Concept

Weber number — where it appears

The ratio of a flow's dynamic pressure to the pressure surface tension can supply across a curved interface. It decides whether a drop or a jet keeps its shape, and for a falling drop it is formed on the drop's own terminal speed.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

The Ohnesorge diagram, with the boundaries where they belong. The classical map of jet break-up: the Ohnesorge number against the jet Reynolds number, with the five nozzles placed on it. The three sloping lines are Reitz's transitions in the gas Weber number, and their geometry is computed rather than sketched — a fixed We_g means Oh·Re is fixed, which is a straight line of slope exactly −1 in these coordinates, and a decade in Reynolds number is checked to move each line by exactly one decade. Where they sit is borrowed; that they are straight and parallel is not. A nozzle below and to the right of the last line atomises.

Where a jet stops being a jet

A tap makes drops a few centimetres down, a garden hose makes a stream that carries, a sprayer makes a mist and a diesel injector makes fog. Same liquid, same mechanism, four regimes — and the number that separates them is not the jet's inertia but the surrounding air's.

regimes · Atomisation

A falling drop is a bun, not a tear. The shape of a drop pressed on by the air it is falling through, computed by matching the Legendre component of a sphere's own potential-flow pressure distribution against the change in curvature it produces. The result is oblate — flattened along the direction of travel — because the pressure is high at the poles and low round the equator. The teardrop of every illustration has the wrong symmetry entirely: a drop in free fall has no up, and one at terminal speed is being pressed on from in front.

The drop that is not a tear

A falling raindrop is flattened along the direction it is going, by the pressure of the air passing it rather than by its own weight, and the group that decides is the Weber number. The teardrop of every illustration has the wrong symmetry entirely — there is no up in the problem it is drawn for.

regimes · Drop shape

A water sheet two millimetres thick leaves the lip above 0.270 m/s. The effective tension of a sheet of water, 2σ − ρU²h per metre of its width, against the speed it is poured at, for sheets one, two and four millimetres thick. At rest every sheet carries the tension of its two surfaces, 145.4 mN/m, and the momentum it carries along itself subtracts from that. A 1 mm sheet reaches zero at 0.382 m/s, a 2 mm sheet reaches zero at 0.270 m/s and a 4 mm sheet reaches zero at 0.191 m/s. Below its own crossing a sheet bent round a lip is pulled onto it; above, it is flung off. The quantity that decides is a tension, not a pressure, and the speed at which it vanishes is the speed of waves along the sheet.

The teapot effect is a tension, not a pressure

A slow pour runs back under a spout and down its outside, and the name it is usually given is the Coandă effect. The Coandă effect borrows the ambient pressure, and a liquid in air has none to borrow. A liquid sheet is held to a lip by its own surface tension, and it lets go at the one speed that tension cannot carry — the speed of waves along the sheet — whatever the lip's radius.

misconceptions · Coanda

The air pulls on the crests, and short ripples start to grow. The growth rate of a ripple on an inviscid jet against its wavenumber times the radius, at gas Weber numbers of 0, 0.4, 2, 6 and 13 on the diameter. The air flowing over a rippled jet is faster over the crests and its pressure lower there, which pulls them further out. Without it nothing shorter than the circumference grows; at a gas Weber number of 2 ripples up to ka = 1.45 grow, at 13 up to 6.19, and the fastest moves with them.

The air shortens a jet's fastest ripple, and the drops follow

A jet in a vacuum breaks into drops nearly twice its own width, whatever its speed. A jet in air does not, and the reason is a pressure the air puts on its surface: flowing over a rippled jet it is faster over the crests and its pressure lower there, which pulls them further out. That pull lets ripples shorter than the jet's circumference grow, shortens the fastest one, shrinks the drops, and puts a ceiling on how long a fast jet can be — at the gas Weber number where the measured break-up regimes change.

regimes · Atomisation

Named alongside it

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

Surface tension Model limit Atomisation Dimensionless Drop Instability Potential flow Regime Young laplace Coanda Correlation Free surface

All concepts