IN A TIME when most of the results of science have to do with things remote from everyday experience- such as fundamental particles of matter, the inner workings of the living cell and the strange behavior of distant celestial objects-one tends to overlook the scientific opportunities that are to be found under one's nose. This month I have collected several examples based on nothing more complicated than a cup of coffee (or tea). You have undoubtedly encountered some of them, but you may not have given them much attention.

Late one night, escaping for a few minutes from work on his doctoral dissertation, my friend John Hudak was idly mixing instant coffee into a mug of hot water, clinking his metal spoon on the bottom of the mug as he stirred. The pitch of the clinking noise fell abruptly as the powder went into the water, meaning that the sound waves had become longer and had decreased in frequency. As Hudak stirred for the time required to mix the powder the frequency slowly increased to its former value. He obtained the same results when he added a spoonful of a powdered cream substitute. Indeed, any powder dissolved in the hot water caused the same type of frequency shift.

Before any powder is added a particular note is heard from the clinking because the spoon excites resonant standing waves in the column of water and in the rim of the mug. The waves are similar to the resonant waves in an organ pipe that are responsible for the sounds you hear from the pipe. The harmonic frequencies in the coffee cup, however, are a bit more difficult to calculate than those in the organ pipe. The frequencies depend on the thickness, radius, density and elasticity of the rim, the radius of the column of liquid and the speed of sound in the liquid.

I first thought the powder would lie on top of the water and thus would have an influence in determining the resonant frequencies of the mug. It turns out, however, that any powder lying on the water only damps the oscillations in the mug, thereby muffling the clinking noise. It does not change the resonant frequencies. Moreover, the powder dissolves rather quickly.

When the powder first dissolves, tiny air bubbles are released from the powder grains. The speed of sound is considerably less in air (about 340 meters per second) than in water (about 1,450), so that the bubbles lower the speed of sound in the liquid. If the volume of the bubbles is a hundredth the volume of the liquid, the velocity of sound is reduced 30 times. As a result the frequency of any standing wave is lower when the bubbles are released. As the bubbles gradually burst, the speed of sound (and hence the frequency of the standing wave produced by the clinking) returns to normal.

A similar change in frequency can be observed in a freshly poured glass of beer. As the air bubbles in the beer (not the ones on top of it) dissipate, the pitch of the sound of a spoon tapped against the side of the glass rises slowly.

One rather simple experiment in a coffee cup serves as a rough model of vortex motion on a much larger scale in the atmosphere (dust devils, tornadoes, fire storms and hurricanes). Smoothly stir a cup of hot coffee or hot tea, lift the spoon out and then carefully pour cold milk or cream into the center of the cup If the stirring and pouring are done carefully enough, a vortex develops in the center of the coffee. It is noticeable for two reasons. First, the angular speed of the fluid is greater in the center than it is just outside the region where the milk was poured. Second, the vortex may be so well developed that the surface in the center dimples. Neither characteristic appears if the milk is warm or hot. Instead the angular speed in the center of the cup decreases.

The different results with hot and cold milk stem from the difference in their densities with respect to the hot water in the cup. Cold milk is denser than the water and so will sink when it is added to the water. The descending stream captures existing small vortex columns from the surrounding fluid, pulls them in toward the center and (on the average) stretches them. The angular speed of the fluid in the columns then increases, causing the fluid in the center of the cup to swirl faster than the fluid outside the area occupied by the milk.

If the milk is quite hot, it may be lighter than the water in the cup. With no descending stream (or a much smaller one) the vortex columns are not drawn into the center to be stretched, and so the angular speed around the center of the cup does not increase.

The demonstration with cold milk may be analogous to the amplification of vortexes in the air. Convective motion of the air may stretch already existing vortex tubes just as the descending milk stream does. Stretching increases the angular speed of the vortexes. In the air the necessary convection can be either up (if the stream is lighter than the surrounding air) or down (if the stream is heavier than the surrounding air). In either case the convection can intensify vortexes left by other sources, such as the swirling (due to overheating of the air near the ground) that can develop into dust devils.

If you stir a cup of tea or coffee in which you can see on the bottom a few specks, tea leaves or bits of undissolve sugar, you find that they are forced to the center of the bottom. The motion seems a bit paradoxical. One would suppose material lying on the bottom of the cup would be pushed outward to the walls by the centrifugal force created in the rotation of the fluid around the central axis of the cup.

The centrifugal force does attempt push material to the walls. Consider small parcel of water rotating around the central axis. The farther the parcel is from the axis, the greater the centrifugal force it experiences is. As a result the pressure in the liquid increases outward from the axis, in a sense to counter the centrifugal force. The rotating fluid should therefore have no radial motion only angular motion around the center.

Radial motion does develop, however, because of the friction between the bottom layer of fluid and the bottom of the cup. The reduced rotation in the bottom layer means that the pressure difference there between fluid near the wall and fluid near the center is not as much as it is on the top surface. This reduced pressure in turn means that the pressure near the wall is greater in the top layer than in the bottom layer. As a result fluid is forced downward along the wall and then radially inward to the bottom center of the cup, upward along the central axis and radially outward in the to layer. This fluid motion, known as secondary flow, can carry tea leaves or other submerged objects along the bottom of the cup and deposit them in the center as the fluid begins its central ascent.

You can follow the secondary flow by carefully dropping food coloring into stirred water in a clear cup or beaker. Although the fluid flow is not as ideal as implied in the illustration on the opposite page, the colored water does spiral around the center of the cup with a radial motion roughly like the one depicted.

The same type of secondary flow is partly responsible for the meandering of rivers. Similar meandering can also be seen in the Gulf Stream and other ocean currents and in water channels on the surface of a glacier. Even when a straight section of a stream is found, closer inspection usually reveals that the movement of the water is not really straight but rather exhibits a weaving back and forth between the walls of the stream. Small perturbations introduced into the course of the stream by the local terrain initiate the meandering. The mystery lies in the regularity of the resulting pattern.

When water rounds a bend, a secondary flow similar to the one in the teacup created. Because of the retardation of flow near the bottom the pressure difference between the inside and the outside of the bend is different in the top and bottom layers of the water. The greater pressure on the outside top layer forces fluid down the outside wall. Reaching the bottom, the fluid is forced toward the inside of the curve, then upward and finally out again to the outside of the curve along the top surface. During this time the horizontal velocity of the water is greater on the outside of the turn than it is on the inside. The faster flow tears away portions of the outside bank, and the loose material is carried by the secondary flow to the inside bank. The result is an enhancement of the stream's curve, because the outside bank is eaten away as the inside bank is built up. Given an initially young, straight stream, the secondary flow will enhance any perturbations in its bed into small meanderings, which in turn will be enhanced into larger meanderings. If the looping becomes extreme, the stream eats its way from one loop to another to strand a loop in between.

Vincent J. Schaefer has described in American Scientist a surprising geometric pattern on the surface of his early-morning coffee. With bright sunlight shining almost horizontally across a cup of hot coffee filled to the brim, the surface exhibited dusty-looking polygons traced out with dark lines. This type of geometric surface pattern was first discussed in detail by Henri Bénard in 1901. Examples of the pattern can be found in other evaporating fluids and in circulation systems in both the atmosphere and the sea.

The pattern in the coffee cup is caused by the circulation of the hot water that rises from the bottom to the top, cools and then turns to the bottom Over the areas of rising hot water small drops condense, supported by the vapor pressure from the surface of the liquid. The drops are of roughly uniform size, because larger drops cannot be supported by the vapor pressure and smaller ones scuttle away. Over the areas where the cooled water descends there are no such suspended drops, and the surface appears clear. Since the coffee is dark these areas are also dark. What one sees on the surface is small patches of drops (over rising water) that are outlined by relatively narrow dark lines where the fluid descends.

If the lighter areas are examined with a microscope, they appear to consist of layers of closely packed drops. The density of the drops depends on the vapor pressure available from the liquid and on the number of condensation nuclei in the air. A dirty atmosphere will in principle provide more condensation nuclei for more droplets.

To observe such phenomena you need not wait for a setting or a rising sun. You can see the Bénard-circulation patterns more easily by directing the light from a slide projector or a motion-picture projector over the surface of a cup of coffee. If you would rather not waste coffee, substitute hot water dyed with a dark color (black food coloring or a dark ink). To maintain the heat in the water you can put the cup (or even better a Pyrex beaker) on a low-temperature ho plate. I initially brought the water nearly to the boiling point to degas it (the bubbles are a nuisance) and then allowed the water to cool. The best Bénard cell appeared several minutes later.

If the surface became contaminated with a film, I briefly laid a piece of paper towel on the liquid to collect and remove the film. If you would like to see the effect of such a contamination, place a drop of corn oil on the surface. The oil slowly spreads over the surface and eliminates the Benard cells.

Schaefer has also described the effect of bringing charged objects near the light areas in the Benard cells. Running a hard-rubber comb through your hair or across a length of wool or plastic charges the comb by transferring electrons either to the comb or to the other material. With some types of material the comb gains electrons and become negative. With other types of material the comb loses electrons and become positive. In either case the charged (comb destroys the light areas, indicating that the drops already carried a charge.

When Schaefer held a charged hard-rubber comb near the surface of the water, he sometimes saw drops form near the teeth of the comb. I saw this phenomenon when I held a wire lead from an electrostatic generator near the surface of the water, with the other lead from the generator attached to the metal cup holding the water. In both cases the ions created in the air near the tip of the charged object are condensation nuclei for the formation of drops. A radioactive source accomplishes the same thing because it too provides ions in the air just above the water surface. A lighted match or any other source of small airborne particles will similarly increase the drop formation.

When the drops are illuminated in bright white light, they display rapidly changing colors, delicate and iridescent. The scattering of light that gives rise to these colors is called the higher-order Tyndall scattering, after John Tyndall, who investigated them starting in 1869. Tyndall scattering can also be seen in other natural phenomena. The corona at is sometimes seen around the sun, which can show several complete spectra of colors, is the result of Tyndall scattering from small drops in the thin clouds lying between the viewer and the sun. (It is not the corona seen during an eclipse.) So is the similar corona seen around the moon. The scattering is likewise responsible for the delicate colors seen in the mother-of-pearl, or nacreous, clouds that are occasionally visible after sunset in the high latitudes. The mathematical models of this scattering are complex because the size of the drops approximates the wavelengths of visible light. The drops are a micron or so in diameter and therefore lie between the larger drops that can produce rainbows (geometric scattering) and the smaller particles that are responsible for the blueness of the sky (Rayleigh scattering).

In addition to the constantly changing patterns on the surface of your coffee cup or some other vessel you will also find dark lines that scud across the dusty-looking areas. Schaefer points out that these lines are due to small whirlwinds that develop just above the surface and last for only a fraction of a second. The layer of air just above the liquid is unstable because it is much warmer than the air slightly higher up You can create your own vortex by, holding an index card vertically with2 one edge near the surface. Any small air current flowing past the edge sheds a vortex that then skims across the surface. Even without an edge larger whirlwinds occasionally develop over the surface, lasting for 10 seconds or so as they whip the evaporating vapor and small droplets around.

How fast does a cup of coffee or tea cool? To push back the frontiers of modern physics (at least a millimeter or two) I measured the rate at which water cooled from the temperature to which it would be heated to make instant coffee. I wanted to know which of several procedures would cause the water to cool fastest. I boiled water in a teakettle and poured 200 milliliters into a 250-milliliter Pyrex beaker, which was then left on a metal plate. The temperature of the water was measured with a thermometer (scaled from zero to 100 degrees Celsius) that was left in the beaker with the mercury reservoir resting on a corner of the bottom of the beaker. The initial water temperature in all the runs was 93 degrees C. I measured temperature until the water was below 45 degrees which I believe would correspond to an unpleasantly cool cup of coffee.

Water with no additives and no stirring cooled smoothly, reaching 45 degrees in about 33 minutes. With a teaspoon of instant coffee put into the beaker before the water was added the water cooled in almost the same way for the first 15 minutes but then cooled faster than it had in the first run. The results were almost identical when three lumps of sugar were first placed in the beaker and when a metal spoon was left in it (nothing else having been added). One might guess that the inclusion of instant-coffee powder would cool the water faster for two reasons. The powder, being initially at room temperature, absorbs heat from the water. It also darkens the solution, thereby increasing the thermal radiation somewhat. The latter effect must be negligible, since the addition of sugar to the water did not darken the solution but gave similar results. The spoon can be expected to increase the cooling rate of the water because initially it absorbs some of the water's heat and thereafter acts as a radiator of heat to the room.

In another run I added 20 milliliters of light cream at an initial temperature of 10 degrees C. immediately after the water was poured. The water was stirred only three times to mix he cream with out producing a cooling effect by the stirring. The temperature immediately dropped about four degrees, but after five minutes the mixture of cream and water began to follow the same cooling curve followed by water alone. After 15 minutes, however, the cream mixture cooled faster.

The addition of alcohol might increase the cooling rate because of the enhanced evaporation from the top surface. After I had added 20 milliliters of 80-proof vodka that was at room temperature the cooling rate was almost the same as when I added cream.

Of all the additives the one most effective in altering the cooling curve of the water was Reddi wip (a whipping cream in a pressurized can) that I applied to the top of the water, much as one would do in making Irish coffee. The cream was cool and might have initially lowered the surface temperature of the water somewhat, but its main effect was to trap the heat in the water and eliminate evaporation. As a result the water took an additional 14 minutes to reach 45 degrees C.

I figured that stirring unmodified water during the cooling would significantly increase the cooling rate. Vigorous stirring with the thermometer for the first 15 minutes, however, typically reduced the water temperature by only a couple of degrees. Apparently my stirring was not much better than the normal convection cells in the water at transporting hot water from the center to the surface.

In my last test I sprayed the outside of the beaker black. With a black surface the walls should radiate heat better, causing the liquid to cool faster. The water did cool faster, approximately following the cooling curve I had obtained by stirring the water.

Two conclusions emerge from these data. If you want to cool your coffee quickly but without adding a large amount of cream and sugar, stirring the coffee vigorously with a metal spoon in a black coffee cup is the best procedure. The cooling seems hardly worth the effort, however, since it amounts to only a few degrees. On the other hand, if you want to keep your coffee as hot as possible, the best thing to do is to fix yourself an Irish coffee and relax.

If you would like to do more work on the problem, you might consider the effects of adding cream, sugar or a powdered cream substitute five or 10 minutes after the water is poured. Is the temperature of the coffee lower if the coffee is allowed to cool by evaporation and convection before the cream, powdered substitute or sugar is added? You might also like to find out how the temperature of an Irish coffee depends on the proof of the whiskey. Investigating this question would be a particularly enjoyable experiment for two.

Bibliography

ON THE NOTE EMITTED FROM A MUG WHILE MIXING INSTANT COFFEE. W. E. Farrell, D. P. McKenzie and R. L. Parker in Proceedings of the Cambridge Philosophical Society, Vol. 65, Part 1, pages 365-367; January. 1969.

OBSERVATIONS OF AN EARLY MORNING CUP OF COFFEE. Vincent J. Schaefer in American Scientist, Vol. 59, No. 5, pages 534-535 September-October, 1971.

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