MATLAB Particle Size Functions

Copyright 2024 - Austin M. Weber

Description

This repository contains 5 files (4 functions written for MATLAB and 1 binary file) for evaluating log-normal particle concentrations, converting particle diameters sizes in metric units to phi "φ" units (and vice versa), and classifying particles sizes according to the Wentworth Scale (Wentworth, 1922).

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normconc.m

Log-normalized particle concentration.

Description - Calculates dN/dlogDp or dV/dlogDp, which are the normalized concentrations or normalized volumes of particles based on the diameter size channels of the particles. The function performs the following calculation:

dN/dlogDp = dN / (log10(Dupper) - log10(Dlower))

where dN is a vector of particles size concentrations, Dupper is the upper limit of the particle size channel, and Dlower is the lower limit of the particle size channel. For instance, the concentration of particles in the 1.0 - 2.0 micron size range is 500, then the normconc() can be used to convert the particle concentration into a log-normalized concentration:

concentration = 500; 
lower_diameter = 1.0; % in microns
upper_diameter = 2.0; % in microns
lognormconc = normconc(concentration,...
    upper_diameter,lower_diameter)

lognormconc =
    1660.96

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diameter2phi.m

Convert metric units into the phi (φ) scale.

Description - The phi scale is defined as:

phi = -log2(diameter)

where diameter is the diameter of a particle in metric units (i.e, millimeters, microns, etc.). The diameter2phi() function applies this equation to a vector of particle sizes. For example, to convert a particle diameter of 0.80 microns into phi units:

diameter = 0.80; % microns
phi = diameter2phi(diameter,'um')

phi = 
    10.29

Note that you need to specify the metric unit of the particle diameter. For microns, 'um', 'microns', and 'micrometers' are valid funcion inputs. The function is comptable with many other common metric size units as well, including 'm', 'cm', 'mm', and 'nm'. If the metric unit is not specified, the function assumes units of millimeters by default.

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phi2diameter.m

Convert phi (φ) scale units into metric units.

Description - The phi2diameter() function performs the inverse operation of the diameter2phi() function. For example, if you have a vector of particle sizes with phi scale values, you can convert them into metric values:

phis = [5 8 10 14];
diameters_nm = phi2diameter(phis,'nanometers')

diameters_nm = 
    [31250.00 3906.25 976.56 61.04]

If the metric unit is not specified, the function will convert from φ units to millimeters by default.

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grainsizeterm.m

Wentworth Scale grain size classification

Description The grainsizeterm() function classifies a vector of particle diameters (in phi units) to their corresponding morphological categories based on the Wentworth Scale. For example:

phis = [1 3 10];
terms = grainsizeterm(phis)

terms = 
    1x3 categorical array
        Coarse sand    Fine sand    Clay

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diameters.mat

MATLAB binary file containing two variables: diameters_microns and diameters_phi. You can load the variables into MATLAB with the load() function:

load diameters.mat

The diameters_microns variable is a vector of particle diameter sizes in units of micrometers. The diameters_phi variable contains the same particle diameter sizes as diameters_microns but expressed in terms of the phi scale.

References

Wentworth, C.K., 1922. A scale of grade and class terms for clastic sediments. The Journal of Geology 30, 377-392.