Researchers improve century-old equation to predict movement of hazardous air pollutants

A new method developed at the University of Warwick offers the first simple and predictable way to calculate how nanoparticles – a dangerous class of airborne pollutants – are carried through the air.

Every day, we breathe in millions of microscopic particles, including soot, dust, pollen, microplastics, viruses and synthetic nanoparticles. Some are so small that they can slip deep into the lungs and even enter the bloodstream, helping with conditions like heart disease, stroke and cancer.

Most of these airborne particles are irregular in shape. Yet the mathematical models used to predict how these particles behave usually assume they are perfect spheres, simply because the equations are easier to solve. This makes it difficult to monitor or predict real-world movements.

Now, a University of Warwick researcher has developed the first simple method to predict the motion of irregular particles of any shape. The study, published in Journal of Fluid Mechanicsreworks a 100-year-old formula to address a key gap in aerosol science.

“The motivation was simple: if we could accurately predict the movement of particles of any shape, we could significantly improve models of air pollution, disease transmission, and even atmospheric chemistry,” said the paper’s author, Professor Duncan Lockerbie, School of Engineering, University of Warwick. This new approach builds on a very old model.

Reclaiming a century-old formula

This development results from a reexamination of a cornerstone of aerosol science: the Cunningham correction factor. Developed in 1910, this factor was designed to predict how small particles are drawn by classical fluid laws.

In the 1920s, Nobel laureate Robert Milliken improved this formula, but in doing so neglected an easy and common correction. Consequently, the modern version was limited to perfectly spherical particles.

Professor Lockerbie’s new work refines 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, without the need for any empirical fitting parameters.

Professor Duncan Lockerbie 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 any shape.

“This provides the first framework for accurately predicting how non-persistent particles travel through the air, and because these nanoparticles are closely linked to air pollution and cancer risk, it is an important step for both environmental health and aerosol science.”

The new model provides another solid foundation for understanding how airborne particles move—from air quality and climate modeling to nanotechnology and medicine. This could help researchers better understand how pollution spreads in cities, how volcanic ash or forest fire smoke travels, or how they behave in engineered nanoparticle manufacturing and drug delivery systems.

To drive this progress, Warwick’s School of Engineering has invested in a state-of-the-art aerosol generation system. The facility will allow researchers to produce and precisely study a wide range of real-world, non-spherical particles, allowing the new method to be further validated and extended.

“This new facility will allow us to explore how real-world airborne particles behave under controlled conditions, helping to translate this theoretical progress into practical environmental tools,” said Professor Julian Gardner, School of Engineering, University of Warwick, who is collaborating with Professor Lockerbie.