Concept

Squeeze film — where it appears

The thin layer of fluid between two surfaces closing on or opening from each other, which resists the motion because the fluid must flow out of or into the gap. Its force goes as μVc³/h³ when viscosity governs and as ρV²c³/24h² when inertia does, and the gap Reynolds number decides which.

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

$A film with nothing useful to show for itself. The pressure under two discs squeezed together, as a fraction of the pressure at the centre. It is a parabola, and it holds an enormous load — but nothing is sliding, so there is no output at all and every joule put in becomes heat in the oil. The two routes to that heat share no arithmetic: one integrates the dissipation function over the film, the other multiplies the force by the approach speed.$

The last of the oil

A wet plate on a table is held down by nothing but the difficulty of getting air in underneath it. The force required to separate two flat surfaces with a film between them goes as the inverse cube of the gap, which means there is no finite energy that removes the last of the film and no finite time in which it drains away.

viscous · Squeeze film

The cushion changes its physics 0.36 mm from the ground. The two forces on a plate 10 cm across closing on a plane at 1 m/s in air at 20 °C, per metre of span, against the gap on logarithmic axes. The viscous squeeze film, Reynolds' lubrication result μVc³/h³, rises as the cube of the closeness; the inertial one, ρV²c³/24h² from the potential flow's added mass, as the square. They are equal where the gap Reynolds number ρVh/μ is exactly 24, at 0.361 mm, where each is 3.84e+2 N/m. Above that gap the cushion is the fluid's inertia and below it the fluid's viscosity — and at the crossover neither formula is accurate, since it is where one limit hands over to the other rather than a solution of the flow between them.

A cushion that changes its physics

A plate closing on a plane is resisted by the fluid it has to squeeze out, and the resistance is two different forces with two different laws — one from the fluid's inertia and one from its viscosity. They hand over at a gap of twenty-four kinematic viscosities per unit of closing speed, which for a wing in air is a third of a millimetre, and the two films disagree about whether the plate ever lands at all.

misconceptions · Ground cushion

Named alongside it

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

Viscosity Added mass Adhesion Damping Dissipation Ground effect Image system Load capacity Lubrication Lubrication film Misconception Model limit

All concepts