Archimedes' law of buoyancy turned upside down

During the 69th Annual Meeting of the American Physical Society's Division of Fluid Dynamics (DFD), being held Nov. 20-22, in Portland, Oregon, Randy Ewoldt, an assistant professor who runs the Ewoldt Research Group in the Department of Mechanical Science and Engineering, and Jeremy Koch, a doctoral candidate, will present their work studying bubbles within complex fluids.

"Certain complex fluids are 'solid-like' when you don't push on them very hard," Koch explained. "One consequence of this is that they can trap air bubbles and hold them in place indefinitely."

This phenomenon begs the question: How do you get the air bubbles to move? "We can stir the fluid and move the bubbles around manually, or we can also put the fluid's container on a centrifuge and force the bubbles out," Koch said. "How does the centrifuge make this happen, and why do the bubbles move in the direction that they do? By understanding those questions, we'll be able to describe how to move the bubbles in other directions."

In terms of the basic concepts behind the group's work, one is acceleration, which requires force. "Shaking, aka 'accelerating,' a container of liquid creates a pressure force through the liquid," Ewoldt said. "The air bubbles inside are along for the ride and feel the same force as the liquid, but at a lower density so the force they feel is 'larger' than needed to match the liquid acceleration. When this force counteracts buoyancy, it can potentially move air bubbles downward within the surrounding fluid."

To put their theories to the test, the group introduced bubbles and solid spheres with diameters on the order of a few millimeters into fluids of various thicknesses. They used a rigid container to control the movement of the immersed particles.

Their results revealed the necessary conditions and fluid properties to prevent or produce the sinking motion of the bubbles and heavy particles both with and against gravitational forces.

"Complex fluids are actually quite common in everyday life, from whipped cream to custard to pumpkin pie and fresh concrete," Ewoldt said. "All of these materials can be sculpted into a shape (in a liquid state) and hold their shape even under gravity (as a solid)."

In other words, their work shows that rigid-body accelerations affect buoyancy and weight in the same way gravity does. "But you can't simply accelerate a container indefinitely in one direction, so we focused on periodic motion: the container returns to its initial position and speed after a certain time interval," Koch said.

They demonstrated a scenario in which bubbles sink while dense steel spheres rise, which is counterintuitive to common expectations of how buoyancy works. Intuition says bubbles will rise and steel objects will sink within the liquids, although they found the exact opposite was true. "Archimedes' famous law of buoyance doesn't consider accelerations or 'complex' fluids," Ewoldt said.

This made the group wonder: Has it really taken humans this long to reveal this basic behavior? And, if so, what else are we missing?

There are countless applications for suspensions within real-world fluids and, thanks to this work, more information is now available to help make better decisions. When the motion involved is periodic, does it mean the effect is cancelled out? "If viscosity is constant, the answer is yes," Ewoldt said. "But if viscosity isn't constant if it changes the more you flow the fluid the answer is no."