Thursday, 17 February 2011

Sticky Fingers

An example of a 'viscous fingering' fractal
An example of "viscous fingering" between two glass plates
This is a “finger fractal” that I noticed on the pavement a few days ago, embedded in somebody's basement skylight window. The effect is sometimes known as “viscous fingering”, and it happens when you glue two plates of glass or perspex together, and then slowly prise the plates apart at one edge before the glue is properly set.

Air penetrates between the plates, but the thick surface of the glue clings to the glass and doesn't want to retract. Eventually a weak point in the wall “fails”, and the glue behind the tip of the inclusion finds it easier to retract than the glue at the sides, and a finger of air extends into the glue.

These sorts of inclusions tend not to meet up and join – in fact they seem to avoid each other and maintain a critical distance – so presumably a region of glue that has a lot of “edge” (anchored to the glass by curved meniscus surfaces on multiple sides) is more strongly connected to the glass, and more difficult to get rid of. Once an air finger penetrates within a certain radius of another inclusion or edge, it seems to be easier for further penetration to happen somewhere else, so when a finger starts getting too near to another edge, or the plate separattion within the wedge reaches a critical point, the penetrating finger's progress "stalls", and a new finger breaks through the perimeter somewhere else. What we end up with is a branching system of inclusions, and a branching network of remaining glue, interleaved. 

We don't usually think of glue as being a "clever" material, and yet here it is, unwittingly helping to create complex, self-regulating branching designs that look more like the results of some sort of encroaching lifeform's growth pattern.

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