A new mathematical method developed at the University of Warwick offers the first simple and predictive way to calculate how irregularly shaped nanoparticles move through the air.
While most airborne particles are irregularly shaped, scientists have long relied on mathematical models that assume they are perfect spheres – a simplification that makes equations easier to solve but less representative of real-world conditions. This gap has made it difficult to accurately monitor or predict the behaviour of non-spherical and often more hazardous, particles.
Now, Professor Duncan Lockerby from Warwick’s School of Engineering has developed the first general and practical method to predict how particles of any shape move through air. The research, published in Journal of Fluid Mechanics Rapids, updates and generalises a 100-year-old equation, bridging a key gap in aerosol science.
Professor Lockerby said: ‘The motivation was simple. If we can accurately predict how particles of any shape move, we can significantly improve models for air pollution, disease transmission, and even atmospheric chemistry.
‘This new approach builds on a very old model – one that is simple but powerful – making it applicable to complex and irregular-shaped particles.’
The breakthrough stems from revisiting one of the foundational principles of aerosol science: the Cunningham correction factor, first developed in 1910 to describe how drag on microscopic particles deviates from classical fluid laws. Nobel laureate Robert Millikan refined the formula in the 1920s, but in simplifying it, he inadvertently restricted its use to spherical particles.
Professor Lockerby’s work restores Cunningham’s broader vision. His new model introduces a “correction tensor,” a mathematical framework that captures the complex drag and resistance forces acting on particles of any shape – from compact spheres to thin discs – without relying on empirical fitting.
He explains: ‘This paper is about reclaiming the original spirit of Cunningham’s 1910 work. By generalising his correction factor, we can now make accurate predictions for particles of almost any shape – without the need for intensive simulations or experimental tuning.’
The new model could reshape understanding of how pollutants spread through cities, how wildfire smoke and volcanic ash travel, and even how engineered nanoparticles behave in industrial and medical contexts.
To extend this work, Warwick’s School of Engineering has invested in a new state-of-the-art aerosol generation facility, designed to produce and study a wider range of real-world, non-spherical particulates.
Professor Julian Gardner, also from the School of Engineering, who is collaborating on the project, said: ‘This new facility will allow us to explore how real-world airborne particles behave under controlled conditions, helping translate this theoretical breakthrough into practical environmental tools.’
The full research can be read here.
Image: Lockerby DA. A correction tensor for approximating drag on slow-moving particles of arbitrary shape and Knudsen number. Journal of Fluid Mechanics. 2025;1022:R1. Doi:10.1017/jfm.2025.10776
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