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

Shear rate — where it appears

The rate at which adjacent layers of a fluid slide past one another, the gradient of velocity across the flow. A viscosity is the stress divided by it, and for a material whose viscosity depends on it the quantity has to be quoted with the measurement.

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

Seven fluids in one pipe at one pressure gradient. Velocity profiles of power-law fluids in a round pipe, all at the same pressure gradient and the same consistency, scaled to the fastest. A shear-thinning fluid (n below one) is flatter in the middle and steeper at the wall; a shear-thickening one is the reverse. The flattening is often called plug-like, which invites the reading that the fluid is moving more freely — what has actually happened is that all the shear has been pushed into a thin annulus at the wall, which is the expensive place to put it.

A viscosity that depends on the question

Blood, paint, molten polymer and drilling mud have no viscosity. They have a relation between stress and strain rate that is not proportional, so the ratio of the two depends on how hard they are being sheared — and an instrument that reports one number is reporting a property of itself.

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-newtonianApparent viscosityBoundary conditionConstitutive lawDissipationInstrumentModel limitThe no-slip conditionPipe flowPolymerPower law

All concepts