# Fun with low Reynolds number Flows

EDIT: Seems to be some trouble with embedding YouTube videos. Sorry for the inconvenience.

Last week the Tectonics class I’m TAing had an extra “throwaway” lecture. We decided to let the students build their own experiments to gain some intuition about Low Reynolds number flows, and what the Reynolds number means.

First we showed them a video produced by the National Committee for Fluid Mechanics Films which was an awesome NSF funded project to develop and film these complex and/or expensive experiments (which can be found on YouTube).

One of my favorite aspects of flow is the phenomenon of low Reynolds number flows. Low Reynolds number flows are flows where inertia plays only a small roll.

The Reynolds number is a dimensionless number that can be characterized as:

Re = (Density * Length * Velocity) / Viscosity

or…

Re = Inertia / Viscosity.

Generally if the Reynolds number is below 2000 the flow is laminar, greater than 2000 the flow is turbulent.

To tie it to geology we helped the students work through an order of magnitude calculation of mantle viscosity. Try it for yourself: Density = 3300 kg/m^3, Length = 3 X 10^6 m, Velocity = 1 cm/yr, Viscosity = 10^21 Pas. What do you get? Is the mantle a turbulent or laminar flow?

After the video we gave the students a set of ingredients and beakers to play with: canola oil, molasses, water, food coloring, and glycerin. Fun fact about glycerin, the pharmacy only sells small bottles and employees will give you VERY strange looks when you ask for a liter of the stuff.

Here are the experiments the students came up with. You’ll here conversation about flows, mantle winds, and non-school stuff in the background.

First up we have molasses poured into glycerin:

and a small amount of molasses…

My favorite: a two layer system. Bottom layer is glycerin and top layer is oil.

And a turbulent flow for good measure…

Some things to take away from the student’s experiments: our containers were too small in height for the low Reynolds number plumes to fully develop before hitting the bottom. This would also require much more glycerin, and more weird looks.

And for fun here’s a video I found of a low Reynolds number (~1000) vortex ring collision. Science is so sexy.

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## About Tim Sherry

Tim is a graduate student at McGill University studying Earth Science and Structural Geology. He blogs at Up-Section.
Categories: Uncategorized

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