A new method developed at the University of Warwick offers the first simple and predictive way to calculate how irregularly shaped nanoparticles - a dangerous class of airborne pollutant - move through air.
Every day, we breathe in millions of microscopic particles, including soot, dust, pollen, microplastics, viruses, and synthetic nanoparticles. Some are small enough to slip deep into the lungs and even enter the bloodstream, contributing to conditions such as heart disease, stroke, and cancer.
Most of these airborne particles are irregularly shaped. Yet the mathematical models used to predict how these particles behave typically assume they are perfect spheres, simply because the equations are easier to solve. This makes it difficult to monitor or predict the movement of real-world, non-spherical - and often more hazardous - particles.
Now, a researcher at the University of Warwick has developed the first simple method to predict the motion of irregular particles of any shape. The study, published in Journal of Fluid Mechanics Rapids, reworks a 100-year-old formula to bridge a key gap in 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 generalising 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 modelling 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."
