What governs the speed at which raindrops fall, sediment settles in river estuaries, and matter is ejected during a supernova?
These questions circle around one, deceitfully simple factor: the rate at which a fluid filled with particles mixes with a particle-free one. Raindrops travel from one layer of air to another; sediment falls from river to seawater, and ejecta travels from the exploding star through the surrounding dust cloud. The same principle dictates sediment mixing in rising smoke, dust storms, nuclear explosions, hydrocarbon refining, metal smelting, wastewater treatment, and more.
New simulations have now provided researchers and engineers with unprecedented access to these fundamental fluid mechanics. While plainly visible in everyday life, the phenomenon has eluded scientific scrutiny due to their complexity. For the first time, researchers have derived a general formulation of how layers of heavy particles mix and described the common characteristics of the phenomena. The team, comprising researchers from the Okinawa Institute of Science and Technology (OIST) and the University of Turin, has now published their findings in Physical Review Letters. Simone Tandurella, study first author and PhD student in the Complex Fluids and Flows Unit at OIST, explains: "Both the simulations and the model we obtain enable exciting research into a wide range of fundamental physics phenomena, as well as applied research in fluid engineering. They provide the basic puzzle pieces that can help us understand fluid-particle instabilities at large scales."
Committing complexity to paper
While the general laws of physics that govern the behavior of most fluids are relatively straightforward, solving the equations to predict the behavior is extremely complicated. Intuitively, falling sediment should be easy to study, but scientifically describing the mechanics of how individual grains of sand fall to the bottom of a river, or even the overall rate of mixing between sediment-filled and clear water, is made difficult by the immense complexity of the forces involved and the unpredictability of long-term interactions. These factors include the weight and volume displacement of each particle, how each particle drags liquid along through friction, the influence of gravity or any other acceleration field, and how the presence of any one particle affects all the others around it. As Tandurella puts it, "if the three-body problem is famously complex, imagine the 100,000-body problem."
To capture this complexity, which cannot be accurately replicated and studied experimentally, and which was - until now - thought impossible to render computationally, the team simulated the movement of 100,000 3D particles suspended in a fluid composed of hundreds of millions of points. "For each solid particle - with its own set volume and weight - we calculate the forces it exerts through its surface on the surrounding points in the fluid, and how the surrounding points exert force on the particle. We then sum the forces for each particle, simultaneously solve the fundamental Navier-Stokes equations of fluid motion throughout the grid, and move one step. This is done over millions of steps," says Tandurella.
"It took the combination of highly specialized research software capable of handling the fluid-modelling equations at scale, which our unit has developed over many years, and the unique architecture of the OIST supercomputing cluster to allow this to happen. Without either, it wouldn't be possible."
One phenomenon the team observed through the simulations is the formation of sediment plumes. They found that as the suspended heavy particles sink under gravity, they drag the surrounding fluid down with them due to friction. The downward-moving fluid then pulls along surrounding particles, which in turn move more fluid, leading to the formation of a sediment plume. The plume displaces an equivalent volume of clear fluid, which rises at an equivalent rate and further pushes sediment-filled fluid down. And because the terminal velocity of a particle is relative to the fluid that surrounds it, the particles in the center of the plume accelerate to ever faster speeds, driving a feedback mechanism that also increases the overall rate of mixing. Professor Marco Rosti, head of the Complex Fluids and Flows Unit, adds: "These phenomena couldn't have been observed with previous simulations that neglected the full particle-fluid interactions. This is the first time that we've been able to replicate and study these behaviors accurately."
Armed with these simulations and the theoretical framework to accurately describe the velocity of sediment mixing, researchers now have better access to a wide range of fundamental phenomena in physics and other fields as well as to applied research in fluid systems, ranging from optimizing flow in wastewater treatment or in chemical refining processes, to waterways engineering or environmental protection against soil run-off, and beyond.
