Fractal Fluids

I am fascinated by how form develops in nature, and particularly how complex forms can develop from simple underlying rules. Even more interesting is how universal forms can develop from seemingly disparate physical phenomena — so that tree branches and river basins share many characteristics. One of these characteristics is “self similarity”: the branching pattern of a tributary looks remarkably like the branching pattern of the river itself, only reduced in size.

 

My most recent  work explores one phenomenon through which form is created in the natural world: a physical phenomenon known as “Viscous Fingering”. It occurs when one fluid displaces another, more viscous, fluid – such as air displacing oil. Instability in the boundary causes the intruding fluid to break into fingers, and for the fingers to break into smaller finger, and those into even smaller fingers and on and on. It is interesting to observe how some of the shapes so formed mimic other shapes in nature, from lightning strikes to snowflakes to mountain ranges. Here is a gallery.


Behind the scenes

Viscous fingering is demonstrated in a device called a Hele-Shaw cell, named after engineer who first built one. It consists of two flat plates separated by a small gap. The gap is occupied by one fluid. A second fluid is introduced under pressure either at one end or through a small hole in the center of one of the plates.

Sketch of the Hele-Shaw cell I constructed
Sketch of the Hele-Shaw cell I constructed
Completed Hele-Shaw cell
Completed Hele-Shaw cell. The two plates are separated by small pieces of shim stock.

Clamps are used to hold the plates together. The entire assembly is placed on a light table on a copy stand.

Assembled Hele-Shaw cell on a light table on a copy stand.
Assembled Hele-Shaw cell on a light table on a copy stand.

The first fluid may be poured on to the bottom plate and then the top plate carefully put in place, or the cell can be assembled and the first fluid introduced through a hole in the center of (in this case) the bottom plate. The second fluid is then introduced through the center hole while the camera is taking photographs in continuous drive mode. I used a length of Tygon tubing with a hypodermic needle (sharp end cut off) at one end and a 60ml syringe on the other. Below is a “time-lapse” image of one fluid entering the other.

Superposition of images taken at consecutive intervals as a low viscosity fluid is forced into a higher viscosity fluid. The gray features are air bubbles.
Superposition of images taken at consecutive intervals as a low viscosity fluid is forced into a higher viscosity fluid. The gray features are air bubbles.

The fluids used to create these images were glycerin, olive oil, hand lotion, water, air and food coloring.

 

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