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Physicists at the University of Bayreuth have investigated the so‑called history force acting on particles in fluids. Owing to the difficulty of calculating it, this force is often neglected — a fact that Bayreuth doctoral researcher Frederik Gareis already identified as a secondary school pupil during a student research project with his supervisor. The researchers report their new findings on the history force in the renowned journal Physical Review Fluids.
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Why it matters
When particles such as air bubbles, bacteria or microplastics move in a fluid, a viscous drag force acts on them. In situations where both the particles and the fluid are constantly in motion — for instance in a shaken liquid — this viscous drag is greater than for particles moving at a constant velocity relative to the fluid. The reason is the so‑called Basset–Boussinesq history force, which depends not only on the current motion of the particle but also on its past motion and on the vortices forming around it. Calculating this “memory term” is computationally demanding and is therefore often neglected in simulations of particle motion in fluids. However, this can lead to systematic errors: in simulations, particles respond too quickly and experience less resistance than in reality. A proper understanding of the history force enables more accurate predictions of the dispersion, deposition and residence time of aerosols, biological particles or microplastics.
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When particles move in liquids or air with velocities that change over time, several forces act on them, including the often overlooked history force. It arises from the formation of vortices around accelerating particles in fluids. In this way, the surrounding fluid “remembers” previous particle motions and influences their subsequent movement.
“The history force is often ignored because it is mathematically complex and makes calculations significantly more demanding. It is frequently unclear whether neglecting it leads to larger errors in modelling particle motion in fluids,” says Frederik Gareis, a doctoral researcher at the Theoretical Physics I research group at the University of Bayreuth and first author of the study. In their new work, Gareis and his supervisor, Prof. Dr. Walter Zimmermann, building on Gareis’s earlier student research, propose investigating the motion of particles such as microplastics, other solid particles, droplets or bacteria in a controlled experiment with horizontally shaken fluids. “In this setup, the particles are continuously accelerated or decelerated. For this experiment, we provide precise and experimentally testable predictions of the effect of the history force on particle motion,” says Zimmermann. One key result is that theories neglecting the history force can overestimate the motion of small particles relative to the fluid by as much as 60%.
The researchers also predict how the influence of the history force can be identified from the shape of certain measurement curves. This enables models and simulations to be tested systematically and improves the reliability of predictions for practical applications. In addition, Gareis and Zimmermann explain in detail how vortices form around accelerating particles and how this gives rise to the history force.
“Our results now make it possible to estimate when the history force should not be neglected in calculations of particle motion in flows in nature and technology,” says Gareis.
The origins of this research are remarkable. Frederik Gareis was still at school when, as part of a student project for an international competition, he investigated the motion of air bubbles in shaken water at the TAO student research centre at the University of Bayreuth. When he attempted to compare his experimental results with theories from the literature, he and his supervisor Professor Zimmermann discovered that existing theories on gas bubbles in shaken fluids ignored the history force. This observation marked the starting point for the research project, which Frederik pursued alongside his physics studies at the University of Bayreuth and has now published.
Prof. Dr. Walter Zimmermann
WE Heraeus Senior Professorship
Coordinator of the TAO Student Research Centre
Theoretical Physics
Phone: +49 921 55 3181 and 3315
Email: walter.zimmermann@uni-bayreuth.de
Impact of the history force on the motion of droplets in shaken liquids, Frederik R. Gareis and Walter Zimmermann, Physical Review Fluids (2026)
DOI: https://doi.org/10.1103/y1zd-lpyw
Criteria of this press release:
Journalists, Scientists and scholars
Physics / astronomy
transregional, national
Research results, Scientific Publications
English
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