"Perpetual Torque" Air Molecule Motor

An earlier air molecule motor

Several years before working on the "perpetual force" air molecule motor discussed in my last few posts, I worked on an earlier idea, which I now call a "perpetual torque" air molecule motor. (I had originally called it a "Semi-Maxwell's Demon"). Here is the report I wrote on it, from the late 1980s:—

                                                        [quote begins]

A SEMI-MAXWELL'S DEMON

— A report containing the elements of a specification

1. INTRODUCTION

   Since the publication of "Theory of Heat" by James Clerk Maxwell in 1871 it has been recognised that if a device could be constructed which would sort air molecules in an appropriate way, then energy could be extracted from them (Ref 1). It would therefore provide an inexhaustible, non-polluting and portable energy source, having no fuel cost, and able to operate continuously anywhere within the earth's atmosphere.

   The sorting device has been termed a "Maxwell's Demon." A "complete" Maxwell's Demon would not only sort molecules, but would also extract energy from them, and in doing so would return them to their original conditions of temperature and pressure. A complete Maxwell's Demon would clearly break the second law of thermodynamics. It is generally accepted that it would be impossible to construct such a device.

   Most of the investigation of this subject has followed Maxwell's original idea of sorting air molecules by velocity (i.e. speed and direction), to achieve a temperature difference. Sorting by direction only, to achieve a pressure difference, has been mentioned (Ref 5), but little investigation of other possible methods of operation seems to have been made.

   The main theoretical objections to a Maxwell's Demon follow from its requirement for a kind of intelligence (e.g. Ref 2), or at least a kind of memory (Ref 3) or information gathering ability (Ref 4). This is also usually associated with a requirement for animation at the molecular level.

   If all the air in the earth's atmosphere is potentially available as the working fluid, then the requirement for a complete Maxwell's Demon to return the air molecules that interact with it to their original conditions is of no practical significance. If this requirement is abandoned, then various devices can be envisaged which would extract energy from air molecules by using some kind of sorting process, but would not break the second law of thermodynamics, and would not require any of the attributes listed in the previous paragraph. One such "semi-Maxwell's Demon" is discussed further in the remainder of this report.

2. PURPOSE

   It is the purpose of this report to describe a device which will extract energy in a useful form from the thermal motion of air molecules. It has the following features:—

   1.  It has no requirement for intelligence, memory, information gathering or animation at the molecular level.

   2.  It sorts air molecules by direction only to achieve an energy output in the form of rotational mechanical energy.

   3.  It takes in air at ambient temperature. Its working fluid is, in theory, the whole of the earth's atmosphere.

   4.  It exhausts air at a temperature below ambient.

   5.  It has only one moving part: a rotor made up of a very large number of identical "blades".

   6.  It requires the distance between adjacent parallel blades to be less than the mean free path of the surrounding air molecules. (At normal atmospheric pressure the mean free path of air molecules is about 0.1 micrometre).

3. DESCRIPTION OF THE DEVICE

   The device is a single structure, i.e. a rotor made up of many "blades" of the correct shape and size, which will experience a torque as a result of the impacts of air molecules when it is immersed in the atmosphere. Molecules arrive at these impacts from completely random directions, with no direction more prevalent than any other. However the design of the device ensures that the net effect of the molecular impacts from certain directions is to produce a couple on each blade, which in turn gives rise to a net torque about a central axle. This torque is not cancelled by the effects of molecular impacts from all other directions. Thus the device is designed to achieve, automatically, and by its structure alone, a sorting process sufficient for its purpose.

Figure 1

   Figure 1c shows a portion of the device. With the notation shown, this portion consists of a series of blades of width Δr in the x direction, and spacing d. The blades are all inclined at an angle Φ to the z axis. Both Δr and d are smaller than the mean free path of the surrounding air molecules, λ. As a starting point, possible values are:—

   Δr = 0.2 × λ ;   d = 0.05 × λ ;   Φ = 45 degrees.

   The blades are fixed together at suitable intervals with spacers S, to ensure rigidity.

   The blade thicknesses are made small compared to their widths.

   The series of blades may be extended indefinitely in the positive and negative y and z directions, to form a "sheet" of blades. In other words, the blades may be any length, and there may be any number of blades.

   Figure 1b shows portions of some sheets of blades.

   Figure 1a shows the complete device, which consists of many sheets of blades, each formed into a cylinder. These cylinders are arranged concentrically, with some small separation (greater than λ) between each cylinder and its neighbours. However each cylinder is fastened to its neighbours at intervals, so that they form a rigid rotor which can turn as a single unit about the axle A.

   The complete device can be made any convenient size.

   It will probably be desirable to design the fastenings between cylinders, and between the innermost cylinder and the axle, in the form of blades of a radial flow fan, to promote gross air movement through the cylinders.

4. ANALYSIS

   A complete analysis would aim to determine the exact result of immersing the device in the atmosphere. That is, it would determine the net effect of all the molecular impacts occurring on the device, or a representative portion of it, over a given period.

   For an initial analysis, some simplifying assumptions were made. The three most significant were:—

   - It was assumed, for simplicity, that all molecules have equal mass and speed.

   - It was assumed that molecules entering between the blades of the device undergo only specular impacts with blades (i.e. impacts with incidence and reflection angles equal), until they exit. In this case, each impact force is proportional to the cosine of the angle of incidence between the molecule's track and the normal to the blade hit.

   - It was also assumed that the blade widths and spacings are sufficiently small that the number of inter-molecular collisions inside the blades is generally negligible.

   Consider molecules entering any pair of adjacent blades on the outermost cylinder. If the product

   Fz.r = (impact force resolved in z direction) × (perpendicular distance from impact point to an imaginary plane at x = r1 + Δr/2)

is calculated and summed for every impact, a graph of the form shown in Figure 2 is obtained.

Figure 2

   NOTE: The dashed portion of the graph requires further comment. Referring to Figure 1c and setting Φ = 45 degrees, if molecules enter the blades with a velocity component in the xz plane at an angle just less than 45 or 225 degrees, then a few such molecules will undergo very many rebounds, giving a net high negative Fz.r product. It is assumed, as shown in the dashed portion of the graph, that these few molecules will, as a result of their increasingly long track length, eventually end this behaviour. This could be from either an inter-molecular collision, or a non-specular molecule/blade collision.

   The form of Figure 2 shows that forces resolved in the z direction from impacts of molecules arriving onto the blades from angles in the xz plane between 45 to 90 degrees, and between 225 to 270 degrees, produce a couple centred on, and parallel to, the plane P. This couple is not cancelled by impacts of molecules arriving from other directions. As shown in Figure 3, the couples from each blade in the outermost cylinder add circumferentially.

 

Figure 3

   Similarly, considering all other cylinders, the couples from every blade in the complete device add together to produce a net torque about the axle A in Figure 1. (Forces resolved in the x direction produce no net effect. Forces resolved in the y direction are always zero).

5. CONCLUSIONS

   This report describes a device which will experience a torque from molecular impacts when immersed in the atmosphere. Therefore, if permitted to rotate, it will convert some of the kinetic energy of air molecules impacting on it into rotational mechanical energy.

   In giving up some of its kinetic energy, the air exhausted from the device will be cooled below ambient temperature. This difference between the final and initial states of the air (i.e. the working fluid) is the reason why the device does not break the second law of thermodynamics. To regain its original temperature the exhaust air must acquire energy from an outside source, e.g. the sun. The device is therefore an energy converter, drawing free energy from the sun via the environment, as does, for example, a hydro-electric power station.

   The device will have all the benefits listed in the first paragraph of this report. In addition, the cooling of the exhaust air will be beneficial in most applications.

   Detailed modelling on a large computer seems necessary to determine precisely how far inter-molecular collisions are tolerable inside the device, and how specular/diffuse individual molecule/blade collisions should be. The modelling should consider the effects of many molecules interacting with a representative portion of the device. The results should be compared with what may become achievable in practice, and what would be required to optimise the design. The requirement for a fairly low rate of internal inter-molecular collisions seems essential, but the requirement for specular collisions could probably be relaxed considerably — perhaps to an already achievable value (Ref 6).

   The effects caused by molecules that could potentially undergo very many rebounds, e.g. those discussed in the NOTE of section 4, should be thoroughly investigated. Perhaps, for some particular combinations of design parameters, the effects of these molecules could largely cancel the effects of all other molecules. However it does not seem possible that this could occur generally.

   Other matters requiring further investigation include the optimum separation between adjacent cylinders, the optimum design of fastenings between cylinders, filtration of incoming air, and how much of the energy output should be used to achieve forced air circulation. A full analysis should also take proper account of the velocity distribution of air molecules.

   A problem exists at present in constructing a device to the design described in this report, in that the manufacture of blades with the extremely small dimensions required seems to be beyond the present state of the art. However, as progress in nanotechnology continues, it is to be expected that the manufacturing problems would eventually be solved.

   It might be possible using available methods to build a low-power prototype device to operate at reduced air pressure, where the longer mean free path would allow larger blade sizes.

6. REFERENCES

Ref 1: Theory of Heat. J. Clerk Maxwell, Longmans, Green and Co, (1871).

Ref 2: Mathematische Vorlesungen am der Universitat Gottingen VI, Leipzig und Berlin. M. U. Smoluchowski (1914) — quoted in Ref 5.

Ref 3: "On the Reduction of Entropy of a Thermodynamic System Caused by Intelligent Beings," L. Szilard in Z. Physik 53 840-856 (1929).

Ref 4: "Maxwell's Demon Cannot Operate: Information and Entropy I," L. Brillouin in J. Applied Physics, 22/3, 334-337 (March 1951).

Ref 5: "Maxwell's Demon," W. Ehrenberg in Scientific American, 217/5, 103-110 (November 1967).

Ref 6: "On Stresses in Rarefied Gases Arising from Inequalities of Temperature," J. Clerk Maxwell in Proceedings of the Royal Society, 27, 304 (1878); Appendix dated May 1879. [About 50% of air molecules striking a glass surface were specularly reflected]. 

                                                    [quote ends]

Remarks

1.  I did do some 3D computer analysis of this idea, to obtain the graph shown in Figure 2. Because no more advanced methods were available to me at the time, I wrote and used a BASIC program. This modelled air molecules arriving with equal probability from any direction (actually any equal-area portion of two hemispheres; one on each side of an array of blades). Those molecules that were able to strike a defined, fixed-area region of the blades were tracked, with the torque generated from each impact aggregated, until they exited. Every impact was fully specular.

2.  At the present time, I don't think that this "perpetual torque" approach holds as much promise for real-world applications as the "perpetual force" motor discussed previously. But I decided to include this report anyway, as it completes the record of my investigations into air motors of these kinds, and shows some of the history and background of what I now think is the better "perpetual force" version.


Back in 2015

I leave for my Christmas/New Year holidays tomorrow, so this longer than usual post will be my last for 2014. I'll be back in a fortnight or so.