PSD-Analyser

PSD Analyser: A set of Python/MATLAB tools for particle size distribution (PSD) analysis and visualisation

Hugh Patrick Rice, 2022

Quick-start guide

Run the standalone executable (currently Windows only)

• Go to the Releases on the right of the page
• Download the executable file (ending .exe) and any of the spreadsheet example files from the main page if you wish to try loading them
• Once downloaded, double-click the executable file and it will run, then try loading any of the example spreadsheets to view some PSD data

Run the code directly

• Clone the repository via git clone https://github.com/paddy-r/PSD-Analyser or download files individually from here or the Releases page as you wish
• (Python) Import into your Python environment
  • Create a suitable Python environment using the environment file provided via the command conda env create -n psd -f environment.yml followed by conda activate psd (or source activate psd, depending on your system)
  • Install PSD Analyser in your Python environment via pip install -v -e .
  • There are several examples given in the psd_analyser script to demonstrate functionality, specifically: loading and saving data, plotting PSDs, fitting PSDs to log-normal distributions; and reducing them to $N$ components using the product difference algorithm (PDA); comment out the code as appropriate
• (MATLAB) Import each function and class individually (to be completed)
  • Download and call the functions individually (more functionality under development)

Detailed guide

How PSD Analyser works (Python)

The app (PSDA_app) creates a user interface for loading, interacting with and saving PSD data. However, the hard work is done by the PSDAnalyser class within the psd_analyser library, which can be used without the app and contains some functionality not available in the app (see below).

Summary of PSD Analyser functionality

1. Parsing of Mastersizer files in spreadsheet (CSV, Excel) formats
2. Log-normal modelling of PSDs, where fitting can be performed to either the cumulative distribution function (CDF) or probability density function (PDF) of the PSD data
3. Application to PSDs of the product difference algorithm (PDA) to PSDs, which computes the discrete distribution of N elements with the same statistical moments (mean, etc.)
4. (With standalone Python app) Visualisation of results in an interactive viewer, allowing output of figures in various formats (currently Python only)
5. Saving PSD data, with fitted log-normal parameters, into a single spreadsheet for further analysis

Running the PSD Analyser standalone app (Python)

• See the quick start guide above to get started
• Once PSD Analyser is running, load one of the spreadsheets provided as examples; these are all outputs from the Mastersizer laser diffraction-based particle sizing device manufactured by Malvern Panalytical (formerly Malvern Instruments)
• A summary of the user interface is provided below
  • Load file Select a spreadsheet from which to load PSD data; several example files are provided
  • Save data Dump all loaded and modelled data to a single spreadsheet; by default the file format is the same as the original load-file, but the user can specify otherwise; the index of each dataset corresponds to the row in which it appeared in the original data file
  • Export figure Dump current plot to an image file for later use; user can specify image format
  • Forward and back arrows If the file loaded contains multiple PSD datasets, these arrow buttons scroll through them; the dataset number is shown in the information panel (bottom left)
  • Fit to PDF/CDF buttons These buttons toggle between the two methods for fitting of a log-normal distribution to the dataset displayed; see code for more information, and note that each can give different results for the log-normal fit parameters
  • Plot PDF/CDF buttons These buttons toggle between plotting the loaded and log-normal fitted data in CDF and PDF form, depending on the user’s preference
  • Plot log/linear buttons Toggle between logarithmic and linear scale on the x-axis (i.e. particle size)

Using PSD Analyser in code form (Python)

• Create an environment as described in the quick start guide
• Navigate to the folder containing setup.py and install the PSD Analyser package into your environment as described in the quick start guide
• There are then multiple ways to use various functionalities of PSD Analyser, for example:
  • From the command line, run the app as follows: python psdanalyser\PDSA_app.py
  • In your Python kernel, instantiate the app with import psdanalyser.PSDA_app as app, then run it with apptest = app.TkApp()
• Running the code directly provides additional flexibility not available in the app, in particular:
  1. The product difference algorithm (PDA) can be used to model a given PSD as another with an arbitrary number of elements and the same moments, N; this is intended as a tool in computationally expensive applications that rely on size-fraction-dependent calculations
  2. Log-normal fitting can be executed with or without pre-fitting (pre-fitting is used by default in the app) via linear regression using a linearised version of the equation for the log-normal CDF; pre-fitting has a computational cost but makes it more likely that a subsequent non-linear fit will be successful

Creating your own standalone app using the PSD Analyser source code (Python)

The app was created using the Python library pyinstaller, and you can do the same. A rough outline of the necessary code for doing so is below.

1. In the command line in your Python environment, install pyinstaller (see here):

pip install pyinstaller

1. Create an executable using the command below, where: the noconsole option creates an executable without a console window (this option can be removed if you wish; doing so causes the app to create a console window for debugging); and the onefile option creates a single executable file (if this option is removed, the resulting executable may be smaller but a number of directories will be created alongside the executable)

pyinstaller --onefile --noconsole psdanalyser/PSDA_app.py --hidden-import=openpyxl

Important equations used by PSD Analyser

The statistical tools used by PSD Analyser are all described in more detail in the “equations” document

1. The log-normal cumulative distribution function (CDF). See here and here.
2. The log-normal probability density function (PDF). See here and here.
3. The product difference algorithm (PDA). See references below.

Contact and issue reporting

Please either raise an issue here at Github or contact me directly.

Contact: Hugh Rice, h.p.rice@leeds.ac.uk

How to cite this repository

• Copy or click the Zenodo link above, which has a corresponding DOI attached, and construct your own citation that contains it
• Depending on your style, your citation should look something like this: Rice HP (2022), PSD Analyser: A set of Python/MATLAB tools for particle size distribution (PSD) analysis and visualisation, Github code repository, DOI: <latest DOI, see above>
• If you’re unsure, please contact me

References and notes

Note on history, development and previous implementation

• The concepts behind PSD Analyser were developed during research that led to the production of references (1) and (2). Please refer to those for more details and examples.
• The standalone app was constructed using the Python GUI library Tkinter and relies heavily on standard Python numerical and mathematical libraries scipy, numpy and pandas, as well as matplotlib for visualisation.

(1) Rice HP, Fairweather M, Peakall J, Hunter TN, Mahmoud B and Biggs SR (2015), Constraints on the functional form of the critical deposition velocity in solid–liquid pipe flow at low solid volume fractions, Chemical Engineering Science 126 759-770, DOI: https://doi.org/10.1016/j.ces.2014.12.039

(2) Rice HP, Peakall J, Fairweather M and Hunter TN (2020), Extending estimation of the critical deposition velocity in solid–liquid pipe flow to ideal and non-ideal particles at low and intermediate solid volume fractions, Chemical Engineering Science 211 115308 (9 p.), DOI: https://doi.org/10.1016/j.ces.2019.115308

(3) McGraw R (1997), Description of Aerosol Dynamics by the Quadrature Method of Moments, Aerosol Science and Technology 27 (2) 255-265, DOI: https://doi.org/10.1080/02786829708965471

(4) Marchisio DL, Vigil RD and Fox RO (2003), Implementation of the quadrature method of moments in CFD codes for aggregation–breakage problems, Chemical Engineering Science 58 (15) 3337-3351, DOI: https://doi.org/10.1016/S0009-2509(03)00211-2

(5) Gordon RG (1968), Error Bounds in Equilibrium Statistical Mechanics, Journal of Mathematical Physics 9 655-663, DOI: https://doi.org/10.1063/1.1664624

(6) Wheeler and Gordon (1971), Bounds for averages using moment constraints, In: Baker and Gammel (eds.), The Padé Approximant in Theoretical Physics, New York and London: Elsevier Science, ISBN: 9780080955803

(7) Farr SF (2013), Random close packing fractions of lognormal distributions of hard spheres, Powder Technology 245 28-34, DOI: https://doi.org/10.1016/j.powtec.2013.04.009

(8) Mwasame, P (2016), Modeling the viscosity of polydisperse suspensions: Improvements in prediction of limiting behavior, Physics of Fluids 28 061701 (6 p.), DOI: http://dx.doi.org/10.1063/1.4953407

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