the two areas, each area is integrated over the respective intervals, see Equation (7). The variables represent a measure for the congruence of the two curve.

_{ss}increases as the difference between derivatives decreases, i.e., higher agreement of the curves, whereby the positive effect is amplified. By computing Equation (7) on all curves to be compared, two vectors containing the positive and negative congruence of each curve is obtained. In the next step, two vectors are divided element wise to determine the overall congruence, as shown in Equation (8). Where f is described in Equation (10). The variable $\mathrm{a}$

_{sum}has the same dimensions as $\mathrm{a}$

_{ss}and $\mathrm{a}$

_{os}.

_{ss}and $\mathrm{a}$

_{os}, the values within the vector are normalized to their respective minimum and maximum. The minimum is not normalized however to zero, so that the curve for which $\mathrm{a}$

_{os,norm}is minimal does not result in division by 0. To further enhance the prediction factors$\text{}\mathrm{f}$

_{ss}and $\mathrm{f}$

_{os}are used, as shown in (8). These factors are formed from the number of intervals with the same and opposite sign, $\mathrm{N}$

_{ss}and $\mathrm{N}$

_{os}respectively, as shown in (10). The factor $\mathrm{z}$ describes a number of power 10, where $\mathrm{z}$ is strictly greater than 10.

_{sum}. An example of curve comparison is shown in Figure 3.

#### 2.2. Particle Systems

^{®}polystyrene particles (PS), purchased from Micromod Partikeltechnologie GmbH (Rostock, Germany), with various particle diameters ranging from 0.5 µm (PDI < 0.2, PDI = polydispersity index) to 2 µm (PDI < 0.2). Spherical sicastar

^{®}silicate particles, sourced from Micromod Partikeltechnologie GmbH in Germany, with particle diameters ranging from 0.5 µm (PDI < 0.2) to 1 µm (PDI < 0.2).

#### 2.3. Experimental Setup

^{3}, thus easily adaptable to micro channels. The holder of the glass cuvette is mounted on a rail which is attached to a laboratory lifting platform. Thus, the glass cuvette has two degrees of freedom, displacement horizontally on the rail and vertically by adjusting the laboratory lifting platform. The laser is mounted on a vertical rod, independent of the test table.

## 3. Results

_{sum}, described previously, which is the congruence of the measurement signal to each simulation, where a single peak is present at approximately 700 nm.

## 4. Discussion and Future Work

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Batch file for MiePlot to automate stepping through particle sizes for intensity versus scattering angle simulations.

**Figure 3.**Classification of curves and division into intervals based on their gradient direction ((

**a**) data normalized; (

**b**) data normalized and differentiated)

**.**

**Figure 4.**Example of a congruence diagram of the 500 nm scattering pattern compared to the simulation.

**Figure 5.**Diagram illustrating the calculation of congruence to determine the particle size of a fitted curve from the simulation database.

**Figure 7.**Particle size characterization for 681 nm silica particles (particle size displayed is rounded to 680). Light scatter measured in 2° increments from 20° to 160°. (

**a**) Measurement and sinusoidal fit with 95% confidence intervals shown in gray; (

**b**) comparison to best fit result; (

**c**) comparison to actual particle size.

**Figure 9.**Particle size characterization for 1000 nm polystyrene particles. Light scatter measured in 2° increments from 20° to 160°. (

**a**) Measurement and sinusoidal fit; (

**b**) comparison to best fit result with 95% confidence intervals shown in gray; (

**c**) comparison to actual particle size.

**Figure 11.**Particle size characterization for 1000 nm polystyrene particles after filtering simulation database for signals with similar number of local extrema. Light scatter measured in 2° increments from 20° to 160°. (

**a**) Measurement and sinusoidal fit; (

**b**) comparison to best fit result with 95% confidence intervals shown in gray; (

**c**) comparison to actual particle size. Using the signal feature of number of local extrema allows confounding signals to be filtered out and prediction is improved.

**Figure 12.**Overall congruence of 1000 nm measurement to simulation database after filtering for signals with similar number of local extrema.

**Figure 13.**(

**a**) Fiber sensor in a semi circle form to detect scattered light over a range of angles and forward it to the customized photon multiplier (CPM). Between the sensor and the CPM is a rotating slit which allows only the signal from one fiber at a time to reach the CPM. (

**b**) The fiber ends are placed next to each other in an arc, and through each rotation of the slit the array of fibers is exposed sequentially.

**Table 1.**Wavelength dependent refractive index for silica and polystyrene [51].

Wavelength (µm) | Silica | Polystyrene |
---|---|---|

0.43584 | 1.4667 | 1.6170 |

0.47998 | 1.4635 | 1.6070 |

0.58756 | 1.4585 | 1.5916 |

0.70652 | 1.4551 | 1.5825 |

Polarization | Predicted Result (nm) | Data Sheet (nm) | Relative Error |
---|---|---|---|

Unpolarized | 330 | 310 | 6.5% |

Unpolarized | 480 | 507 | 5.3% |

Unpolarized | 690 | 681 | 1.3% |

Unpolarized | 880 | 900 | 2.2% |

Unpolarized | 960 | 987 | 2.8% |

Polarization | Predicted Result (nm) | Data Sheet (nm) | Relative Error |
---|---|---|---|

Unpolarized | 460 | 500 | 8.0% |

Unpolarized | 990 | 1000 | 1.0% |

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**MDPI and ACS Style**

Ross-Jones, J.; Teumer, T.; Wunsch, S.; Petri, L.; Nirschl, H.; Krause, M.J.; Methner, F.-J.; Rädle, M.
Feasibility Study for a Chemical Process Particle Size Characterization System for Explosive Environments Using Low Laser Power. *Micromachines* **2020**, *11*, 911.
https://doi.org/10.3390/mi11100911

**AMA Style**

Ross-Jones J, Teumer T, Wunsch S, Petri L, Nirschl H, Krause MJ, Methner F-J, Rädle M.
Feasibility Study for a Chemical Process Particle Size Characterization System for Explosive Environments Using Low Laser Power. *Micromachines*. 2020; 11(10):911.
https://doi.org/10.3390/mi11100911

**Chicago/Turabian Style**

Ross-Jones, Jesse, Tobias Teumer, Susann Wunsch, Lukas Petri, Hermann Nirschl, Mathias J. Krause, Frank-Jürgen Methner, and Matthias Rädle.
2020. "Feasibility Study for a Chemical Process Particle Size Characterization System for Explosive Environments Using Low Laser Power" *Micromachines* 11, no. 10: 911.
https://doi.org/10.3390/mi11100911