Professor Duncan Lockerby’s study introduces a simplified method for predicting how irregular-shaped nanoparticles behave as they drift through gases. Published in the Journal of Fluid Mechanics Rapids, this breakthrough bridges a scientific gap that has puzzled aerosol researchers for over a hundred years.
A Neglected Equation Gets a Second Life
Each day, billions of airborne particles, such as dust, soot, pollen, microplastics, viruses, and synthetic nanoparticles, are inhaled by people worldwide. Many of these particles are too small to be caught by the body’s natural defenses. Once inside the respiratory system, they can penetrate deep into the lungs, enter the bloodstream, and potentially contribute to conditions like heart disease, stroke, or cancer. Yet, despite the health stakes, scientific models still tend to treat these particles as perfect spheres.
This simplification may make equations easier to compute, but it fails to reflect how particles actually behave in the real world. The vast majority are asymmetrical, with jagged surfaces or stretched shapes that don’t follow uniform motion. According to research conducted at Warwick’s School of Engineering, that assumption limits the predictive power of current models, especially when it comes to health-critical particles.
Recognizing this flaw, Professor Lockerby set out to update one of the oldest tools in aerosol science: the Cunningham correction factor. Initially formulated in 1910 to describe how small spherical particles deviate from classical fluid laws, the model was later modified by Nobel laureate Robert Millikan. But Millikan’s version, while popular, narrowed the model’s scope, restricting it to spheres and introducing unnecessary empirical parameters.
Redefining Drag With a New Correction Tensor
Lockerby’s paper reinterprets Cunningham’s early work through a modern lens. Instead of focusing solely on spheres, the new model uses what the author calls a “correction tensor” to account for the full range of resistance forces acting on particles, regardless of shape. This tensor bypasses the need for empirical fitting and applies cleanly to discs, rods, and even highly complex geometries.
“It provides the first framework to accurately predict how non-spherical particles travel through the air,” Lockerby said in the study. “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.”
The updated formula replaces the empirical constants of previous models with directly calculable values derived from known physics. Its effectiveness has been verified against experimental data and kinetic theory, notably outperforming traditional methods in predicting how thin discs and elongated spheroids behave under various flow conditions. According to the Journal of Fluid Mechanics, these calculations held up across a wide range of particle sizes and gas conditions, especially within the difficult transition zone between continuum and free-molecular flow.
Rigorous Tests Show Strong Agreement With Simulations
To validate the new tensor-based model, the study compared its predictions against detailed simulations and historical experiments. For spherical particles, the model’s drag predictions differed by less than 4 percent from experimental data gathered by Allen and Raabe in 1985, showing a high level of accuracy despite the absence of fitted parameters.
For non-spherical particles, such as spheroids and thin discs, the model’s predictions were tested against data from recent Direct Simulation Monte Carlo (DSMC) studies. These simulations, conducted by researchers including Clercx, Livi, and Toschi, represent the most reliable benchmarks currently available. According to those comparisons, Lockerby’s method showed excellent agreement for both prolate (stretched) and oblate (flattened) shapes, across a range of orientations and Knudsen numbers.
The model also demonstrated robustness when applied to complex cases. One test involved an infinitely thin disc moving perpendicular to its surface, a challenging case for most theories. The new correction tensor accurately mirrored results from the Bhatnagar-Gross-Krook (BGK) kinetic theory model, with deviations again under 4 percent.
Building Tools for Real-World Impact
To expand on the findings, the University of Warwick has invested in a state-of-the-art aerosol generation system. According to Professor Julian Gardner, a collaborator on the project, this facility will allow researchers to generate real-world, non-spherical particulates under tightly controlled conditions. The goal is to further validate the model and bring it closer to practical application.
“This new facility will allow us to explore how real-world airborne particles behave under controlled conditions,” Gardner said, “helping translate this theoretical breakthrough into practical environmental tools.”
While the tensor-based method doesn’t replace large-scale simulations, it offers a far simpler and more general framework. The results suggest it could help researchers understand how pollutants spread in urban environments, how wildfire smoke moves through the atmosphere, and how drug-carrying nanoparticles navigate the human body, all without the need for supercomputers or experimental approximations.