Since then I have blown other bubbles that lacked the protection of a glass cover. They have survived for a few minutes or even a few hours, depending on such conditions as drafts and the amount of dust in the air. In any case the bubbles have lasted long enough for experimentation. For example, I have made bubbles into inexpensive instruments that measured the viscosity of gases, determined the surface tension of fluids or served as ultrasensitive manometers for measuring atmospheric pressure. Other bubbles have been blown to demonstrate simple geometric propositions and to solve mathematical equations related to electrical circuits and optical lenses. Mostly, however, I have been blowing bubbles for fun: spheres up to two feet in diameter, small bubbles blown inside larger ones, "weightless" bubbles that float in containers of heavy gases, configurations of adjoining bubbles that resemble the lattice structure of crystals, and so on.

It all began early last winter when I visited A. V. Grosse, president of the Research Institute of Temple University in Philadelphia. Much of Grosse's career has been devoted to nuclear research and the investigation of high temperatures. For this reason I was scarcely prepared, on entering his office, to see a huge display of soap bubbles. They were on tables and bookshelves, and one bubble, suitably protected, even served as a paperweight. Since the career of most bubble blowers ends at about the age of 10, I wondered why soap bubbles continued to interest the administrator of a prominent research establishment. In answering that question Grosse not only revived my own interest in bubbles but also agreed to share his enthusiasm with readers of this department. He writes:

"During a pleasant discussion several years ago with my former colleague Willard F. Libby we concluded that as members of the older generation of atomic scientists we might well spend part of our spare time devising simple new experiments for the entertainment and education of the younger generation. The discussion eventually led me to the investigation of soap bubbles. This field of experimentation seemed appropriate because soap bubbles are inexpensive and very pretty and present many unanswered questions. I set up a small bench in my basement at home and have been blowing bubbles ever since. So many new facts and phenomena turned up that until now I have neglected my original objective of passing my findings along to amateurs.

"A soap bubble behaves somewhat like an inflated rubber balloon. The skin of the bubble is stressed, because of surface tension, and like stretched rubber it compresses the air trapped inside. As soon as the bubble is blown the compressed air begins to make its way through the permeable skin. The bubble shrinks. Eventually the bubble collapses to a flat film stretched across the blowpipe. I call this interval-the time required for the bubble to shrink to a flat film-the natural life-span of the bubble.

"My first bubbles all died in infancy. Few lasted more than a minute. They were blown with much the same kind of soap that Isaac Newton used for his n classic bubble experiments. I turned to

the literature and found that a much better soap was described more than a century ago by the blind Belgian physicist Joseph A. F. Plateau, who laid the foundations of our present knowledge of soap bubbles. Bubbles blown with Plateau's solution will last for several minutes in an ordinary room and for several hours with proper protection.

"Amateurs can make this solution with materials that are available from dealers in chemical supplies. To 40 ounces of distilled water add one ounce of chemically pure sodium oleate. Sodium oleate comes as a white powder that floats for a time on water. Do not mix the powder in the water; put the powder on the water and let the container stand in a dark place for 24 hours. The powder will then have dissolved. Add 10 ounces of U.S.P. glycerin and mix the solution thoroughly by pouring the fluid slowly into a clean container and back again several times. Store the mixture in darkness for about a week. Then siphon off the clear fluid below the scum. Add two drops of household ammonia to the clear fluid, stir the solution gently to mix the ingredients and bottle it for use.

"Small bubbles blown from this solution to a radius of four or five centimeters usually last for two or three minutes in ordinary room air. About 10 years ago the Canadian chemist A. L. Kuehner described a solution that makes more durable bubbles. He first purified oleic acid by a painstaking procedure and then by the addition of bromine converted it into 9,10-dibromostearic acid. When this acid is carefully neutralized with sodium hydroxide and mixed with glycerin, it forms bubbles that will last for months if they are protected by an enclosure.

"Having experimented with Kuehner's solution, I decided to take advantage of recent developments in polymer chemistry in the hope of compounding a solution of even greater interest. The result is what I call a 'double bubble' solution: two solutions that are mixed just before use. Bubbles can be blown with either solution, hence the name 'double bubble.' Large bubbles blown with the mixture have lasted for three years so far and are likely to last for many more. From the rate at which one bubble is shrinking I estimate a natural life of more than 20 years.

"One of the two solutions consists essentially of Kuehner's dibromostereate soap. The other one is a solution of polyvinyl alcohol, water and glycerin. Bromine is an extremely hazardous substance before it has reacted with the acid, and compounding these mixtures calls for controls that are not available in the home. For these reasons amateurs should not attempt to make double bubble solution. It can be bought from the Techno Scientific Supply Company, Inc., P.O. Box 191, Baldwin, N.Y. 11510. The solution costs $4 a pint, a quantity sufficient to blow thousands of bubbles.

"Bubbles can be blown with almost any pipe. As was pointed out by the English experimenter C. V. Boys, however, moisture from the breath tends to condense inside the pipe and drain into the soap film, where it dilutes the solution and hence reduces the life of the bubble. Pipes that are blown by mouth should have a trap of some kind to catch the exhaled moisture. The carbon dioxide in the breath may also be harmful to the bubble. Therefore it is best to do the blowing with compressed air. Small compressors of the kind used for supplying air to aquariums are ideal for blowing bubbles. The rate at which the bubbles are blown can be adjusted by placing a pinch clamp on the tubing that leads from the compressor. To blow big bubbles it is advisable to interrupt the blowing periodically.

"Dust is the archenemy of bubbles, particularly dust that contains crystals of salt. It is interesting to set up a bubble in one corner of a room filled with clean air and with a perfume atomizer inject a puff of brine into the air at the opposite corner. Microscopic crystals of salt from the evaporated mist will make their way across the room; within a minute or two they will break the bubble! For this reason I blow my bubbles with 'glycair,' which is air that has been filtered through glycerin. An adequate filter can be made by cutting the bristle sections from four to six test-tube brushes and inserting them into a glass tube they fit snugly. The tube is closed at the ends by perforated rubber stoppers. An ounce or so of glycerin is placed inside the tube, which is kept in the horizontal position. The bristles are moistened with glycerin periodically by rotating the tube.

"Big bubbles require more solution than small ones. A relation also exists between the ultimate size to which a bubble can be blown and the diameter of the blowpipe from which it is blown, since the bubble is held only by the surface tension between the solution and the rim of the pipe. Bubbles up to about 10 centimeters in diameter can be blown with a pipe one centimeter in diameter, but I prefer a ratio of about five to one. Bubbles that are intended to last their full natural life must be blown inside a protective enclosure, preferably one with a spherical shape, such as a Florence flask.

"I first wash the container carefully, put about 10 milliliters of bubble solution in it and flush it with glycair for a few minutes to remove as much dust as possible. A blowpipe is pushed into a perforated stopper that fits the neck of the container. I dip the lower end of the pipe into soap solution, insert it in the container and blow the bubble. The stopper is pressed firmly into the neck of the container and the free end of the blowpipe is sealed by a stopper.

"Bubbles made in this way may break after a short time because of dust trapped in the container. The bubble traps the dirt, however, and purifies the air of the flask. Therefore, without opening the flask to the dusty air outside, I push the blowpipe through its supporting stopper down into the solution inside the container, slide it back up and blow another bubble. The second or third bubble should last for its natural lifetime. The container is stored on a mat of foam rubber for protection against mechanical shock. The diameter of each bubble is measured at weekly intervals and the shrinkage is plotted against time. From these data I estimate the ultimate life.

"Bubbles can be blown inside one another by several methods. An easy way is to blow a small bubble, about the size of an orange, and put it on the rim of a paper cup that has been moistened with bubble solution. Detach the blowpipe from the bubble by turning the pipe at a right angle to the film and lifting it gently. The film will close and peel away from the pipe.

"Immerse the end of the pipe in bubble solution to a depth of a few centimeters and push it into the top of the bubble. It will penetrate the bubble without breaking the film. As you blow the inner bubble the outer one will expand in proportion. Detach the inner bubble by pulling the pipe upward, abruptly but not violently. This is a knack that comes with practice.

"Concentric bubbles can also be blown by means of coaxial pipes telescoped together and supported by spacers of rubber or plastic. Place a soap film across the end of the outermost pipe and blow the outer bubble. Slide the next smallest pipe, with a film, into its supporting pipe axially and blow the second bubble, which enlarges the first one. Additional bubbles can be blown. I have had triple bubbles, with beautiful colors, that have lasted for more than a year.

"Foams are also easy to make. Tie a bag of terry cloth around the end of a blowpipe, soak the cloth in bubble solution and blow. The walls between adjacent bubbles make interesting geometric patterns. To observe the walls clearly, blow foam between two sheets of window glass, spaced about an inch apart, that have been moistened with bubble solution.

"The air pressure inside a bubble increases as the bubble shrinks. For this reason the wall that is shared by two adjoining bubbles, as in foam, always curves toward the larger of the two bubbles by an amount that can be predicted by simple geometry. For example, make a dot on a sheet of paper. From the dot draw three straight lines spaced at angles of 60 degrees. Then draw a straight line that intersects the three lines. Place the point of a compass at each of these intersections successively and, with the dot as the radius, draw three circles. The two smaller circles mark the boundary that would be formed if two bubbles of this size were placed in contact with each other. The smaller circles intersect the largest circle at two points. The arc of the largest circle included between these two points marks the position of the wall that would be shared by the adjoining bubbles.

"This theory was worked out by Plateau. You can prove it by experiment. Place a diagram so drawn under a sheet of window glass moistened with bubble solution. Blow a pair of hemispherical bubbles against the glass, about the size of the two smaller circles. Detach the blowpipe from each bubble and with the end of the pipe center the bubbles over the circles. The size of the bubbles can be adjusted by adding air or letting air escape through a small blowpipe, such as a soda straw. When you have matched the size of the bubbles to the diagram, you will find that the curvature of the shared wall conforms to the geometric prediction. This combination of bubbles can be used to find the total resistance of an electrical circuit consisting of parallel resistors and to predict the distance at which a scene will come to focus behind a lens of known focal length.

"Observe also that any three walls of the bubbles make equal angles of 120 degrees at the point where they come together. This must be so because the surface tension of the three soap films is equal: all three films exert pull on the point where they meet. They balance only when the three pulls are exerted in mutually opposing directions.

"To prove that surface tension acts uniformly in all directions, cut two wires about 10 centimeters long, bend small loops at the ends and tie the mating pairs of loops together with silk threads about 10 centimeters long. The resulting structure is a rectangle with ends of wire and sides of thread. Attach a bridle thread to one of the wires and dip the assembly in bubble solution. When you pull it out of the solution, a soap film will cling between the wires and the threads. The film will have straight ends and curved sides. If the sides curve inward excessively, hang wire weights to the bottom member.

"Tie a length of silk thread into a loop, dip the loop in bubble solution and toss it onto the film. Touch the film inside the loop with a point of dry paper. The film will break, and surface tension outside the loop will snap the thread into a perfect circle. The circle is the only possible shape the loop can assume when it is pulled outward by a uniform radial force.

"As mentioned, surface tension compresses the gas inside a bubble. If you punch a small hole in the bubble, air will flow out. The bubble will collapse at a rate that increases with the size of the hole and with the surface tension and decreases with the density of the gas. To make a bubble deflate slowly twist a length of fine wire into a row of three small loops that lie in a common plane. With silk thread tied to the end loops, dip the assembly in bubble solution and suspend the wire against the bubble. To let the air out, puncture the soap film in the middle loop with a splinter of dry wood.

"I recently devised a similar experiment that amateurs can use for measuring the surface tension of soap film or the viscosity of a gas if either quantity is known. If both quantities are known, the experimenter can accurately predict in advance of the experiment how long it will take the bubble to deflate from any size to any smaller size. All you need for the experiment is bubble solution, a slender blowpipe, a fixture to support the pipe, a small aquarium and a watch with a second hand.

"Blow the bubble, plug the blowpipe with a stopper and measure the diameter of the bubble. Remove the stopper. Time the interval during which the bubble shrinks. Measure the diameter of the shrunken bubble. With these data and the known dimensions of the blowpipe you can easily determine the quantities of interest.

"My blowpipe is 29 centimeters long with an inner radius of .183 centimeter. (It is a length of four-millimeter glass tubing.) The ends were pushed into perforated rubber stoppers and the stoppers were in turn pushed into three-centimeter lengths of 10-millimeter glass tubing. These large glass nipples at the ends prevent bubble solution from entering the bore of the small tube. Either nipple will also accept a stopper for plugging one end of the blowpipe. The dimensions are not critical. Any slender tube of about this size will work. It is essential, however, to determine the actual dimensions as accurately as possible. The length can be measured with a ruler. To find the radius fill a portion of the slender tube with mercury and measure the length of the filled portion in centimeters. Transfer the metal to a container and determine its net weight in grams. Divide the weight of the metal by 42.55 times the length of the column. The square root of this quotient is equal to the radius of the tube in centimeters. For example, a 10-centimeter length of my tube holds 14.2 grams of mercury. Therefore its radius is (14.2 / 42.55 x 10)^1/2 = (.0333)^1/2, or .183, centimeter.

"I blow the bubble inside a small aquarium of the type used for keeping tropical fish. (Any large glass beaker or battery jar will do.) The aquarium is covered with a sheet of transparent plastic that has two narrow slots along the middle that lead almost to the hole in the cover through which the blowpipe is inserted; the slots are thus on a straight line through the center. Through the slot I suspend two small plumb bobs made with a silk thread and a penny. To measure the diameter of the bubble I slide each plumb bob toward the bubble until the thread is within .5 millimeter of the soap film, as judged by eye. This brackets the bubble and gives its diameter within one millimeter.

"The experimental procedure is simple. Blow a bubble of any diameter. Remove the air hose from the blowpipe, plug the pipe and measure the radius of the bubble. Remove the stopper from the blowpipe and time the interval during which the bubble shrinks. Insert the stopper and measure the smaller radius.

"It turns out that the time of efflux varies as the fourth power of the radius of the bubble. Raise each radius to the fourth power (multiply it by itself four times). Subtract the smaller figure from the larger one. Assume, for example, that you let the bubble contract from a radius of two centimeters to a flat film across the end of the blowpipe. The figure would be (2 x 2 x 2 x 2) - 0 = 16. If the bubble had contracted from a radius of 20 centimeters to one of 18 centimeters, the corresponding figures would be (20 X 20 x 20 X 20) - (18 x 18 x 18 x 18) = 55,024.

"Assume that you want to determine the surface tension in a soap bubble that contracts from a radius of two centimeters to a flat film in 4.94 seconds. The next consideration is viscosity, which is a measured in units of poises; olive oil at room temperature has a viscosity of about one poise. The viscosity of air at 20 degrees Celsius is 1.83 x 1O^-4, or .000183, poise. The surface tension of the two-centimeter bubble is equal to twice the length of the blowpipe, multiplied by the viscosity of the air and the fourth power of the radius as determined above, divided by the product of the time in seconds multiplied by the fourth power of the radius of the blowpipe. The example works out as follows: 2 x 29 x 1.83 x 1O^-4 X 16/4.94 x 11.31 X 1O^-4 = 30.4 dynes per centimeter. (A force of one dyne is about equal to the weight of a hungry mosquito.) Both the surface tension and the viscosity of the air are now known, so that the efflux time can be predicted. With the same blowpipe, how long would a bubble take to shrink from a diameter of 40 centimeters to one of 36 centimeters? The difference in the fourth power of the radii is 55,024. To compute the efflux time, multiply twice the length of the blowpipe by the viscosity of the air and divide the product by the surface tension multiplied by the fourth power of the radius of the blowpipe. The resulting quotient is a constant: 2 X 29 X 1.83 X 10^-4. 30.4 X 11.31 X 10^-4 = .309. Multiply the difference in the fourth power of the radii by the constant to get the time in seconds. In this example, 55,024 X .309 = 17,002 seconds, or about 4.7 hours.

"Assume that the surface tension of the bubble is known and you want to determine the viscosity of a gas, such as hydrogen. Blow the bubble with hydrogen and proceed as above. Experiment would reveal that the efflux time needed for a hydrogen-filled bubble to shrink from a radius of 20 centimeters to 18 centimeters is about 8,100 seconds. The viscosity of the gas is equal to the product of the surface tension, the fourth power of the radius of the blowpipe and the difference of the fourth power of the radii divided by twice the length of the blowpipe multiplied by the efflux time in seconds: 30.4 x 11.31 X 10^-4 X 8,100 . 2 x 29 x 55,024 = 8.76 x 10^-5 poise. I find it interesting to blow bubbles with different gases, such as a variety of Freons, and determine their viscosity by this procedure.

"A more ambitious project involves the construction of a useful manometer in which a nearly flat soap film functions as the sensing element. The instrument is capable of indicating directly changes in air pressure of less than a millionth of an atmosphere. Cut a circular hole, 45 millimeters in diameter, through the bottom of a plastic Petri dish to take a No. 10 rubber stopper. Perforate the stopper axially to accommodate a sleeve of 20-millimeter glass tubing four centimeters long. Push the sleeve through the stopper from the smaller end until it is flush with the top, and insert the assembly into the Petri dish from the top. Plug the top of the sleeve with a No. 2 rubber stopper perforated by two holes and plug the bottom by a similar stopper that has one central hole.

"The assembly rests on a tabletop, preferably one that is covered with hard, smooth plastic. Drill a hole in the table to take the glass sleeve and couple the sleeve to a five-gallon carboy under the table. The carboy must be well insulated against heat, preferably by a covering of rock wool 12 centimeters thick.

"Place about 10 milliliters of bubble solution in the Petri dish and blow a soap film across the edge of the dish. Insert a roundheaded pin through the film and into the doubly perforated No. 2 stopper. Drill a second hole in the tabletop near the Petri dish to admit a snugly fitting glass sleeve and couple the lower end of the sleeve to a glycair filter. Invert a cake plate over the Petri dish and insulate it with at least five centimeters of rock wool. Make two holes in the rock wool insulation for observing the relative distance between the pinhead and the soap film. As the barometric pressure changes, the soap film will move up or down in relation to the n pinhead. You can observe the changes through a small telescope. I constructed the device to demonstrate one of many possible applications of soap films. The details of construction are obviously amenable to modification, as is the method of reading the instrument.

"In conclusion, I invite both amateurs and experts to help me solve a fascinating puzzle that turned up during a recent experiment. I wondered how a bubble would behave if it were blown with hydrogen in an atmosphere of hydrogen at low pressure. I blew the bubble in a round-bottomed flask that had a side arm and stopcock connected to an air pump. The blowpipe was inserted through a glass sleeve in a perforated stopper that fit the flask, and the telescoping joint between the blowpipe and the sleeve was sealed with a thin rubber tube. Bubble solution was placed in the bottom of the flask. The flask was exhausted to the limit of the air pump, flushed with hydrogen twice and again evacuated. The pump was shut off. Hydrogen was admitted to the flask until a manometer in the system indicated a pressure of 40 torr. The blowpipe was lowered into the bubble solution and withdrawn, and hydrogen was admitted to blow a bubble with a radius of about two centimeters.

"Next I shut off the hydrogen supply, intending to observe the rate at which the diffusion of hydrogen through the soap film caused the bubble to shrink. To my amazement the bubble began to expand! Within about four hours it doubled in size. Thereafter it slowly shrank to a flat film as expected. I then blew the flat film into another bubble. The cycle was repeated.

"The experiment has been performed with other apparatus and under other conditions but always with the same result. The bubble expands without apparent cause! None of the obvious explanations is satisfactory. My stopcocks do not leak, the vacuum is held constant for weeks and the apparatus is trust worthy in other respects. I can only conclude that much remains to be learned about soap bubbles, and I urge amateurs to join me in the fun of solving the puzzle."

Bibliography

SOAP-BUBBLES. THEIR COLOURS AND THE FORCES WHICH MOLD THEM. C. V. Boys. Dover Publications, Inc., 1959.

THE NATURAL LIFE OF SOAP BUBBLES. A. V. Grosse in Report RITU 1967-1. The Research Institute of Temple University; 1967.

The Society for Amateur Scientists (SAS) is a nonprofit research and educational organization dedicated to helping people enrich their lives by following their passion to take part in scientific adventures of all kinds.