麻豆传媒

Rings of confidence

Question: How do smoke rings form and why are they so stable?

Answer: Smoke rings are an example of objects known in fluid dynamics as vortex rings. They form when smoke is discharged through a rigid circular hole or an approximation of one鈥攆or example the mouth formed into an 鈥淥鈥� shape.

Smoke rings are formed mainly because of the phenomenon of boundary layer separation. Imagine a smoke-filled cavity with a circular hole at the end. At the other end of the cavity is a piston that can be pushed to discharge a small amount of smoke through the hole.

It is at the hole where the boundary layer鈥攖he thin layer of smoke next to the wall of the hole鈥攕eparates. Separation occurs because the pressure gradient is in the direction of the flow at the edges of the hole, and smoke tends to stick to the outside of the container, even beyond the aperture.

When the boundary layer separates, and the smoke continues in the direction of the initial velocity, a rotational force called the vorticity is set up at the edge of the tube of smoke, which is known as the vortex sheet. This vorticity results in the rolling up of the vortex sheet into a ring, which is rotating around a central vortex core and travelling forward at some velocity. All this happens quickly, to give the familiar rolling smoke ring. The stability of the ring is due to the fact that the vorticity is independent of the velocity of the ring.

Smoke rings have been studied in depth for some time. For example, Lord Kelvin, after discussion with German scientist Hermann von Helmholtz, came to some amazing conclusions about them. Both analysed the stability of vortex rings, experimentally and analytically. Helmholtz published his vortex theorems in 1858 and Kelvin his circulation theorem in 1867.

The stability of vortex rings was a subject of great interest to Kelvin, who expanded on Helmholtz鈥檚 results. In an 1867 letter to Helmholtz, Kelvin described his experiments with smoke rings, and went on to outline a remarkable theory based on the stability of vortex rings in ideal fluids鈥攖hat is, fluids that are incompressible and have no internal friction or viscosity.

鈥淚f there is a perfect fluid all through space, constituting the substance of all matter, a vortex ring would be as permanent as the solid hard atoms鈥� Thus, if two vortex rings were created in a perfect fluid, passing through each other like links of a chain, they could never come into collision, or break one another, they would form an indestructible atom鈥� a long chain of vortex rings, or three rings, would give each very characteristic reactions upon other such kinetic atoms.鈥�

Kelvin鈥檚 鈥渧ortex atom鈥� theory of matter鈥攖hat all matter could consist of tiny linked and knotted vortices鈥攚as the driving force behind his hydrodynamic research, as he says in his 1867 paper. If we remember that the concept of an ideal fluid permeating all space was a valid one at that point, and consider Kelvin鈥檚 theory was 40 years ahead of Bohr, it is a remarkable theory.

Unfortunately for Kelvin鈥攚ho believed smoke rings collapse through viscous effects or turbulence, and ideal vortex-rings could exist forever鈥攈is theory was disproved. In 1977, Sheila Widnall and Charles Tsai did a more careful analysis of vortex- ring stability that showed they are inherently unstable. The instability of vortex rings occurs in the form of bending waves around the perimeter, which grow in amplitude as time proceeds, leading to the ultimate collapse of even an ideal vortex ring.

William von Witt

New Town, Tasmania

Cold war

Question: In a film I saw, a bomb squad froze an explosive, saying it could delay the explosion by about 2 seconds. At very low temperatures, would ordinary explosives detonate? Chemical reactions must progress slowly at about 鈭�200 掳C.

Answer: This scene is the usual Hollywood hokum, but it is based on an element of truth.

The idea of freezing explosives was developed in the Second World War by British Ministry of Supply scientists and Royal Engineers staff to combat the threat of German bombs containing the Y fuse. This fuse contained a drycell battery and three sensitive mercury switches. It acted as a booby trap to kill bomb disposal operatives.

The British had theorised that using liquid oxygen to render the dry batteries inert would defeat the Y fuse. The technique was attempted on 24 January 1943 by Major J. D. Hudson of the Royal Engineers on an unexploded 500-kilogram bomb that had caused the closure of the Albert Bridge over the Thames in London. After two hours of pouring liquid oxygen into a clay cup around the fuse pocket, Major Hudson disarmed the fuse.

For a full description of the Y fuse story, see Designed To Kill: the history of British bomb disposal by Major Arthur Hogben.

Hugh Bellars

Chippenham, Wiltshire

Answer: A bomb would still explode at low temperatures. The temperature of the explosive has little to do with rate of reaction.

Chemistry has the concept of 鈥渉eat of reaction鈥濃�攖he heat given off when a chemical reacts or 鈥渂urns鈥�. There is also 鈥渉eat of activation鈥濃�� the heat needed to set off a chemical. If heat of reaction is greater than heat of activation, you have an explosive mixture鈥攖his is how a bomb detonator operates. Just getting a small portion of the chemical to burn is enough because this portion generates enough heat to set off a bigger portion, which sets off an even bigger portion and so on until it blows up.

Lakshmi Chakrapani

Atlanta, Georgia

Answer: All explosives need some initial energy input to start the reaction, usually from localised heating by mechanical shock or electrical spark. Cold explosive will need greater initial input to raise the temperature above the critical point but after this, there would be no significant effect.

Once the reaction begins, it releases heat and quickly makes the immediate area very hot. This heat cannot be transferred to the cold mass of the explosive because there isn鈥檛 time, so the explosion progresses through the the explosive. If the explosive is a detonating one, the reaction travels through the explosive material faster than the speed of sound, creating a shock wave. For example, the detonation velocity of nitroglycerine is more than 7500 metres per second.

Ernest Ager

Exmouth, Devon

This week鈥檚 questions

Kiss and tell: Kissing is a very enjoyable aspect of human sexual activity. Is it universal among human cultures? Does it occur in other species?

Pete Fowler

Southland, New Zealand

Ear marked: What are the origins of the question-mark? It鈥檚 shaped like an ear. Is there a connection?

Duncan Sylvester

San Rafael, California

The wonder years: Why don鈥檛 we remember much about our early childhood? In particular, the period from 0 to 5 years seems to be totally forgotten.

Ummar Abbas

Bangalore, India