The low-Reynolds-number gravitational settling of a sphere through a fluid interface

What is Reynolds number?

The Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations.

Magmas typically consist of a mixture of molten liquid, bubbles, and solid crystals. As they mix, those crystals can sink from one viscous layer into another. To investigate this sort of process, researchers studied solid particles sinking across an interface between two viscous liquids. This is what we see above. One fluid is clear; the other is dyed red, and gravity points toward the left so the particles fall from right to left.

What happens when the particle reaches the interface between fluids depends on three main factors: the gravitational force acting on the particle, the surface tension at the interface, and the ratio of the viscosities of the two fluids. The researchers observed two main outcomes.

In one (top), the particle slows at the interface and breaks through slowly, its surface wetted by the second fluid so that it drags little to none of the previous fluid with it. The researchers named this the film drainage mode. It tends to occur when the viscosity ratio between fluids is large.

The second method, shown in the bottom image, is the tailing mode. As the particle approaches, the interface deforms. A thick layer of the first fluid coats the particle even as it pass through, forming a tail that destabilizes behind the falling particle. This mode occurs when the viscosity ratio is small or the gravitational force is large compared to the surface tension.

Image and research credit: P. Jarvis et al.

Source: https://myfusimotors.com/2019/03/12/the-low-reynolds-number-gravitational-settling-of-a-sphere-through-a-fluid-interface/