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The thread: Everything happens in a thin layer — page 15

Page 15 of 15, continuing through the 128 essays this motif runs through.

128 essays carry this thread — page 15 of 15.

A drop on a plate too hot to touch lives a hundred times longer than one on a merely hot plate. The lifetime of a drop of 2.5 mm radius against the plate's temperature, in contact (nucleate boiling) and on its film. At 130 °C, in contact, 11 s; on its film at 210 °C 1062 s, and at 500 °C 229 s. Where the two branches meet depends on the plate: Leidenfrost's point on polished metal is about 200 °C for water, and on a rough plate can be well above it.

A Leidenfrost drop floats on a bearing it feeds itself

A bead of water on a hot pan vanishes in seconds, unless the pan is much hotter, when it skates about for minutes. Between the drop and the plate is a film of its own steam a tenth of a millimetre thick, and that film is a lubricated bearing with no shaft and no pump: its supply is the drop's own evaporation, which keeps it thin where it is thick and thick where it is thin. Its thickness obeys a fourth root of everything. On a plate too hot to touch, the drop's lifetime is a hundred times what it is on a plate that is merely hot.

The friction a coil adds is one curve in one number, and it is near a square root at large Dean number. Friction over a straight pipe's, at the same flow, against De = Re √(a/R): 1.01, 1.13, 1.4, 1.79, 2.36 at De = 11.6, 30, 70, 150, 300, beside White's fit to measurements and a large-Dean boundary-layer law. Below about 11.6 the ratio is one within a per cent.

Fluids at work

A coil's friction is one number, and the coil holds its flow laminar

Bend a pipe into a loose coil and the flow inside is not the same flow bent. The fast core is thrown outward, slow fluid returns round the walls, and a pair of counter-rotating cells appears, about a tenth of the mean speed in an ordinary coil. Dean showed in 1927 that one number governs all of it: Reynolds times the square root of the tightness. Below about 12 nothing changes. Above it the friction rises by a curve the coil's geometry never enters again. And the same secondary flow does something unexpected to transition. A coil stays laminar at four or five times the Reynolds number that breaks a straight pipe.

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