AN AUTOMOTIVE engineer designing a fuel tank is not likely to give much thought to the effects of surface tension. He knows from experience that gravity pulls gasoline to the bottom of the tank, where it flows into the fuel line. He ignores the meniscus pulled upward by surface tension around the wall of the tank where the fluid wets the metal. In tanks of conventional size the total upward force of surface tension amounts to less than a quarter of an ounce. It is easily overcome by the weight of the gasoline.

In contrast, surface tension is a major concern of engineers who design space vehicles for operation in gravitational fields that range from 1 g (the force of gravity at the earth's surface) to the weightless state. As the force of gravity approaches zero, fluid in the tanks of space vehicles tends to creep over all accessible surfaces, creating a bubble of vapor that can drift randomly through the fluid. The surface configuration of the interface between the fluid and the vapor must be controlled by forces other than gravity if the tank is to be vented and fuel is to be reliably fed to the engine.

Various schemes have been devised for investigating the behavior of propellants in tanks subjected to reduced gravity. For example, fluid in model tanks made of transparent materials has been photographed in aircraft flown on zero-gravity trajectories. Models have also been dropped from towers and photographed in free fall by high-speed flash lamps.

An interesting device for investigating how surface tension alters the shape of fluid in a closed container is the reduced gravity simulator developed at the Lewis Research Center of the National Aeronautics and Space Administration. This apparatus enables the investigator to observe in two dimensions the successive changes in the shape of a fluid as gravity is reduced. A simplified version of the simulator that amateurs can make was suggested by William Olsen of 209 Inwood Boulevard, Avon Lake, Ohio 44012, who developed the simulator at the Lewis Center. Armed with Olsen's description and several NASA research papers on zero gravity, I made a simulator and conducted various experiments with it.

The simulator consists essentially of a pair of closely spaced glass plates separated by rubber gaskets that conform to the boundary of a selected cross section of the tank [see illustration at right]. The space enclosed by the gaskets is partly filled with ethyl alcohol, which serves as a two-dimensional model of the fuel. The angle the sandwich makes with respect to the horizontal can be varied from 90 degrees to 0 degrees. By changes in the angle the two-dimensional model can in effect be subjected to gravitational acceleration that ranges from 1 g to almost zero. The influence of gravity on the shape of the interface diminishes as the horizontal position is approached, and the influence of surface tension increases. When the assembly lies in the horizontal plane, the interface assumes the shape it would take if the container were in free fall.

Essentially the simulator is an application of an apparatus devised about 1900 by H. S. Hele-Shaw of University College in Liverpool and subsequently developed by A. D. Moore, now professor emeritus of electrical engineering at the University of Michigan, for simulating potential fields [see "The Amateur Scientist"; SCIENTIFIC AMERICAN, July, 1967]. Both mathematical and experimental demonstrations have established that the behavior of ethyl alcohol in the simulator closely approximates the behavior of propellants such as liquid hydrogen in full-scale, three-dimensional tanks that are subjected to comparable gravitational fields. The simulator also enables the experimenter to investigate techniques for controlling the position the liquid and vapor occupy in the tank during free fall so that propellant can be fed to the engine when desired and vapor can be vented continuously with minimum loss of liquid.

The assembly includes two pieces of plate glass at least 3/8 inch thick that can be as large as eight inches wide and 10 inches long. The glass should be as flat as possible and free of scratches. One plate is supported by a plywood base about 12 inches wide, 14 inches long and 3/4 inch thick [see illustration at left]. The glass can be held in position by strips of wood glued to the base.

The spacing between the sheets of glass is fixed by four strips of sheet steel approximately 1/2 inch wide, two inches long and .05 inch thick. The strips can be made of steel shim stock that is available from dealers in automobile supplies. When you cut the metal, take care to preserve its flatness. File all buns from the edges. The four strips must be of identical thickness, the object being to create a space of uniform thickness between parallel glass plates. The four spacers are placed at the corners of the lower plate.

The boundary of the model tank to be investigated is cut from soft rubber sheeting, preferably neoprene, that is a few thousandths of an inch thicker than the spacers. A spherical tank is represented in two dimensions by a circular gasket, a cylindrical tank by a rectangle and so on. The rubber model is centered on the lower plate and covered by the upper plate. Before assembly the glass and rubber must be thoroughly cleaned with detergent and water followed by a rinse with alcohol.

The sandwich is clamped together. A pair of adjustment screws are added to the base at one end to serve as pivots on which the apparatus tilts. A third adjustment screw at the center of the opposite end controls the angle of tilt. In 3 operation the apparatus rests on three pads (small rectangles of metal) cemented to a solid, vibrationless, horizontal foundation such as a concrete floor.

To conduct an experiment place the apparatus on its pads. Insert a fine hypodermic needle through the rubber model at the top, which is the end closest to the adjustment screw that controls the tilt. This needle serves as a vent. A similar needle at the bottom admits fluid to the model.

With a hypodermic syringe completely fill the model with alcohol. I use 200-proof ethyl alcohol. Rubbing alcohol should work almost as well, but I have not tried it. After the model is filled inject a small bubble of air, approximately four millimeters in diameter, by sucking alcohol r to the syringe. Turn the pivot (lateral-adjustment) screws as required to center the bubble at either the top or the bottom of the model. Turn the tilt adjustment screw as required to cause the bubble to drift slowly from the top to the bottom, or vice versa.

The direction of the gravity field should make a right angle with respect to the line on which the apparatus pivots. When the path of the bubble is properly adjusted, it is parallel to the direction of the gravitational field. If it is not, adjust one of the pivot screws as required to correct the angle of the bubble's path.

Finally, tilt the apparatus just enough to cause the bubble to drift slowly into contact with the tip of the vent needle. By operating the hypodermic syringe remove fluid until the bubble expands to a diameter of one centimeter. Adjust the tilt screw to cause the expanded bubble to drift to the bottom of the model. Next turn the tilt screw to the point at which the bubble drifts toward the top at the rate of .01 centimeter per second (one centimeter per 100 seconds) or slower. When the apparatus is so adjusted, the influence of gravity on the shape of the fluid has been reduced to close to zero.

The simulator can now be used for duplicating many of the experiments done with models in drop towers and in aircraft that are flown on zero-gravity trajectories. Remove some of the alcohol, thus making a larger bubble. Tilt the simulator to the vertical plane to observe the shape of the interface at 1 g and return it to the horizontal plane to examine the configuration in free fall.

The simulator can also be used for investigating interface configurations that lie between these two extremes. Most interesting are those that appear when the apparatus is adjusted to small angles with respect to the horizontal plane. All inclinations are usefully described by a quantity known as the Bond number (for W. N. Bond, who investigated capillary effects some 40 years ago); it expresses the ratio of the gravitational force to the surface-tension forces. This quantity can be calculated by timing the velocity at which a bubble moves through the fluid. One must take into account the nature of the fluid, the size of the bubble, the size of the model and the inclination of the apparatus.

At low inclinations the Bond number of simulators that contain ethyl alcohol is expressed by the equation , in which B is the Bond number, V is the velocity in centimeters per second of a bubble one centimeter in diameter and W is the diameter (in centimeters) of the model tank. Assume that the experimenter wishes to investigate the interface at an inclination such that the force of surface tension is 10 times that of gravity (a Bond number of .1) in a model 3.8 centimeters wide. The corresponding velocity of a bubble one centimeter in diameter would be centimeter per second, or one centimeter in 100 seconds.

In general Bond numbers smaller than 1 indicate that the force of surface tension predominates. Numbers larger than 1 indicate that the force of gravity predominates. The influence of surface tension on the shape of the interface is decreasingly apparent at Bond numbers ranging from 5 to 50. At Bond numbers of 300 and higher the interface is substantially the same as it is at 1 g.

Having adjusted the apparatus for a Bond number of .1 or less, the experimenter can observe phenomena at higher Bond numbers by inserting spacers of selected thickness between the tilt adjustment screw and the metal on which it rests. It is interesting to observe the shape of the interface through a series of Bond numbers as fluid is withdrawn from the model. One can also get an idea of the effects of acceleration on the distribution of a propellant by abruptly altering the inclination of the simulator. For example, increasing the Bond number from .1 to 100 during an interval of a few seconds is approximately equivalent in its effect on the distribution of fuel to starting the engine of a space vehicle that is in orbit.

To ensure reliable feeding of fuel to a rocket engine, why not store the fluid in an expandable tank, such as a rubber bag? This expedient might work for some fluids. It would not solve the problem of venting, which becomes a major concern in the case of volatile propellants such as liquid hydrogen. Moreover, liquid hydrogen boils at-423 degrees Fahrenheit. At this temperature most organic materials become as brittle as glass. The designer must rely on forces other than stretched rubber to keep the fluid and vapor where they are wanted- forces such as surface tension, inertia, electrostatic fields and heat.

The position at which the fuel tends to collect can be altered by modifying the shape of the tank and installing systems of baffles. For example, fluid in a spherical tank that contains a smaller sphere, which is offset with respect to the center of the tank, tends to collect in the narrowest zone between the inner and the outer sphere [see illustration upper left]. Simultaneously the vapor tends to remain in the widest zone of separation, where the bubble can most closely approach the shape of a sphere: the shape of minimum surface.

The work that must be expended to move the fluid involves the concept of surface energy, which is related to the concept of surface tension. Surface tension is defined as the force a fluid exerts perpendicularly to a line that lies in the surface. It can be likened to the force exerted by a stretched sheet of rubber. Work expended in stretching the "rubber" is conserved in the form of surface energy. Liquids tend to assume shapes of minimum surface and hence of minimum surface energy. It is for this reason that rain falls in the form of spherical drops and that vapor in the spherical tank tends to assume the shape of a spherical bubble, thereby shifting the fluid to the opposite side of the tank.

Baffles can similarly be used to control the position of fluid in a cylindrical tank [see illustration at right]. For example, at low Bond numbers fluid in a cylindrical tank tends to collect inside a coaxial tube if the diameter of the tube is less than one-third of the diameter of the cylinder, as in the upper part of the illustration. In effect the tube fills with fluid by capillary attraction.The tube can be welded to the bottom of the tank and perforated near the weld to admit fluid to its interior. Fuel can be withdrawn through an opening in the bottom of the tank that is coaxial with the tube. Vapor can be similarly vented at the top of the tubular baffle. If the diameter of the tube is less than one-third of the diameter of the tank, vapor tends to fill the tube at low Bond numbers, as in the lower part of the illustration.

The principle of dielectrophoresis has been suggested as a technique for positioning liquid and vapor in a propellant tank. When liquid that is a poor conductor of electricity is placed in a nonuniform field, it tends to migrate toward the region of highest field strength. For example, if the charged electrode at on end of a cylindrical tank consists of disk and the electrode at the opposite end consists of a sharp point, liquid would migrate toward the point.

In the simulator the disk could be represented by a length of straight wire at one end of a rectangular rubber gasket. The tip of a hypodermic needle thrust through the middle of the opposite end would serve as the pointed electrode. A suitable dielectric fluid is available in most households in the form of Carbona (carbon tetrachloride), a highly toxic cleaning agent. Use it only in well-ventilated room and avoid inhaling the vapor. Potential for creating the electric field can be derived from a small electrostatic generator.

Another physical effect that invite experimentation is the dependence o surface tension on temperature. Surface tension varies inversely with the temperature of the liquid and vanishes the boiling point. Temperature gradient can exist in fluids in free fall because convection currents largely disappear the absence of gravity.

A bubble of vapor will move through the temperature gradient. Surface tension is lower on the warmer side of the bubble. Liquid at the warmer interface flows to the region of lower temperature, where surface tension is higher. Simultaneously the bubble drifts from the cooler side to the warmer side.

This effect can be investigated in the simulator by suspending a short length of Nichrome wire in a model tank and heating it with electric current from a No. 6 dry cell. The opposite end of the model can be a strip of sheet copper that can be cooled with a piece of ice. In addition to demonstrating how a fluid can be moved by variations in temperature the apparatus can also be made to function as a two-dimensional heat pipe [see illustration at above leftt].

Numerous other experiments can be undertaken with the simulator, including the observation of currents induced at low Bond numbers by inertial forces, the diffusion of two liquids at an interface and so on. These effects can be observed by placing a few particles of a coloring substance such as potassium permanganate on the lower plate of glass or injecting solutions of differing colors into the model tank.

LAST December, Octave Levenspiel, who teaches chemical engineering at Oregon State University, described in this department an osmotic pump for creating a continuous fountain of fresh water in the ocean. The proposed pump would consist of a vertical pipe closed at the bottom by a semipermeable membrane. At a depth of 700 feet or more external pressure becomes sufficient to induce reverse osmotic flow and fresh water enters the pipe through the membrane.

Levenspiel suggested that in a pipe extending to a depth of five miles the difference in density between salt water outside the pipe and fresh water inside might conceivably develop an additional pressure difference sufficient to lift fresh water above the surface of the ocean, creating a perpetual fountain. He agreed to submit further comments after readers were given an opportunity to appraise the merits of the exotic invention.

Many readers responded, including a number of specialists in thermodynamics. I now join Levenspiel in expressing gratitude to the respondents for explaining why man must look to other sources for fresh water. Levenspiel writes as follows:

"Since the assumption of different water levels leads to this absurd result, one must conclude that the water level in the pipe stays unchanged no matter how far the pipe is lowered. If the ocean is not in equilibrium, in either temperature or salinity, the chimney effect could elevate fresh water a little above the critical depth of 700 feet, but not nearly enough to reach the surface. We must consign the osmotic fountain to the historical junk.

Bibliography

SIMULATOR FOR STATIC LIQUID CONFIGURATION IN PROPELLANT TANKS SUBJECT TO REDUCED GRAVITY. William A. Olsen in NASA Technical Note D-3249. Scientific and Technical Information Division, National Aeronautics and Space Administration.

ELEMENTARY MECHANICS OF FLUIDS. Hunter Rouse. John Wiley & Sons, Inc., 1946.

STATIC AND DYNAMIC BEHAVIORS OF THE LIQUID-VAPOR INTERFACE DURING WEIGHTLESSNESS. E. W. Otto in A.l.Ch.E. Chemical Engineering Progress Symposium Series, Vol. 62, No. 61, pages 158-177; 1966.

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