Researcher Improves Century-Old Equation To Predict Movement of Dangerous Air Pollutants

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."

Reference: Lockerby DA. A correction tensor for approximating drag on slow-moving particles of arbitrary shape and Knudsen number. J Fluid Mech. 2025;1022:R1. doi: 10.1017/jfm.2025.10776

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