Israeli Researchers Develop AI-Assisted Equation for Particle Behavior in Fluids
Israeli scientists from the University of Haifa and Tel Aviv University have developed a novel mathematical equation that explains why particles sinking in a liquid can suddenly slow down or even move upward when transitioning between layers of different densities. The findings were published in the journal Machine Learning: Science and Technology.
The new equation, formulated with the assistance of an artificial intelligence system, accurately describes the particles' deceleration in the transition zone and, in some cases, their reversal of direction. Dr. Teddy Lazebnik from the University of Haifa stated that the AI did not replace the researchers but aided them in searching for a formula within the framework of experimental data and physics laws, resulting in an understandable and testable equation.
Understanding particle movement in stratified fluids is crucial for various natural and engineering processes, including sediment settling in lakes, pollutant dispersal, wastewater treatment, and material separation. While particle sinking in a uniform liquid is governed by gravity, buoyancy, and fluid resistance, the phenomenon becomes more complex in layered liquids due to additional forces acting on the particle at the interface.
Previous models struggled to encompass all stages of this movement in a single formula. The research team, including Dr. Lazebnik, Professor Alex Liberzon, and research student Chen Mortenfeld from Tel Aviv University, aimed to find an explicit mathematical expression for the force generated during the transition between liquid layers.
Through 321 experiments involving small metal spheres sinking through layered water and salt or glycerol solutions, researchers used high-speed cameras and laser illumination to track particle trajectories with high precision. The data was fed into SciMED, an AI system developed by Dr. Lazebnik, which searches for explicit mathematical formulas matching experimental data and physical laws. The researchers selected a formula that was both accurate and physically plausible.
In 84.7% of the experiments, the spheres decelerated after crossing the interface before resuming their sinking speed. The equation reveals that the force develops gradually and can oscillate, potentially explaining the change in direction. Compared to existing models, the new equation showed significant improvement in predicting prolonged deceleration, directional changes, and the duration of particles' stay in the transition zone.
Professor Liberzon noted that the explicit nature of the equation allows for understanding the force's temporal variation and the mechanism at play. If validated under broader conditions, the equation could enhance predictions of sediment and pollutant movement, aiding processes like wastewater treatment and material separation. However, the researchers caution that the equation has only been tested within a specific range of particle sizes and flow conditions.
