Concept

Rectification — where it appears

The steady mean left behind by an oscillation whose own mean is zero, because the response is not symmetric in the forcing. A gas film's pressure rising more on a squeeze than it falls on a release is one, and it is second order in the amplitude, invisible to any linear calculation.

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

Where a film stops being a damper and starts being a spring. The stiffness and the damping of a circular gas film against its squeeze number, both in units of ambient pressure times disc area. At the left the stiffness is nothing and the damping is Stefan's incompressible law; at the right the damping has gone and the stiffness has reached π, which is an isothermal gas trapped in the gap with no way out. They cross at σ = 6.23, and neither limit was put in by hand — both fall out of a Bessel function of a complex argument.

A damper that turns into a spring

A film of oil squeezed between two plates resists motion and stores nothing, and that is a property of the oil rather than of the film. Fill the same gap with air and the same equation gives a film that stores and resists nothing — above a squeeze number of six, with nothing changed but the frequency and the gap.

viscous · Squeeze film

At a levitator's own thermal numbers every gas lifts within a few per cent of the isothermal film; only a thick, slow film lifts more. The mean pressure excess of a trapped film squeezed by a quarter of its gap, over the isothermal film's 0.0328 of ambient, against the thermal number ωh²/κ, for three ratios of specific heats; dots, the six gases of a 20 kHz, 20 µm levitator at one atmosphere: helium 1 at Ω = 0.29; air 1.002 at Ω = 2.4; argon 1.005 at Ω = 2.5; carbon dioxide 1.005 at Ω = 4.7; xenon 1.042 at Ω = 7.9; sulphur hexafluoride 1.003 at Ω = 16. At Ω = 300 a monatomic gas lifts 1.21 times the isothermal film, against the 1.69 a core on the walls' mean temperature would give.

A levitator lifts by its amplitude, not its gas

A squeeze-film levitator holds its load up by the mean of a pressure that swings symmetrically about nothing, and the gas in the gap was expected to decide how much: a gas that cannot shed its heat of compression in time is stiffer, so it should lift more. Solved to every order in the amplitude, with the heat crossing the gap, it barely does. At a levitator's own thermal numbers every common gas lifts within a few per cent of the isothermal film while its losses differ several-fold, and even a gas far too slow to shed its heat lifts only a fifth more, because the walls quietly pump heat out of it and cool its middle.

viscous · Squeeze film

Named alongside it

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

Compressibility Levitation Squeeze film Damping Dimensionless Dissipation Heat transfer Lubrication film Nonlinearity Reynolds equation Stiffness Thin film

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