Particle size distribution¶
A distribution specifying relative particle amount by size for a powder, granular solid, or dispersion.
Core Idea¶
A particle-size distribution (PSD) describes how the particles in a powder, granular material, aerosol, suspension, or other particulate sample are apportioned across size. It may be given as fractions in discrete size intervals or as a cumulative or continuous function. Each value states a relative amount—commonly by mass, number, volume, or another declared weighting basis—rather than merely listing the smallest and largest particles. The distribution is inseparable from its operational definition of size.
Scope of Application¶
A particle-size distribution applies wherever a defined particulate population is sampled, assigned an operational size, weighted by a declared amount basis, and normalized across ordered size classes or a continuous size function. - Powders and granular industrial products. — toner, ceramics, metals, pigments, cosmetics, pharmaceuticals, and other formulated powders are specified and controlled by the relative amount in required size classes. - Soils, rocks, and sediments. — grain-size distributions support geotechnical, geological, and sedimentological descriptions of packing, load-bearing behavior, transport, and material history under stated disaggregation procedures. - Aerosols and emission particles. — atmospheric and industrial particulate samples are apportioned by aerodynamic, optical, or other operational diameter for monitoring and control. - Suspensions, colloids, and fluid dispersions. — particles dispersed in liquids or gases are sized by counting, settling, scattering, acoustic, or imaging methods while dissolution and agglomeration are controlled.
Clarity¶
A particle-size distribution is interpretable only when the sampled material, preparation and dispersion state, sizing method, operational diameter, weighting basis, size units, and reporting form are stated. “Twenty percent below 10 μm” changes meaning if the percentage is by number rather than mass or volume, or if 10 μm denotes sieve aperture, settling-equivalent diameter, image geometry, or scattering-model diameter.
Manages Complexity¶
A bulk powder, aerosol, suspension, or soil sample may contain enormous numbers of irregular particles across many size decades. A particle-size distribution makes that population tractable by assigning an operational diameter, choosing a mass, number, volume, or other weighting basis, and accounting for the sample in ordered bins or a normalized function. The retained record includes sampling and dispersion state, method, size units, weighting, bin edges, and normalization.
Abstract Reasoning¶
The distribution licenses quantitative moves from thresholds to material fractions. A cumulative curve gives the declared fraction finer or coarser than any selected operational size; differences between successive cumulative values give the fraction in a size interval. Conversely, summing normalized interval fractions reconstructs the cumulative form. Percentile sizes and comparisons between samples are therefore legitimate only after the weighting basis, size definition, units, preparation, and accounted total have been aligned. Diagnostic and intervention reasoning focuses on how the observed population was produced.
Knowledge Transfer¶
Within granulometry and materials analysis, a PSD transfers literally across powders, soils, aerosols, suspensions, and granular products by preserving a representative sample, operational diameter, weighting basis, ordered size classes or function, and normalization. Sieving, settling, imaging, and scattering carry different equivalent-size models, so method, dispersion state, bin convention, and mass-, number-, or volume-weighting must accompany the curve. Re-dispersing agglomerates, checking sample splits, reconciling cumulative and interval forms, or comparing methods diagnoses whether a shift reflects the material population or the measurement procedure. What carries is the distributional accounting; physical particles, equivalent diameter, sample dispersion, sieves, settling, and scattering models remain home-bound.
Relationships to Other Abstractions¶
Current abstraction Particle size distribution Domain-specific
Parents (1) — more general patterns this builds on
-
Particle size distribution is a kind of Measurement Prime
A particle-size distribution is a strict granulometric measurement whose target attribute is the apportionment of a particulate population by operational size.
Hierarchy path (1) — routes to 1 parentless root
- Particle size distribution → Measurement
Neighborhood in Abstraction Space¶
Particle size distribution sits in a sparse region of the domain-specific corpus (87th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Measurement Standards & Material Properties (10 abstractions)
Nearest neighbors
- Measurement Method — 0.82
- Radial Immunodiffusion — 0.81
- Flocculation — 0.81
- Characteristic Property — 0.81
- Growth curve (biology) — 0.80
Computed from structural-signature embeddings · 2026-10-08