Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Thermocapillary migration — where it appears

The motion of a bubble or drop towards the warmer side of a liquid, driven by surface tension that falls with temperature. No force acts on it; in slow flow its speed is Young, Goldstein and Block's, in proportion to its radius and to the gradient.

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

Below 9.8 µm in silicone oil, a gradient of a degree per millimetre outruns gravity. The speed of a clean air bubble in 10 cSt silicone oil against its radius, on logarithmic axes: migrating in a gradient of 1 K/mm, which grows in proportion to the radius, and rising under its weight, which grows with its square. They cross at 9.81 µm and 31 µm/s. The crossing radius, 3|dσ/dT|G/(2ρg), has no viscosity in it: both speeds are set against the same viscous drag.

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.

viscous · Mobile interface The same cap costs a rising bubble a quarter of its speed and a migrating one four-fifths. Speed as a fraction of the clean bubble's against the half-angle of a stagnant cap over the rear: for a bubble migrating in a temperature gradient, and for the same bubble rising under its weight. A 90° cap leaves the rising bubble 74 per cent of its speed and the migrating one 21 per cent; a 120° cap, 68 and 4. The rising bubble can only fall to a rigid sphere's two-thirds; the migrating one falls to nothing.

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.

viscous · Mobile interface

Named alongside it

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

BubbleHadamard rybczynskiMarangoniModel limitStokes flowBoundary conditionBuoyancyConductionDrag coefficientDropFar fieldReciprocity

All concepts