The introduction of aircraft and submarines with unique weapons and sensor technologies into the fields of war in the early 1900’s changed regional land and sea warfare to one of a global, three dimensional context.
Since this introduction, nations have spent billions of dollars, rubles and pounds to develop air and ocean systems to detect and localize submarine platforms. The task continues to be difficult, for the ocean is nearly opaque and filled with anomalies which limit finding submarines. These warships are in turn making their detection a more complex art as their envelope of operations grows with their greater submerged speed, depth, endurance, maneuverability and sound quieting systems. Nevertheless, today’s sophisticated sensor technologies coupled with high speed, large capacity signal processing systems offer to enhance the probability of quick and accurate detection, especially if every ocean phenomenon is fully exploited. Even old concepts must be looked at again and again to discover their golden kernel. One, for example, is the detection of effects on the ocean’s surface generated by submarines.
Can such an effect be detected, let alone measured quickly with assurance? The answer seems to be yes — more specifically a “suprasurface” effect, stemming from some recent discoveries made about the phenomenon called surface tension or capillarity.
We know that atmospheric pressure on the water exists because of the weight and impinging of air (and water vapor) molecules upon the surface of the water. Molecules penetrate the water surface to varying degrees depending upon collision parameters of the colliding particles. For saturated conditions (100% humidity), the rate of entry of water molecules equals the rate of departure. Within the liquid, pressure is effected by a combination of intermolecular forces and collision forces.
A common manifestation of the surface tension phenomenon is provided by capillary tubes. Consider a circular capillary tube with a radius of one tenth of a millimeter partially filled with water having a surface tension of 75 dynes/em and a zero wetting angle hemispheric surface. In this state the water would rise slightly over 15 centimeters (5.9 inches) at sea level. From the macroscopic viewpoint, there would be a pressure discontinuity of 15,000 dynes/cm2 at the surface (atmospheric pressure being slightly over one million dynes/cm2) of the water.
What of molecular dimensions and spacing? The spacing of water molecules in the sea is of the order of one or two Angstroms (A) (one ten-billionth of a meter). The mean free path between collisions in the vapor region is of the order of 1000A With this curved capillary surface there is a .. spread loss” situation for the rate of molecules crossing per unit area in going from the vapor region into the liquid; a gain for molecules going from the sea water into the vapor.
This “spread loss” it was felt, could be equated with surface tension. Using the Equation of State provided in the revision to Keenan & Keyes “Steam Tables,” I developed a computer program which, in a lengthy manner, calculated the “spread loss” rate. The operative distance across which the spread losses developed was one-third a mean free path. This distance coincides with the one-third mean free path encountered in the theory of gas viscosities. Here, the geometry of curved surfaces replaces the motion in viscosity theory. Furthermore, there is a small, but significant, contribution derived in the vapor region, across one-third a mean free path.
Analysis of the results of these calculations showed a very close correlation with long-established values of surface tension throughout the entire range of liquid water temperatures and pressures.
In addition to this analytical correlation with established values, I developed a “quick and dirty” home experiment to provide further verification. Smaller particles would travel further between collisions, thus yielding a greater mean free path. The helium molecule has a collision diameter, determined from viscosity measurements, of 2.45A compared with 3.5A for nitrogen and 3.4A for oxygen. I then predicted an increase in the surface tension of water of approximately 30% in a helium atmosphere based on these diameters, and marked with fingernail polish the rise in a capillary tube in this atmosphere. I inverted a 3-liter beaker in a water-filled laundry tub, released commercial grade helium from a balloon into the beaker, and noted the capillary rise. It increased approximately 30% as predicted. A crude experiment, but it worked.
While these discoveries may be of scientific interest, what are the naval applications? Firstly, the theory suggests the small droplets in the upper atmosphere are liquid in subfreezing ambient conditions. This theory also provides insights into the formation of larger and larger raindrops and energy exchanges such as in hurricanes. I will not go into these matters in this article, but will address ASW applications.
Over a century ago, Lord Kelvin in England determined a relationship between sea wave velocities and surface tension. The velocity equates to the square root of the sum of two terms. One is proportional to the product of the wavelength and the gravity constant; the other is proportional to the surface tension divided by the product of density and wavelength. When the wavelength appears as a term in both the numerator and the denominator term, a minimum velocity wave occurs which is of calculable velocity and wavelength. Water, for surface tension of 75 dynes/em, would provide a minimum velocity wave of about 1. 7 em wavelength and a velocity of approximately 23 em/sec. (One knot is approximately 51 em/sec.).
Previous approaches to surface tension has presumed an imbalance of intermolecular forces between liquid molecules at and near the liquid surface while treating the vapor space above the liquid as essentially a void. But my theory not only produces a vapor contribution to surface tension, it also measures it – about 3 1/2 dynes/em at 20 degrees Celsius, compared with the about 69 1/2 dynes/em liquid contribution. When Lord Kelvin’s wave velocity relationship is used — where the surface tension term is proportional to the surface tension divided by the product of the density and wavelength – low air density compared with that of liquid water nevertheless markedly changes the minimum velocity wave characteristics, producing a minimum velocity ‘Wave” of velocity of about one knot, and wavelength of about 10 1/2 em.
A surface ship of sufficient speed leaves a visible set of wake streaks on both sides of the stem which diverge according to Lord Kelvin’s surface tension/gravity relationship. Nature processes the array of waves, moving those faster than the minimum velocity waves on out and leaving visible waves of calculable speed and wavelength. Because of this vapor contribution to surface tension, I propose that above a certain minimum speed a ship would also generate “vapor wakes” of predictable velocity and wavelength, and a wind shear abaft the ship. Moving in the horizontal direction there would be compressions and expansions, producing non-visible waves.
We would hope that radar detection of the phenomenon just described would be feasible at a frequency related to the vapor wake wavelength. A mechanism for a detection system appears to be achievable, but would such a system operate above the threshold of delectability with today’s technology? Initial experimental verification should be feasible with small surface craft and state-of-the-art radar. Signal processing may be necessary in addition to the signal processing done by Nature in producing minimum velocity vapor wakes.
An explanation of step changes in pressure across curved surfaces certainly derives from “surface tension”, considering the centuries-old development of such theory by very eminent workers. An assumed variation in tension at such surfaces will, indeed, explain the pressure differential. But, could not the reverse be true? A pressure differential, however produced, would translate to a change in surface tension. The question becomes, “Which is cause; which is effect?” Begging the precise answer to that question, let us note there is no inconsistency with surface tension theory and my theory. After all, the Equation of State I used incorporates the effects of intermolecular forces. Furthermore, inasmuch as the pressure generated by the air and vapor equals in magnitude the water pressure, should not a perturbation of the interface, such as curving the surface, involve both media?
There are two primary bases which support my theory of capillarity produced by water vapor:
a. With only minor discrepancies, my calculated surface tension values are consistent throughout the entire range of temperatures from freezing to the critical temperature.
b. The predicted increase in surface tension of water in a helium atmosphere was qualitatively verified by me. I believe that a measurement system can be developed for this concept. Risks are evident, though not of a significant financial nature. The payoff could be significant.