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Viscosity
The thin layer next to a surface that ideal flow ignores, and which supplies drag, separation and the wake.
The heat of a squeeze leaves across the gap
Squeeze a film of air and it warms, and whether that heat reaches the walls in time decides whether the gas is compressed isothermally or adiabatically. The natural estimate has the heat leaving the way the gas does, along the disc, and puts the thermal crossing beside the viscous one. It leaves across the gap instead, a distance hundreds of times shorter, so the crossing sits decades away — and when a film does reach it, what it gains is not stiffness but a second band of loss.
The largest bulk viscosity is the first to expire
A bulk viscosity is not a separate property of a gas. It is the time a molecule's internal motion takes to catch up with a compression, multiplied by the pressure and by how much heat capacity lags, and read from below that time's frequency. So the coefficient that is largest is the one that stops being a coefficient soonest: carbon dioxide's fifteen-hundred-fold value is ten per cent wrong at 24 kHz, and on Mars it is two speeds of sound in the audible band.
A bulk viscosity holds a shock together until it splits
Carbon dioxide's bulk viscosity, fifteen hundred times its shear viscosity, is a vibrational relaxation seen from below its frequency, and a shock is where that description is tested hardest. Carried through a steady shock, the relaxation reproduces the coefficient exactly for the weakest shocks. At a pressure rise of nine and a half per cent the shock outruns the frozen sound speed and splits into a jump and a tail, and the coefficient then draws a shock that does not exist.
A warm bush stops the bearing hunting
A bearing whose motor is derated on its housing's temperature can hunt, jumping between a cool film and a hot one on the housing's clock. Let the bush warm with the housing, and a second feedback joins the first, of the kind that usually makes things run away. It does the opposite: a warm wall is a stiffer drive, the stiffening closes the S the cycle runs round, and past a bush coupling of about a third the bearing settles, warm and derated, however the protection is set.
The gas sets a squeeze film's loss, not its stiffness
A squeeze-film levitator wastes part of every cycle as heat that crosses the gap, and the gas and its pressure decide how much. Fill one levitator with six gases at one atmosphere and its stiffness hardly changes while its loss nearly doubles from helium to xenon. Raise the pressure and every gas stiffens towards a peak near ten atmospheres. Helium wastes least at any stiffness up to a hundred newtons; above that, only the heavy monatomic gases get there.
A thousandth of a monolayer holds a bubble still
A clean bubble rising slowly through water feels two-thirds of a rigid sphere's drag, and real bubbles almost never do, because surfactant swept to the rear holds the surface still over a cap there. Solving the flow with the cap in it shows how little that takes. The drag runs ahead of the area covered — half-way to rigid with a third of the surface held — and the surfactant needed is set by the viscous stress, not by the surface tension. For a bubble a tenth of a millimetre across, a thousandth of a monolayer, spread as a cap, makes it rise within a few per cent of a solid ball.
A point force makes a jet only when it is strong
Push on a fluid at one point and there is an exact solution of the full Navier–Stokes equations for what follows, at any strength. Weak, it is Stokes's point force: fluid pushed forward over a whole hemisphere and drawn in behind. Strong, it is Schlichting's slender jet, with fluid drawn in from every direction outside a narrowing cone. One constant joins them, and it says how strong a push must be before the boundary-layer jet everyone uses is right — at the axis by a jet Reynolds number of a hundred, at the edges only by a thousand.
The warm side pulls a bubble with no force on it
A bubble in a liquid whose temperature varies from place to place moves towards the warm side, with no gravity and nothing pushing it. The surface tension is lower where the liquid is warmer, the surface is pulled towards the cold pole, and the bubble goes the other way. Young, Goldstein and Block's speed comes out of four interface conditions and one more: that the total force on the bubble is zero. That one condition removes the point force a sinking or rising body always carries, so the bubble's disturbance dies a hundred times faster with distance, and the radius at which it balances its own buoyancy has no viscosity in it.
A cap that slows a rising bubble stops a migrating one
Surfactant swept to the back of a bubble holds the surface still there, and for a bubble rising under its weight the worst this can do is turn it into a solid sphere and cost it a third of its speed. A bubble migrating in a temperature gradient has no such floor. Its own surface is the engine, and a cap removes the engine as well as raising the drag. A cap over the cold hemisphere leaves a rising bubble three-quarters of its speed and a migrating one a fifth; a cap of 120° leaves the migrating bubble four per cent. The surfactant it takes is set by the tension difference that drives the migration, and that is tiny.