Concept

Viscosity ratio — where it appears

The viscosity of a drop's or bubble's interior divided by that of the liquid outside, usually written λ. It sets how freely the interface moves: near zero for a gas bubble, which slides freely, and large for a drop that behaves as a solid.

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

$Two-thirds to one, and nothing outside it. The drag on a spherical drop as a fraction of Stokes' drag on a rigid sphere of the same size, against the ratio of the viscosities. It runs from exactly two-thirds for a clean gas bubble to exactly one for a rigid particle and takes no value outside that range, however light or heavy the drop is — the formula has no density in it anywhere. A drop of water in air and a drop of mercury in water sit at opposite ends of it.$

The surface that moves with the flow

A clean gas bubble feels two-thirds of the drag a rigid sphere of the same size would, and the formula has no density in it anywhere. What buys the third is that the bubble's surface is free to move — and real bubbles in ordinary water do not get it, for a reason that is a millionth of a per cent of the water by mass.

viscous · Mobile interface

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

Named alongside it

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

Bubble Drop Boundary condition Buoyancy Conduction Creeping flow Dissipation Drag Far field Hadamard rybczynski Marangoni Mobile interface

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