Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Polymer — where it appears

A liquid of long chain molecules, entangled with one another above a certain chain length. Its bulk viscosity rises as the cube of that length while the friction of its own monomers against a wall does not, which is why it slips.

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 Three dies, one melt, three flow curves. The apparent flow curve a capillary rheometer reports, for three dies whose radii differ by a factor of four. A material property cannot depend on the instrument, so the fact that these three do not lie on one another is a measurement of something other than a viscosity. The single curve drawn beneath them is what the same melt gives with the wall condition set to no slip.

The wall a melt really does slip on

For a simple liquid the slip length is under two nanometres, which is why no-slip is safe everywhere. For an entangled polymer melt it is a millimetre, which is larger than the die it is being pushed through — so the melt moves as a plug and the viscosity a rheometer reports is a property of the instrument.

misconceptions · The no-slip condition

Named alongside it

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

MeasurementNon-newtonianViscoelasticityBoundary conditionConvolutionDeborah numberInstrumentMemory kernelModel limitModel validityThe no-slip conditionRegime

All concepts