Researcher improves century-old equation to predict movement of dangerous air pollutants

A new method developed at the University of Warwick offers the first simple, predictive way to calculate how irregularly shaped nanoparticles – a dangerous class of air pollutants – move through the air.

Every day we breathe millions of microscopic particles, including soot, dust, pollen, microplastics, viruses and synthetic nanoparticles. Some are small enough to penetrate deep into the lungs and even enter the bloodstream, contributing to diseases such as heart disease, stroke and cancer.

Most of these airborne particles are irregular in shape. Yet the mathematical models used to predict the behavior of these particles generally assume that they are perfect spheres, simply because the equations are easier to solve. This makes it difficult to monitor or predict the movement of real, non-spherical and often more dangerous particles.

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

Paper author Professor Duncan Lockerby, from the University of Warwick’s School of Engineering, said: “The motivation was simple: if we can accurately predict how particles of any shape move, we can significantly improve models of air pollution, disease transmission and even atmospheric chemistry. This new approach builds on a very old, simple but powerful model, making it applicable to complex and irregularly shaped particles.

Reappropriating a century-old formula

This breakthrough comes from reexamining one of the cornerstones of aerosol science: the Cunningham correction factor. Developed in 1910, this 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 in a more general and elegant form. From this basis, 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 disks, without the need for empirical fitting parameters.

Professor Duncan Lockerby added: “This paper aims to recover 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 adjustments.

“It provides the first framework to accurately predict how non-spherical particles move through the air, and since these nanoparticles are closely linked to air pollution and cancer risk, this is an important step forward for environmental health and aerosol science.”

The new model provides a stronger foundation for understanding how airborne particles move in areas ranging from air quality and climate modeling to nanotechnology and medicine. This could help researchers better predict how pollutants spread in cities, how volcanic ash or smoke from wildfires move, or how engineered nanoparticles behave in drug manufacturing and delivery systems.

To capitalize on this major breakthrough, the Warwick School of Engineering has invested in a new state-of-the-art aerosol generation system. This facility will allow researchers to accurately generate and study a wider range of real-world non-spherical particles, thereby validating and extending the new method.

Professor Julian Gardner, from the University of Warwick’s School of Engineering, who is collaborating with Professor Lockerby, said: “This new facility will allow us to explore the real-world behavior of airborne particles under controlled conditions, helping to translate this theoretical advance into practical environmental tools. »