Why Sinking Particles Briefly Rise: A New Equation from the Lab

A new study led by Dr. Teddy Lazebnik (University of Haifa), Prof. Alex Liberzon, and PhD student Chen Mortenfeld from the Turbulence Structure Laboratory at Tel Aviv University's School of Mechanical Engineering has been published in Machine Learning: Science and Technology — and covered this week by Ynet.

The research shows that particles settling through a fluid can suddenly slow down — and even move upward for a moment — when crossing between layers of different density. This happens in lakes, river outflows, wastewater treatment, and pollutant dispersion, wherever settling particles pass through a density transition.

321 experiments, one equation

The team analyzed 321 experiments in which single spheres about 10 mm in diameter settled through a tank with a light upper layer, a dense lower layer, and a transition zone between them, using salt-water and glycerol-water solutions. High-speed cameras shooting up to 500 frames per second, combined with laser illumination, tracked each sphere's trajectory to within thousandths of a millimeter.

The trajectory data was fed into SciMED, an AI system developed by Dr. Lazebnik that searches for explicit mathematical formulas consistent with both the experimental data and physical law. From the candidate equations, the researchers selected the one that best fit the data while staying simple and physically sound, then compared it to the existing "virtual mass" model.

In 272 of the 321 trajectories — 84.7% — the sphere slowed down while crossing the transition zone before returning to its settling speed. The new equation shows that the extra force isn't instantaneous: it builds up gradually and can oscillate, which helps explain why the particle's direction of motion sometimes reverses briefly.

"The advantage of an explicit equation is that we don't just get a prediction — we can see how the force changes over time and understand the mechanism at work in the transition zone," said Prof. Liberzon. "If validated under further conditions, it could improve predictions of how sediments and pollutants move and accumulate, and support processes like wastewater treatment and separation."

The researchers note that the equation has been tested over a defined range of sphere sizes and flow conditions, so it isn't yet a general law for every system — but it improves particularly on predicting long delays and direction reversals in the transition zone.

Read the full paper in Machine Learning: Science and Technology, or the Hebrew coverage on Ynet.