Illustrated Physics
physics, drawn
Concept

Arrhenius — where it appears

The rule that a thermally activated rate grows as the exponential of minus an activation energy divided by kT. Plotted as the logarithm of rate against inverse temperature it is a straight line whose slope gives the barrier, and it governs reactions, diffusion and the flow of viscous solids.

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

One word, two mechanisms, opposite signs. Viscosity on a logarithmic axis against temperature over the range 280 to 360 kelvin, where gases and liquids can both be measured. The gases rise and the liquids fall, and the two families are separated by three decades of magnitude as well as by sign. The logarithmic slopes at the middle of the range are 0.76 for air, 0.69 for helium, -6.13 for water, -5.41 for ethanol, -23.00 for glycerol, so the steepest liquid responds 30 times more strongly than the gas and in the other direction. Nothing about the word viscosity requires this: what is being measured in both cases is the ratio of a shear stress to a shear rate, and that definition says nothing about what carries the momentum. In a gas it is molecules in free flight, so heating speeds up the carriers; in a liquid the molecules are permanently in contact and what has to happen is one of them getting past its neighbours, so heating removes an obstacle rather than adding a carrier. The obvious question this raises is what a dense gas near its critical point does, where neither picture holds, and the honest answer is that neither formula on this chart applies there at all.

The thickness that goes both ways

Heat a liquid and it thins; heat a gas and it thickens. The two are not a strong effect and a weak one but opposite signs, differing by a factor of thirty in size as well — and the word viscosity names one measurement made on two mechanisms that have almost nothing in common.

fluids · Viscosity Nine drops in eighty-four years. The time between successive drops of the pitch in Thomas Parnell's funnel, cut open in 1930, against the year each drop fell: 8.2, 7.2, 8.1, 8.3, 8.7, 9.3, 12.4, 13.4 years. The first seven intervals average 8.3 years and scatter by about a year either way; after the building was air-conditioned in the late 1980s the next two took 12.4 and 13.4, averaging 12.9. Read as a viscometer through the funnel's geometry, the early rate gives a viscosity of about 2.3 × 10⁸ Pa·s — some two hundred billion times water's.

The drop that takes a decade

In 1927 a physics professor in Brisbane poured heated pitch into a sealed funnel, waited three years for it to settle, and cut the stem. Nine drops have fallen since. The record is a viscometer read about once a decade, and it gives the pitch a viscosity two hundred billion times water's. It also records the building's air-conditioning: after 1988 the drops slowed from eight years apart to thirteen, and a fall of a degree and a half in the average temperature is enough to explain it. The same reasoning, applied to medieval window panes, settles an old story without guessing what glass does at room temperature.

fluids · Viscosity

Named alongside it

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

Activation energyGlass transitionViscosityDeborah numberHard-sphereIntermolecular forcesKinetic theoryMean free pathMomentum diffusionRelaxation timeStokes flowTransport coefficient

All concepts