Concept

Deborah number — where it appears

The ratio of a material's own relaxation time to the time the flow gives it. Below one the material has time to relax and behaves as a liquid; above one it has not and behaves as a solid, and nothing about the material itself changed.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The flow stops and the stress does not. Shear stress against time for a fluid sheared at a constant rate for two seconds and then left alone. Nothing is moving after the second mark and the fluid is still stressed: 37 per cent of the peak one relaxation time later, and 0.7 per cent after five.

The fluid that has not finished its last deformation

Shear a polymer solution for two seconds and stop. Nothing is moving and the fluid is still stressed — 37 per cent of the peak one relaxation time later, and still measurably stressed after five. Two histories imposing exactly the same total strain leave it in states differing by a factor of 3.7.

viscous · Non-newtonian

Eight numbers, one construction. The dimensionless groups this collection has produced, placed on a logarithmic axis at a representative value. Each is a memory time divided by a process time, each was named separately in a different field, and each decides the same question: whether the past is still present.

Every memory number is one time over another

These essays produced eight dimensionless groups in eight different fields, named after eight different people, spanning a factor of four hundred in value. Written out, all eight are a memory time divided by a process time, and all eight govern the same curve.

regimes · Dimensional

Named alongside it

The objects these essays reach for when they reach for this one.

Convolution Measurement Memory kernel Model validity Regime Relaxation time Dimensional analysis Frequency response Non-newtonian Polymer Reduced frequency Similarity

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