A rediscovered formula is changing how we understand the hidden journeys of airborne particles.
Researchers at the University of Warwick have created a straightforward new way to predict how irregularly shaped nanoparticles, a harmful type of airborne pollutant, move through the air.
Each day, people inhale countless microscopic particles such as soot, dust, pollen, microplastics, viruses, and engineered nanoparticles. Many of these particles are so small that they can reach deep into the lungs and even pass into the bloodstream, where they may contribute to serious health problems including heart disease, stroke, and cancer.
While most airborne particles have uneven shapes, existing mathematical models often treat them as perfect spheres because that makes the equations easier to handle. This simplification limits scientists’ ability to accurately describe or track how real, non-spherical particles move, especially those that are more dangerous.
To address this problem, a University of Warwick researcher has introduced the first reliable and easy-to-use approach for calculating the motion of particles of any shape. The study, published in Journal of Fluid Mechanics Rapids, updates and simplifies a century-old equation, closing a long-standing gap in the field of aerosol science.
The paper’s author, Professor Duncan Lockerby, School of Engineering, University of Warwick 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.”
Reclaiming a century-old formula
The breakthrough stems from re-examining one of the cornerstones of aerosol science: the Cunningham correction factor. Developed in 1910, the factor was designed to predict how drag on tiny particles deviates from classical fluid laws. In the 1920s, Nobel Prize winner Robert Millikan refined the formula, but in doing so overlooked a simpler, more general correction. As a result, the modern version remained limited to perfectly spherical particles.
Professor Lockerby’s new work reformulates Cunningham’s original idea into a more general and elegant form. From this foundation, he introduces a “correction tensor” – a mathematical tool that captures the full range of drag and resistance forces acting on particles of any shape, from spheres to thin discs, without the need for empirical fitting parameters.
Professor Duncan Lockerby added: “This paper is about reclaiming the original spirit of Cunningham’s 1910 work. By generalizing his correction factor, we can now make accurate predictions for particles of almost any shape — without the need for intensive simulations or empirical fitting.
“It provides the first framework to accurately predict how non-spherical particles travel through the air, and since these nanoparticles are closely linked to air pollution and cancer risk, this is an important step forward for both environmental health and aerosol science.”
Going Forward
The new model provides a more robust foundation for understanding how airborne particles move – across fields from air quality and climate modeling to nanotechnology and medicine. It could help researchers better predict how pollutants spread through cities, how volcanic ash or wildfire smoke travels, or how engineered nanoparticles behave in manufacturing and drug delivery systems.
To build on this breakthrough, Warwick’s School of Engineering has invested in a new state-of-the-art aerosol generation system. This facility will allow researchers to generate and precisely study a wider range of real-world, non-spherical particulates, further validating and extending the new method.
Professor Julian Gardner, School of Engineering, University of Warwick, who is collaborating with Professor Lockerby, 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.”
Reference: “A correction tensor for approximating drag on slow-moving particles of arbitrary shape and Knudsen number” by Duncan A. Lockerby, 29 October 2025, Journal of Fluid Mechanics.
DOI: 10.1017/jfm.2025.10776
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