On this National Donut Day in the U.S., here is the first chapter of my prize-winning “How To Dunk a Doughnut”: an illustration of how scientists think about the problems of everyday life.
One of the main problems that scientists have in sharing their picture of the world with a wider audience is the knowledge gap. One doesn’t need to be a writer to read and understand a novel, or to know how to paint before being able to appreciate a picture, because both the painting and the novel reflect our common experience. Some knowledge of what science is about, though, is a prerequisite for both understanding and appreciation, because science is largely based on concepts whose detail is unfamiliar to most people.
That detail starts with the behaviour of atoms and molecules. The notion that such things exist is pretty familiar these days, although that did not stop one of my companions at a dinner party from gushing “Oh, you’re a scientist! I don’t know much about science, but I do know that atoms are made out of molecules!” That remark made me realise just how difficult it can be for people who do not spend their professional lives dealing with matter at the atomic or molecular level to visualise how individual atoms and molecules appear and behave in their miniaturised world.
Some of the first evidence about that behaviour came from scientists who were trying to understand the forces that suck liquids into porous materials. I was thus delighted when I was asked to help publicise the science of biscuit dunking, where tea or coffee are sucked into the pores in biscuits, because it gave me an opportunity to explain some of the behaviour of atoms and molecules in the context of a familiar environment, as well as an opportunity to show how scientists operate when they are confronted with a new problem.
I was less delighted when I was awarded the spoof “IgNobel Prize” for my efforts. Half of these are awarded each year for “science that cannot, or should not, be reproduced.” The other half are awarded for projects that “spark public interest in science.” Unfortunately, and to the confusion of many journalists, the organisers at Harvard University deign to say which is which.
Still, it was a pleasure to receive the award and to share the stage in Harvard’s Sanderson theatre with a number of genuine Nobel Prize winners whose sense of humour was greater than their sense of dignity. It was a greater pleasure, though, to receive letters from schoolchildren who had been enthused by the publicity that was accorded to both the prize and the project. One American student had even taken my work further in his school science project, and reported with pride that he had received an ‘A’ for his efforts.
This chapter tells the story of the biscuit dunking project and of the underlying science, which is used to tackle problems ranging from the extraction of oil from underground reservoirs to the way that water reaches the leaves in trees. As a bonus, it even shows that scientists can sometimes have fun.
If recent market research is to be believed, four out of every five biscuit dunks have a successful outcome. The fifth time, the dunker ends up fishing around in the bottom of the cup for the soggy remains.
The problem for serious biscuit dunkers is that hot tea or coffee dissolves the sugar, melts the fat and swells and softens the starch grains in the biscuit. The wetted biscuit eventually collapses under its own weight.
Doughnut dunkers have a much easier life. Doughnuts, like bread, are held together by an elastic net of the protein gluten. Gluten might stretch, and eventually break, but it doesn’t swell or dissolve in hot coffee. The trick is not to over-saturate the doughnut, otherwise the liquid runs down your chin when you lift the doughnut from the cup. Timing is the key to a successful doughnut dunk.
Can science do anything to bring the dedicated biscuit dunker into parity with the dunker of doughnuts? Could science, which has added that extra edge to the achievements of athlete and astronaut alike, be used to enhance ultimate biscuit dunking performance and save that fifth, vital dunk? These questions were put to me by an advertising company wanting to promote “National Biscuit Dunking Week”. The advertisers clearly thought that there would be keen public interest. They little realized how keen. The “biscuit dunking” story that eventually broke in the British media rapidly became world-wide. The depth of public interest in understandable science was revealed when I talked about the physics of biscuit dunking on a ring-in science show in Sydney, Australia. The switchboard of the rock radio station Triple-J received seven thousand calls in a quarter of an hour.
Not all of the calls were about dunking. Many inquirers wanted to know about the science underlying other familiar activities, such as cooking, sun-bathing and using mobile telephones. The supposedly abstruse and difficult scientific principles involved in the answers seemed to pose little difficulty for the questioners, since the principles were being related to something with which they were already familiar.
“The science of the familiar” always attracts public interest. It did so in 1861, when Michael Faraday, the discoverer of electricity, delivered popular lectures on “The Chemical History of a Candle” to packed audiences of London society. It does so today. My colleague Peter Barham invariably has a full house for his talk on “The Physics of Ice-cream”, with experiments during the lecture and a tasting to follow.
As someone who uses the science underlying commonplace objects and activities to make science more publicly accessible, I was happy to give “The Physics of Biscuit Dunking” a try. There was, it seemed, a fair chance of producing a light-hearted piece of research that would show how science actually works, as well as producing some media publicity on behalf of both science and the advertisers.
The advertisers had their own preconceptions about how science works. They wanted nothing less than a “discovery” which would attract newspaper headlines.
Advertisers and journalists aren’t the only people who see science in terms of “discoveries”. Even some scientists do. Shortly after the Royal Society was founded in 1660, Robert Hooke was appointed as a “curator of experiments” and charged with the job of making “three or four considerable experiments” (i.e. discoveries) each week and demonstrating them to the Fellows of the Society.
Given this pressure, it is no wonder that Hooke is reported to have been of irritable disposition, with hair hanging in dishevelled locks over his haggard countenance. He did in fact make many discoveries, originating much but perfecting little. I had to tell the advertisers that Hooke may have been able to do it, but I couldn’t. Science doesn’t usually work that way.
Scientists don’t set out to make discoveries; they set out to uncover stories. The stories are about how things work. Sometimes the story might result in a totally new piece of knowledge, or a new way of viewing the nature of things. But not often.
I thought that, with the help of my friends and colleagues in physics and food science, there would be a good chance of uncovering a story about biscuit dunking, but that it was hardly likely to result in a “discovery”. To their credit, the advertisers accepted my reasoning, and we set to work.
The first question that we asked was “What does a biscuit look like from a physicist’s point of view?” It’s a typical scientist’s question, to be read as “How can we simplify this problem so that we can answer it?” The approach can sometimes be taken to extremes, as with the famous physicist who was asked to calculate the maximum possible speed of a race-horse. His response, according to legend, was that he could do so, but only if he was permitted to assume that the horse was spherical.
Most scientists don’t go to quite such lengths to reduce complicated problems to solvable form, but we all do it in some way – the world is just too complicated to understand all at once. Critics call us reductionists but, no matter what they call us, the method works. Crick and Watson, discoverers of the structure of DNA, didn’t find the structure by looking at the complicated living cells whose destiny DNA drives. Instead, they took away all of the proteins and other molecules that go to make up life, and looked at the DNA alone. Biologists in the following fifty years have gradually put the proteins back to find how real cells use the DNA structure, but they wouldn’t have known what that structure was if it hadn’t been for the original reductionist approach.
We decided to be reductionist about biscuits, attempting to understand their response to dunking in simple physical terms and leaving the complications until later.
When we examined a biscuit under a microscope, it appeared to a scientist’s eye to consist of a tortuous set of interconnected holes, cavities and channels. The channels are there because a biscuit consists of dried-up starch granules imperfectly glued together with sugar and fat. To a scientist, the biscuit dunking problem is to work out how hot tea or coffee gets into these channels and what happens when it does.
With this picture of dunking in mind, I sat down with some of my colleagues in the Bristol University physics department and proceeded to examine the question experimentally. Solemnly, we dipped our biscuits into our drinks, timing how long they took to collapse. This was Baconian science, named after Sir Francis Bacon, the Elizabethan courtier who declared that science was simply a matter of collecting a sufficient number of facts to make a pattern.
Baconian science lost us a lot of biscuits, but did not provide a scientific approach to biscuit dunking. Serendipity, the art of making fortunate discoveries, came to the rescue when I decided to try holding a biscuit horizontally, with just one side in contact with the surface of the tea. I was amazed to find that this biscuit beat the previous record for longevity by almost a factor of four.
Scientists, like sports followers, are much more interested in the exceptional than they are in the average. The times of greatest excitement in science are when someone produces an observation that cannot be explained by the established rules. This is when “normal science” undergoes what Thomas Kuhn called a “paradigm shift”, and all previous ideas must be recast in the light of the new knowledge. Einstein’s demonstration that mass m is actually a form of energy E, the two being linked by the speed of light c in the formula E = mc2, is a classic example of a paradigm shift.
Paradigm shifts often arise from unexpected observations, but these observations need to be verified. The more unexpected the observation, the harsher the testing. In the words of the famous British immunologist and essayist Sir Peter Medawar: “Extraordinary claims require extraordinary proof”. No-one is going to discard the whole of modern physics just because someone has claimed that “Yogic flying” is possible, or because a magician has bent spoons on television. If levitation did prove to be a fact, though, or spoons could really be bent without a force being applied, then physics would have to take it on the chin and reconsider.
One long-lived horizontal biscuit dunk was hardly likely to require a paradigm shift for its explanation. For that rare event to happen, the new observation must be inexplicable by currently known rules. Even more importantly, the effect observed has to be a real one, and not the result of some one-off circumstance.
One thing that convinces scientists that an effect is real is reproducibility – finding the same result when a test is repeated. The long-lived biscuit could have been exceptional because it had been harder baked than others we had tried, or for any one of a number of reasons other than the method of dunking. We tried repeating the experiment with other biscuits and other biscuit types. The result was always the same – biscuits that were dunked by the “horizontal” technique lasted much longer than those that were dunked conventionally. It seemed that the method really was the key.
What was the explanation? One possibility was diffusion, a process where each individual molecule in the penetrating liquid meanders from place to place in stepwise fashion, exploring the channels and cavities in the biscuit but with no outside clue as to which direction to take the next step.
The result of such motion is that it takes four times as long to get twice as far from the starting point. The mathematics is that of a drunken man walking home from the pub, but not knowing in which direction home lies. Each step is a random lurch, and the odds are that, with time, he will be found ever further away from the pub, though not necessarily in the direction of home. Due to his unfortunate habit of taking backward and sideways steps, to get twice as far from the pub will take him four times as long on average. If he takes an hour to get a mile away from the pub, it is likely to take him four hours to get two miles away.
If the same mathematics applied to the flow path of a liquid in the random channels of a porous material such as a biscuit, then it would take four times as long for a biscuit dunked by our fortuitous method to get fully wet as it would for a biscuit dunked “normally”. The reason is that, in a normal dunk, the liquid only has to get as far as the mid-plane of the biscuit for the biscuit to be fully wetted, since the liquid is coming from both sides. If the biscuit is laid flat at the top of the cup, the liquid has to travel twice as far (i.e. from one side of the biscuit to the other) before the biscuit is fully wetted, which would take four times as long according to the mathematics of diffusion.The American scientist E.W.Washburn found a similar factor of four when he studied the dunking of blotting paper, a mat of cellulose fibres that is also full of random channels. Washburn’s experiments, performed some eighty years ago, were simplicity itself. He marked off a piece of blotting paper with lines at equal intervals, then dipped it vertically into ink (easier to see than water) with the lines above and parallel to the liquid surface, and with one line exactly at the surface. He then timed how long it took the ink to reach successive lines. He found that it took four times as long to reach the second line as it did to reach the first, and nine times as long to reach the third line.
I attempted to repeat Washburn’s experiments with a range of different biscuits provided by my commercial sponsor. I dunked the biscuits, marked off with a pencil in five millimeter steps, vertically into hot tea, and timed the rise of the liquid with a stopwatch. The biscuits turned out to be very similar to blotting paper when it came to taking up liquid. Just how similar became obvious when I drew out the results as a graph. If the distance penetrated follows the law of diffusion, then a graph of the square of the distance travelled versus time should be a straight line. And so it proved, for up to thirty seconds, after which the sodden part of the biscuit dropped off into the teaThe results looked very convincing. Agreement with quantitative prediction is one of the things that impresses scientists most. Einstein’s General Theory of Relativity, for example, predicted that the sun’s gravitation would bend light rays from a distant star by 1.75 seconds of arc (about five ten-thousandths of a degree) as they passed close by. Astronomers have now found that Einstein’s prediction was correct to within 1%. If astrology could provide such accurate forecasts, even physicists might believe it.
That’s not the end of the story. In fact, it is hardly the beginning. Even though the experimental results followed the pattern of behaviour predicted by a diffusion model, closer reasoning suggested that diffusion was an unlikely explanation. Diffusion applies to situations where an object (whether it is a drunken man or a molecule in a liquid) has an equal chance of moving in any direction, which seems unlikely for liquid penetrating a biscuit, since the retreat is blocked by the onrushing liquid. Diffusion models, though, are not the only ones to predict the experimentally observed pattern of behaviour. Washburn provided a different explanation, based on the forces that porous materials exert on liquids to draw them in.
The imbibition process is called capillary rise, and was known to the ancient Egyptians, who used the phenomenon to fill their reed pens with ink made from charcoal, water and gum arabic. The question of how capillary rise is driven, though, was first considered only two hundred years ago when two scientists, an Englishman and a Frenchman, independently asked the question: “What is doing the pulling”?
The Englishman, Thomas Young, was the youngest of ten children in a Somerset Quaker family. By the age of fourteen, he had taught himself seven languages, including Hebrew, Persian and Arabic. He became a practising physician, where he made important contributions to our understanding of how the heart and the eyes work, and showing that there must be three kinds of receptor at the back of the eye (we now call them cones) to permit colour vision. Going one better, he produced the theory that light itself is wave-like in character. In his spare time he laid the groundwork for modern life assurance and came close to solving the hieroglyphic riddles posed by the Rosetta stone.
The Frenchman, the Marquis de Laplace, also came from rural origins (his father was a farmer in Normandy) and his talents too showed themselves early on. He eventually became known as “The Newton of France” on account of an incredible ten-volume work called Mécanique céleste. In this work he showed that the movements of the planets were stable against perturbation. In other words, a change in the orbit of one planet, such as might be caused by a meteor collision, would only cause minor adjustment of the orbits of the others, rather than throw them catastrophically out of synchrony.
Young and Laplace independently worked out the theory of capillary rise – in Laplace’s case, as an unlikely appendix to his, literally plenary, work on the movements of the planets. Both had observed that, when water is drawn into a narrow glass tube by capillary action, the surface of the water is curved. The curved liquid surface is called the meniscus, and if the glass is perfectly clean the meniscus will appear to just graze the glass surface.
Laplace’s (and Young’s) brilliantly simple thought was that it appeared as though the column of water was being lifted at the edge by the meniscus. But what was doing the lifting?
It could only be the glass wall, with the molecules of the glass pulling on the nearby water molecules. But how could such a horizontal attraction provide a vertical lift?
Laplace concluded that each water molecule in the surface is attracted primarily to its nearest neighbours, so that the whole surface is like a rope hammock, where each knot is a water molecule and the lengths of rope in between represent the forces holding the molecules together
A hammock supported at the ends sags in the middle. A simplistic picture of capillary rise is that the water column is being lifted in a similar manner. More accurately, the forces of local molecular attraction tend to shrink the liquid surface to the minimum possible area. If the surface is curved, the tendency of the surface to shrink (known as surface tension) produces a pressure difference between the two sides, just as the stretched rubber surface of a balloon creates a high internal pressure. It is the pressure difference across a meniscus that drives capillary rise.
Laplace was able to use his picture of local molecular attraction to write down an equation describing the shape of a meniscus so accurately that the equation has never needed to be modified since. By thinking about the common-place phenomenon of capillary rise, Laplace had also unexpectedly found an answer to one of the big unanswered questions in science at the time, which was “How far do the forces between atoms or molecules extend? Are they long range, like the force of a magnet on a needle, or the force of gravity between the Sun and the Earth? Or are they very short range, so that only nearby atoms are affected?” Laplace showed that only very short-range forces could explain the shape of a meniscus and the existence of surface tension. Knowing how many molecules are packed together in a given volume of liquid, he was even able to make a creditable estimate of the actual range of the intermolecular forces.
Laplace’s experience shows that the science of the familiar is more than a way of making science accessible or illustrating scientific principles. Many of the principles themselves have arisen from efforts to understand everyday things like the fall of an apple, the shape and colour of a soap bubble, or the uptake of liquid by a porous material. Scientists exploring such apparently mundane questions have uncovered some of Nature’s deepest laws.
Laplace and Young showed that the relationship between surface curvature, surface tension and the pressure across a meniscus was an extraordinarily simple one – the pressure difference across the meniscus is just twice the surface tension divided by the local radius of curvature. This relationship, which now bears their joint names, shows (for example) that capillary action alone can raise a column of water no more than fourteen millimeters in a tube of radius one millimeter. As the tube radius becomes smaller, the water can rise higher in proportion. For a tube one thousand times narrower, the water can rise one thousand times higher.
Such tiny channels are present in the leaves of trees. Nature provides a spectacular example in the giant Sequoia, found in the Sierra Nevada range in California. The leafy crown of the largest known specimen, the “General Sherman”, towers eighty-three meters above the tourists passing below. The water supply for the leaves is drawn up from the soil by capillary action. The menisci of these huge columns of water reside in the leaves, and a quick calculation show that the capillary channels containing the menisci can be no more than 0.2 micrometers wide – about one two hundred and fiftieth of the diameter of a human hair.
The pressure across such a tiny meniscus can support a continuous column of water, of which there are many in the bundles of tubes called the xylem, which run up the trunk below the bark. If the column of liquid breaks, however, an airlock develops at a point where the tube is much wider, and where the new meniscus cannot support anything like such a tall column of liquid. Such breaks are frequent events, with the occurrence of each new break being signified by a “click” that can be heard with a stethoscope. Once a column has broken, it seemingly cannot re-form. Eventually, according to the accepted theory, all columns should break and the tree should die. Yet massive trees continue to grow, sometimes for thousands of years, providing botanists and biophysical scientists with a problem that is a long way from being solved.
The Young-Laplace equation nevertheless provides the only reasonable explanation for the uptake of water by trees. It also applies to such serious practical questions as the prevention of rising damp in buildings and the extraction of oil from porous rocks, as well as to the slightly less serious question of biscuit dunking. It tells us how far liquids will rise up a tube or penetrate into a porous material, but it doesn’t say how fast. This is a key piece of information when it comes to biscuit dunking. It was provided by a French physician, Jean-Louis-Marie Poiseuille, who practised in Paris in the 1830s.
Poiseuille was interested in the relationship between the rate of flow of blood and the pressure in veins and arteries. He was the first to measure blood pressure using a mercury manometer, a technique still used by doctors today. He tested how fast blood and other liquids could flow through tubes of different diameters under the pressures that he had measured in living patients, and found that the rate of flow depended not only on the pressure, but also on the diameter of the tube and the viscosity of the liquid. His contribution to science was to describe this relationship by means of a very simple equation.
Poiseuille’s equation can be combined with the Young-Laplace equation to predict rates of capillary rise. Washburn was the first to do this, producing an equation that predicts how far a liquid drawn into a cylindrical tube by capillary action will travel in a given time. The actual equation is:
L2 = (g x R x t)/2h
where L is the distance that the liquid travels in time t, R is the radius of the tube, and g (surface tension) and h (viscosity) are numbers that depend on the nature of the liquid.
Washburn’s very simple equation predicts an equally simple effect – that to double the distance of travel will take four times the time, and to treble it will take nine times the time; exactly the experimental result that Washburn obtained for blotting paper, and that I obtained for biscuits.
In the absence of gravitational effects (which were negligible both for Washburn’s and my experiments), the Washburn equation is extremely accurate, as I found when studying it as a part of my Ph.D. thesis some twenty years ago. By timing the flow of liquid down glass tubes (some of them twenty times narrower than a human hair) I found that the equation is correct for tube diameters as small as three micrometers. Such tubes, though, are a far cry from the interiors of blotting paper or biscuits. There seemed to be no theoretical reason why an equation derived for a very simple situation should apply to such a complicated mess.
There still isn’t. No one, to my knowledge, understands why a liquid drawn by surface tension into a tortuous set of interconnected channels should follow the same simple dynamics as a liquid drawn into a single cylindrical tube. All that we can say is that many porous materials behave in this way. The “drunkards walk” diffusion equation, which predicts a similar relationship between distance penetrated and time taken, may have a role to play. Despite extensive computer modelling studies, though, we still don’t have a full and satisfactory answer.
What we do know is that the Washburn equation works. It’s not the only equation that works when it’s not supposed to. The equation that describes how a thin stream of water dripping from a tap breaks up into droplets, for example, has been applied very successfully to describe the break-up of an atomic nucleus during radioactive disintegration. That doesn’t mean that an atomic nucleus is like a water droplet in all other respects, any more than a biscuit or piece of blotting paper is exactly like a narrow tube. It simply happens that an equation derived for an idealised situation also applies in practice to more complicated situations, and hence can be used to give guidance and predictions in these circumstances.
Such equations are called “semi-empirical”, and often arise when scientists are in the throes of trying to understand a complex phenomenon. They are most useful at an intermediate stage in the understanding of a problem. When a more complete explanation eventually becomes available, semi-empirical equations are usually discarded, although they sometimes retain a value as pedagogical instruments.
The Washburn equation, applied to cylindrical tubes, has a sound theoretical basis. Applied to biscuits or blotting paper, though, it is semi-empirical. To use it in these circumstances, we need to be able to interpret “R”. “R” is a radius, but of what? The best that we can do is to interpret it as an “effective” radius, a sort of average radius of all the pores and channels.
One can try to assess the value of this effective radius (call it Reff) by measuring as many channels as possible under a microscope and taking an average, but there is a simpler way, using the experimental graph for biscuit dunking. The slope of this graph can be used to calculate Reff via the Washburn equation. When I tried the calculation, though, the results didn’t seem to make sense.
The answer seemed to be that the structure of a wetted biscuit is very different from that of the dry biscuit. In a dry biscuit, the starch is in the form of shrunken, dried-up granules. These are quite tiny. In rice, for example (which is almost pure starch), there are thousands of tiny granules in every single visible grain. When these granules come into contact with hot water, they swell dramatically, taking in water as avidly as does an athlete during a marathon.
As it happens, my colleagues and I had studied the swelling process, which is very important in the preservation, processing and reconstitution of starchy foods. We held single potato starch granules in water while we gradually raised the temperature of the water, watching what happened through a microscope. At around 600C the granules suddenly increased their volume by up to seventy times, producing what I subsequently described in a radio interview as the world’s smallest potato pancakes.
The starch granules in biscuits swell similarly when the biscuits are dipped into hot tea. The swollen, crinkled granules become very soft, which is one of the reasons why a dunked biscuit puffs up and eventually disintegrates (the other reason is that the fat and sugar “glue” between the granules melts and dissolves).
The granules that we were studying became so soft that they could be sucked into glass tubes whose diameters were three times smaller. This deformability seems to be the explanation for the extraordinarily low values of Reff calculated from the Washburn equation for dunked biscuits – the softened granules squeeze up against each other like rock fans at a concert, leaving only the narrowest of gaps in between. In practice, it’s just as well. If the pores stayed at their original “dry biscuit” size, the Washburn equation predicts that a biscuit would fill up with tea or coffee in a fraction of a second, and biscuit dunking, like doughnut dunking, would become a matter of split-second timing.
As it is, the Washburn equation not only explains why biscuits dunked by the “flat-on” scientific method can be dunked for four times as long as with the conventional method – it can also be used to predict how long a biscuit may safely be dunked by those who prefer a more conventional approach.
Only one assumption is needed – that the biscuit will not fall apart so long as a thin layer remains dry, and sufficiently strong to support the weight of the wet bit. But how thin can this layer be? There was only one way to find out, and that was by measuring the breaking strength of dry biscuits that had been thinned down. I consequently ground down a range of biscuits on the Physics Department belt sander, a process that covered me with biscuit dust and which caused much amusement among a workshop staff who were more used to manufacturing precision parts for astronomical instruments.
Whole dry biscuits, I found, could support up to two kilogrammes in weight when clamped horizontally by one end with the weight placed on the other end. The thinned down dry biscuits were strong in proportion to their weight, and could be reduced to 2% of their original thickness and still be strong enough to support the weight of a fully wetted remainder (between ten and twenty grammes, depending on the biscuit type).
All that was now needed was to calculate how long the biscuits could be dunked while still leaving a thin dry layer, either in the mid-plane of the biscuit for a conventional dunk or on the upper surface of the biscuit for a “scientific” dunk. The calculation was easily done using the Washburn equation plus the values of Reff for different biscuits. For most biscuits, the answer comes out at between 3.5 seconds and 5 seconds for a conventional dunk, and between 14 and 20 seconds for a “scientific” dunk.
Was there anything else to consider? The only thing remaining was to examine the breaking process itself.
The detailed physics of how materials (including biscuits) break is quite complicated. The underlying concept, though, is relatively simple (as are quite a few scientific concepts – the expertise comes in working out their consequences in detail). The concept here is that, when a crack starts, all of the stress is concentrated at the sharp tip of the crack, in the same way that, when someone wearing stiletto heels steps on your toe, all of the painful pressure is concentrated at the tip of the heel.
If the stress is sufficient to start a crack, it is sufficient to finish the job. That is why brittle materials (including dry biscuits) break completely once a break has started.
The stress that is needed to drive a crack depends on the sharpness of the crack tip. The sharper the tip, the less stress is needed, in the same way that a light person wearing a stiletto heel can produce as much pain as a heavier person wearing a wider heel. It would seem, then, that even the tiniest scratch could potentially grow into a catastrophic break, no matter how strong the material, so long as the tip of the scratch was sufficiently sharp. Engineers up to the end of the Second World War knew from practical experience that there must be something wrong with this theory, or else a saboteur could have caused Tower Bridge to collapse into the Thames by scratching it with a pin. Even though experience showed that this wouldn’t happen, engineers still massively over-designed structures like bridges and ships – just in case.
Even so, there were occasions when the theory took over. One such was when an additional passenger lift was fitted to the White Star liner “Majestic” in 1928. Stresses concentrated at the sharp corner of the new, square hole in the deck drove a crack across the deck and down the side of the ship, where it fortuitously struck a porthole (providing a rather more rounded tip), or the ship carrying 3000 passengers would have been lost somewhere between New York and Southampton. In other cases, such as that of the U.S.S. Schenectady, ships have actually been torn in half.
Sharp corners are now rounded where possible to avoid stress concentration effects. We also understand more about the mechanisms that stop small cracks from growing, which involve plastic flow at the tip of the crack, so that the tip becomes slightly rounded and less sharp. The process can be encouraged by the incorporation of crack-stoppers. These are soft components in a mixed (composite) material whose function is to stop cracks from growing. When a travelling crack hits a particle of crack-stopper, the crack stopper “gives”, turning the crack tip from sharp to blunt and reducing the stress concentration to below a safe limit. The ultimate crack-stopper is an actual hole, such as the porthole in the “Majestic”.
Modern composite materials, such as those used for the manufacture of jet engines, routinely contain “crack stoppers”. Biscuits are also composite materials, and also contain crack stoppers. The crack stoppers are natural materials like sugar, starch and (especially) fat, which, although hard, still have some “give”. As a result, most biscuits are remarkably robust, until they are thinned too far. Then the “graininess” of the biscuit takes over. When a biscuit becomes as thin as the diameter of the individual grains, the separation of any two grains is sufficient to reveal the void below, and the biscuit falls apart.
There is a solution even to this problem – a two-dimensional crack stopper. That crack stopper is chocolate, a material that “gives” slightly when an attempt is made to break it, and which can be (and is) often used to cover part or all of a biscuit surface.
Our final recommendation to the advertisers was that basic physics provides the ultimate answer to the perfect biscuit dunk. That answer is to use a biscuit coated on one side with chocolate, keep the chocolate side uppermost as you dunk the physicists’ way, and time the dunk so that the thin layer of biscuit under the chocolate stays dry.
To my considerable surprise, the story was taken up avidly by the media, with the Washburn equation as the centrepiece. The idea of applying an equation to something as homely as biscuit dunking made a great hit with journalists. Those who published the equation took great care to get it right; some even telephoned several times to check. Only one failed to check, and got it wrong, provoking the following letter:
“Dear Sir, I think there is something wrong with your biscuit dunking equation.
Please send me some biscuits for noticing this.”
Chao Quan (aged 12)
Unfortunately, by the time the letter arrived, my colleagues and I had eaten all the biscuits.
[ADDENDUM: Ten years later, I received another letter from Chao Quan, saying that my reply had been the inspiration for him to take up science and become a doctor!]
Why should an eighty-year old equation become the centre of a news story? At the invitation of the journal “Nature”, I tried to find an answer. My conclusion was:
“Such journalistic excitement over an equation contradicts the normal publisher’s advice to authors – that every additional equation halves the sales of a popular science book. Why was this so? Let me suggest an answer, relevant to the sharing of more serious science. Scientists are seen by many as the inheritors of the ancient power of the keys, the owners and controllers of seemingly forbidden knowledge. Equations are one key to that knowledge. The excitement of journalists in gaining control of a key was surely a major factor in their sympathetic promotion of the story. By making the Washburn equation accessible, I was able to ensure that journalists unfamiliar with science could use the key to unlock Pandora’s box.”
The science of dunking may seem trivial, and in one sense it is. Scientist’s questions often seems like a child’s idle curiosity, the sort of thing that we should have outgrown when we reached adulthood, so that we can concentrate on more serious things like making money or waging war. To myself and other scientists, though, asking “why” is one of the most serious things that we can do.
Sometimes we try to justify it by practical outcomes. To me, that is a big mistake, whether the outcome is landing a man on the moon or finding a better way to dunk a biscuit. The real reason that a scientist asks “why?” is because he or she shares with the rest of the community the most basic of human aspirations – wanting to understand the world and how it works. As members of a thinking species, we all have such aspirations, and express them every time we ponder about religious beliefs, or about our relationships with other people, or about feelings of any kind. Scientists find a similar sense of excitement, though, in additionally addressing a particular corner of the great canvas of life – that concerned with the behaviour of the material world.
In compensation for the narrowness of our compass, scientists have got further in understanding the material world than have psychologists, philosophers and theologians in trying to understand people and their relationships with each other or with that world. It has often happened (as in the case of Laplace) that questions about commonplace phenomena have produced answers to other, and sometimes more important, questions. In the rest of this book, the science of the commonplace is used to open doors for non-scientists. It has often opened doors for scientists as well.
Market Research on Biscuit Dunking Survey commissioned internally by McVitie’s biscuit company, November 1998.
… an elastic net of the protein gluten… “Network” was defined tongue-in-cheek in Johnson’s 1755 “Dictionary of the English Language” as “anything reticulated or decussated at equal intervals, with interstices between the intersections.” It is the interstices, or cross-links, that count; without them there would be no net. For the last fifty years it has been believed that these cross-links in wheat flour dough are formed by disulphide bonds. Only recently has it been discovered (K. Tilley, “Journal of Agricultural and Food Chemistry”, Vol.49, p.2627) that they are formed by cross-links between the totally different tyrosine residues, and that the disulphide idea was not based on hard evidence. It just goes to show that “folk explanations” are as likely to penetrate science as anywhere else. The difference is that, in science, there is at least a way of eliminating them.
Faraday’s Public Lectures Michael Faraday “The Chemical History of a Candle”. Chatto & Windus, London, 1908.
Robert Hooke and the Royal Society “Hooke, Robert” Article in Encyclopedia Britannica, 11th Edn. Cambridge University Press, Cambridge, 1910 -1911.
The exact terms of Hooke’s appointment, as recorded in the Journal Book of the Royal Society for November 5th, 1662, were: “Sir Robert Moray proposed a person [Hooke] willing to be employed as a curator by the Society, and offering to furnish them every day, on which they met, with three or four considerable experiments, and expecting no recompence till the Society should get a stock enabling them to give it.
“Considerable”, it transpired, meant “original”. And today’s Ph.D. students think that they have it tough!
The Structure of DNA James D. Watson “The Double Helix”. Penguin Books, London, 1970.
Francis Bacon and the Nature of Scientific Research Francis Bacon “The Novum Organon (or, A True Guide to the Interpretation of Nature)” (transl. G.W.Kitchin). Oxford University Press, Oxford, 1855. An amazing number of people still think that science works in the way that Bacon suggested.
“Paradigm Shifts” in Science Thomas, Kuhn “The Structure of Scientific Revolutions”, 2nd. Edn. Chicago University Press, Chicago, 1970.
Proof in Science Peter Medawar “The Limits of Science”. Oxford University Press, Oxford, 1985.
The Mathematics of a Drunkard’s Walk “Drunkard’s Walk Helps Unfold Secret of Polymers”. New Scientist Magazine, 136, December 12th, 1992. This article summarises the principles of random walks in an accessible way, and shows how the square relationship and the factor of four that follows arises. There are also numerous web-sites that cover the subject of random walks at different levels of sophistication.
Washburn’s Experiments (and Equation) E.W.Washburn, Phys. Rev., 17, 374 (1921).
Graphs, Symbols and Equations are an immense source of confusion to non-scientists (and to some scientists!), but they needn’t be. The principle is very simple. An equation describes how one thing depends on another. If a car is traveling at 60 kilometers per hour, for example, then the equation (distance in kilometers) = 60 x (number of hours) shows just how the distance travelled depends on the time spent.
To avoid writing everything out in full, scientists use abbreviations. “D” is a common abbreviation for distance, and “t” is the universal abbreviation for time. The equation above thus becomes D = 60 x t, which is much easier to write and just as easy to read with a little practice.
A graph is simply another way of writing an equation to display visually how one thing depends on another. By convention, the thing that is depended on (in this case, the time) is drawn along the bottom (horizontal) axis, and the thing that depends on it (the distance) occupies the vertical axis.
It’s that simple.
Young’s Version of the Young-Laplace Equation Thomas Young, Phil. Trans. R. Soc. London, 95, 65 (1805); “A Course of Lectures on Natural Philosophy and the Mechanical Arts” (2 vols). J. Johnson, London, 1807. Young hated mathematical symbols, and wrote his equations out entirely in words, which makes reading his papers incredibly hard going.
Laplace’s Version of the Young-Laplace Laplace, Pierre Simon de (Marquis), “Supplément au dixième livre du traité de mécanique céleste” (1806). Translated and annotated by N. Bowditch (4 vols) (1829 – 1839) Boston. Reprinted by Chelsea Publishing Co., N.Y. (1966).
Scientists Investigating Familiar Phenomena have frequently made important fundamental discoveries. The famous story that Newton discovered the universal law of gravitation after being hit on the head by a falling apple unfortunately has no foundation (although it is interesting to note that the modern unit of force (the Newton) is approximately equal to the force of gravity on an average-sized apple). There are, though, plenty of real examples of universal laws being derived from the observation of common-place phenomena. These include: Galileo’s discovery of the pendulum laws after observing the swinging of a chandelier in the cathedral of Pisa; Mendel’s deduction of the laws of genetics from his observations on peas growing in a garden; Rumford’s hypothesis that heat is a form of motion, a conclusion that he came to after observing the enormous amounts of heat generated during the boring of brass cannons (anyone who has ever had occasion to drill a hole in a piece of metal will be aware of this phenomenon on a smaller scale). In modern times, the universal theory of chaos, which dominates such diverse topics as the growth and decline of animal populations and financial movements in the stock market, originated from Lorenz’s efforts to understand weather patterns.
Water Movement in Trees Some progress has recently been made REFERENCE TO COME (Science or Nature)
Poiseuille’s Equation is simply
L2 = (∆P x R2 x t)/4 h
where L is the distance travelled by a liquid of viscosity h in time t along a cylindrical tube of radius R under a pressure head DP (J.L.M.Poiseuille, C.R.H. Acad. Sci. 11, 961, 1041 (1840); 15. 1167 (1842)). Note: ∆ is the usual scientific shorthand for “a change in”.
Experiments on the Swelling of Individual Starch Granules were reported in L.R.Fisher, S.P.Carrington and J.A.Odell “Deformation Mechanics of Individual Swollen Starch Granules”. In Starch: Structure and Functionality (P.J.Frazier, P.Richmond and A.M.Donald, eds.). Royal Society of Chemistry (London), Special Publication. No. 205 (1997), p.105.
The Science of How Cracks Form and Grow is discussed in an entertaining and simple fashion in J.E.Gordon “The New Science of Strong Materials”, 2nd. Edn., Pelican, London, 1976, which also gives a photograph of the “Majestic” near-disaster. A picture of the “Schenectady” actual disaster is given in J.E.Gordon “Structures”, Pelican, London, 1978.
Media Coverage of Biscuit Dunking The story was featured in all major British newspapers over 24th-25th November, 1998, appeared on TV and radio news world-wide, and even found a place in the Wall Street Journal. It also became the subject of numerous features.
“Nature” Article on Biscuit Dunking Len Fisher, “Physics Takes the Biscuit”. Nature 397, 469 (1999).