Unexpected Influences on Ultra-Sensitive Bubble Levels
K. P. Trout (1) and Charles A. Gaston (2)
1 Pennsylvania State University York Campus 1031 Edgecomb Avenue York, PA 17403 Telephone: 717 771 4136, e mail: [email protected]
2 Pennsylvania State University York Campus 1031 Edgecomb Avenue York, PA 17403 Telephone: 717 771 4155, e mail: [email protected]
SME numbers: A.6.5; A.8.1; B.1.5; B.3.1; B.6.3; C.3; D.3.3; D.7.10; D.10
Key words: Bubble Level, Spirit Level, Leveling, Wafer Fabrication, Surveying, Machine Installation, Tilt Sensing, Mechanical Effects of Light
ABSTRACT
It is common knowledge that light can produce chemical and electronic changes. However, observable mechanical effects of light are rare. It came to our attention that the bubble in an ultra sensitive level would move toward a flashlight beamed at the level from one end. We hypothesized a number of possible mechanisms and investigated which ones could explain the phenomenon. The investigations described here conclude with a surprising explanation of the phenomenon. The phenomenon is caused by a thermally generated pressure differential between the two ends of the bubble. The bubble shift is large enough that people using these levels in highly sensitive processes, such as the installation of wafer fabrication machines, must be careful in order to avoid inaccurate measurements.
INTRODUCTION
Electronic inclinometers and levels are commonly used in heavy construction grading, ship and barge leveling, deviation surveys, continuous casting, and weapons platform leveling (Jewell Instruments
Website 2007), as well as laser leveling, oil platform leveling, vehicle tilt sensing, headlight leveling, survey instrumentation, crane leveling, monitoring long term movement of buildings, engineering leveling of pipes and beams, and gun sight leveling (Level Developments Limited Website 2007).
Ultra sensitive bubble levels are useful in applications like these, as well as in the installation of sensitive machinery, such as wafer fabrication machinery.
An acquaintance of one of the authors installs wafer fabrication machinery which must be very precisely leveled. He was using a bubble level far more sensitive than an ordinary carpenter’s level.
In a poorly lighted area, he used a flashlight to see the level better, but was amazed to see the bubble move as he watched. When this news reached us, we bought one of the levels so that we could investigate. Simple observations (i.e. getting the bubble tube nearly level and shining a light on it) easily confirmed that the reported phenomenon was real. (See Figure 1.) The mystery: what physical mechanism produces that movement?
Figure 1 - Shining a flashlight on one end of the level shifts the bubble about one division.
INITIAL EXPERIMENTATION
Several different mechanisms were hypothesized to explain the bubble movement:
Light activated changes in surface tension;
Photoelectric effects producing unbalanced charges;
Thermal warping of the metal tray holding the glass tube;
Thermal warping of the glass tube;
Differential expansion between the metal and glass;
Thermal expansion of the glass tube;
Density changes from thermal expansion of the liquid;
Evaporation on one side of the bubble and condensation on the other;
Some mechanism other than any of those listed.
Early efforts sought to analyze which direction the bubble should move, and to quantify, even roughly, how big an effect might be produced by candidate mechanisms. Most of these efforts were frustrated by lack of knowledge about the liquid, the bubble and the interior surface of the glass tube.
If there is any direct effect from light, it isn’t essential. After a series of experiments with various optical filters, a strobe light and a laser, it was discovered that breathing on one end of the level caused the bubble to shift toward that end. Heat obviously was the cause, but there remained at least six possible mechanisms. One thing was clear; the bubble always moved toward the source of energy (if it moved at all; a 5 mw laser pointer produced no visible reaction). Warm breath blown on one end of the level produced dramatic, rapid movement of the bubble and relatively rapid return toward the original position.
Two more of the hypothesized mechanisms were eliminated by separating the glass tube from its metal support tray (after soaking the assembly in acetone for a week). With the metal tray removed, the light sensitivity remained. The effect does not involve the metal tray.
Thermal warping of the glass tube does not seem to be a factor because, with the metal tray removed, light or heat from the side or underneath produced the same effect.
These additional observations now had our hypotheses narrowed to three:
Thermal expansion of the glass tube;
Density changes from thermal expansion of the liquid;
Evaporation on one side of the bubble and condensation on the other; plus, of course, the ones we never thought of:
Some mechanism other than any of those listed.
Eventually we bought a second level to be used for destructive testing. The major goal was to find out what liquid was inside, but by opening it in the right way we also could learn something about the pressure in the bubble.
We clamped the level (with metal tray still attached) in a vertical position and videotaped it as we ground off the bottom tip. (A funnel beneath the level was positioned to direct the draining liquid into a vial.) As the tip was penetrated, the bubble expanded from 6.5 mm to 8.5 mm vertical length. The weight of the liquid would produce an expansion of just 0.4%, so the bubble must have been at a gage pressure of nearly a third of an atmosphere.
A 30% pressure increase could not occur accidentally. Our lab is at an elevation of 540 meters. To get that pressure differential by elevation change, the level assembly operation would need to have been done a kilometer below sea level.
There must be some advantage to manufacturing the levels under pressure. Maybe it just minimizes the evaporation of the liquid while the fill tube is being sealed.
We did not attempt to determine the composition of the bubble, but the liquid smelled like methanol.
It was sent out for analysis; unfortunately, it was handled improperly and allowed to evaporate before the analysis could be done.
The big surprise for us was that after the liquid drained, the tube became cloudy. A small portion of the tube was cut away and examined under optical microscopes. The inner surface had been sandblasted or etched or simply not polished after grinding to shape; it was uniformly rough at a scale near the limits of optical microscopy. Apparently, this etched surface is completely wetted inside the intact level, and therefore the bubble moves smoothly in response to tiny forces. (When we attempted to make a level with smooth glass tubing and water, the bubble would “stick” to dust or imperfections, and would resist moving until the tube was tilted several degrees.)
PRIOR STUDIES AND INDUSTRY CONTACTS
We found no references regarding light or other energy displacing the bubble in a level, nor about the construction of such levels. The French company (Ducourret SA) that manufactures the levels seemed very reticent to share any information. There was a bit of a language barrier, but they implied that the information we sought was proprietary.
There are other companies producing similar levels (even seven times as sensitive!), and we found a contact at a company in England (Level Developments Limited) who was much more receptive – at first. In response to our first inquiry he claimed that they could explain the phenomenon, but the information was rather specialized and not normally given out. He even volunteered that if our efforts could benefit them, they could “help us out”. We wrote back, explaining what we knew and what we hypothesized. We asked a few specific questions, including whether they were aware of any published papers. The response to our second note was rather terse: “I don’t think I can add any more information than you already know about this phenomenon.”
We can speculate that this second company also was concerned about “proprietary” information (and that the initial encouraging response was unauthorized) … or that they really don’t know any more than we know.
EXPERIMENTATION, DATA AND CALCULATIONS
To obtain quantitative data, equipment was designed to hold the level and tilt it by measured amounts
(see Figure 2). The main feature was a lever arm supported at one end by a flexure and at the other end by a micrometer shaft. Knowing the length of the lever arm, we could calculate the angle of tilt produced by any given change in the micrometer support. This apparatus allowed us to initialize the level before any given test, and to calibrate the amount of change indicated as the bubble moved relative to the level‘s inscribed division marks.
Figure 2 - Calibration Apparatus: With a flexure hinge at the right of the long grey lever arm and a micrometer adjustment at the left, this apparatus permits precise centering and cali- bration of the bubble level mounted on it. Also visible in the photo are a camera for recording bubble position, a watch-holder to include time and date in the data pictures, a light meter to measure light source intensity and a cardboard shield to block light from parts of the level.
The bubble tube itself is about 60 mm long and 10 mm in diameter. The walls of the tube are about one mm thick. The bubble inside the tube is about 20 mm long. The glass bubble tube comes glued into a steel tray 79 mm long, with a cross section like the bottom half of an octagon.
One marked division (2 mm of bubble movement) corresponds to 0.006 degrees or about 0.0001 radians of tilt. (Tests with the level on its side or upside down indicate that the tube is not curved; the inside surface is barrel shaped.)
A small incandescent flashlight directed at one end of the level from several centimeters away causes the bubble to shift roughly one division toward the light.
Considering the liquid wrapped around the bubble to represent a U tube manometer (see Figure 3), the pressure and force differentials for a one division shift can be calculated as follows:
P = γ * H (1)
where P is the pressure change (N/m 2), γ is the weight density (N/m 3), and H is the height difference (m). Since a 0.0001 radian tilt causes a one division shift, the height difference can be expressed as:
H = L * 0.0001 (2)
where H is the height difference (m) and L is the bubble length (m).
Since the bubble length is about 0.02 m, and methanol density is about 7950 N/m 3 (CRC Handbook of
Chemistry and Physics), P is about 0.016 N/m 2 (or 0.016 Pascals).
Since the cross section of the bubble appears to be about 0.2 cm 2 (0.00002 m 2), the force required to shift the bubble one division is about 3.2x10 7 Newtons.
Figure 3 – Modeling the bubble level as a U-tube manometer.
The challenge, then, is to explain how the light of a flashlight or a tiny amount of heat can produce a pressure difference of 0.016 Pascals or a force difference of 3.2x10 7 Newtons from one side of the bubble to the other.
Many of the possible mechanisms we hypothesized proved unlikely when we analyzed them more carefully or tried to quantify them. One was the idea that the energy produced an expansion of the fluid. The above analogy with a manometer tells us that if one side of the liquid expands, that side of the manometer would be higher than the other. Since our "manometer" is enclosed, and the two sides are separated by a bubble, the bubble must move from the center to a sloped area in order to have a height difference. As the above diagram reveals, the side with the energy input is lower. Liquid expansion would produce the opposite effect from what is observed!
Expansion of the glass could produce a shift in the observed direction. If the barrel shaped interior thermally expanded at one end, it would correspond to a tilt that would move the bubble toward the warm end. Calculations using the most extreme assumptions – glass with the largest thermal expansion ratio, 0.4C temperature difference along just 2cm of the level, and no expansion of the liquid – still gave a result more than two orders of magnitude too small.
Another hypothesized mechanism was surface tension changes. If the energy input reduced surface tension on that side, the bubble could be pulled toward the light. The possibility of a light energy effect was eliminated with demonstrations that any heat source would work. Calculations based on the change of surface tension with temperature gave forces orders of magnitude too small. Finally, discovery of the complete wetting of the rough inner surface of the tube meant that the assumed liquid solid bubble interface did not exist.
Of all the specific mechanisms hypothesized to explain the phenomenon, the only one not disproved involves evaporation and condensation within the bubble.
Using a thermal imaging camera we attempted to measure actual temperature differences along the level tube, but results were limited. Two different people looked at a dozen photos of noisy images
(see Figure 4), attempting to estimate temperature differences from the right to the left side of the bubble. The average estimate was 0.32C, but that is very subjective. Energy transport seemed far easier to quantify.
Figure 4 - Thermal Image: The isolated glass level tube is the horizontal bar silhouetted against the large whitish area (a warm background). Energy applied at the extreme right end makes that area detectably warmer, but seeing any gradient further to the left is difficult.
In practical experience (as well as in classroom physics problems) gas pressure is considered equal throughout any enclosed space of reasonable size. However counter intuitive it is, consider the possibility of a tiny pressure difference between ends of a two centimeter long bubble.
If a small amount of energy is introduced at one end of the level, heat flow toward the other end will produce a small temperature difference between the two ends of the bubble. That temperature difference can cause a small excess of evaporation at the warmer end. Since the distance to the other end of the bubble is vastly greater than the mean free path, the momentum of the evaporating molecules is dissipated long before they can reach the other end. The average force produced as a series of molecules evaporates is given by F = p/ t (3)
where F is the force (N), p is the change of momentum (kg m/s) and t is the elapsed time (s).
Since molecules evaporate in all directions from a surface, the axial component of the reaction force is just half the total like the ratio of areas between a circle and a hemisphere. Also, momentum is mass times velocity; therefore,
v ⋅ m ⋅ 1( )2 F = (4) t
In this equation F is the force (N), v is the molecule velocity (m/s), m is the mass evaporated (kg) and
t is the elapsed time (s).
The excess mass evaporated per unit time is directly proportional to the power transported by the evaporation process, and inversely proportional to the heat of vaporization. Inserting units, and recalling that a Joule is a watt second and a Newton is a kilogram meter per second squared, our formula becomes:
2 (F : kg m/sec ) = (v : m/sec) • (P : watts) / [2 • (H v : watt sec/g) • (1000 g/kg)]. (5)
With the above units it is clear that units are equal on the two sides of the equation. Now the equation can be expressed more succinctly as:
v ⋅ P F = (6) 2000 ⋅ H v
where F is force in Newtons (N),
v is molecular velocity in meters per second (m/s),
P is the power in watts transported by evaporation condensation (W), and
Hv is heat of vaporization in Joules per gram (1173 J/g for methanol).
At room temperature, oxygen molecules have an average velocity of 483 m/sec (Halliday, Resnick, and Walker). Methanol molecules coincidentally have the same mass (32.04 grams/mole) (The Merck
Index), and therefore approximately the same velocity. Solving the above equation for power, we need
(to produce the mysterious 3.2x10 7 Newtons force):
F ⋅ 2000 ⋅ H P = v (7) v
P = 3.2x10 7 • 2000 • 1173 / 483 = 1.55 x10 3 watts evaporating methanol.
The energy absorbed from a flashlight beam is difficult to quantify, or even to control. We wrapped fine magnet wire around each end of the level tube to provide a way to introduce controlled localized heating. (See Figure 5.) One division of bubble movement was produced with 0.017 watts of coil heating at one end (0.1 A through 1.7 ohms). Thus, if 9% of the applied energy goes into evaporating methanol, the excess pressure created by the momentum of that evaporation can account for the bubble shift.
Figure 5 - Heating Wires Added To Level: These figures show the bubble level tube (separated from its metal tray) with fine wire wrapped around the ends to provide controlled heating by electric current. The left photo shows metal supports being glued onto the ends with nail polish. The right photo shows ultimate mounting on the tilting bar of the leveling/calibration apparatus.
FURTHER EXPERIMENTATION
The hypothesis that evaporation of the fluid at the gas/liquid interface was the main impetus for bubble movement led to the prediction that the delay in the movement of the bubble would be least if the heat were input near the meniscus at the end of the bubble. The apparatus and procedure were redesigned to investigate this. (See Figure 6.) A 0.3 millimeter diameter nichrome wire was laid transversely across the bubble level with a consistent amount of pressure maintained. A constant current of 250 mA was run through the wire for one minute and then shut off. This allowed consistent bursts of heat to be applied to the bubble level at a precise location on the level. The time it took for the bubble to respond to the heat as well as the maximum distance it moved was measured. By tilting the level slightly, the starting position of the bubble end relative to the heating wire was varied from run to run in order to find the position of greatest sensitivity.
Figure 6 - Photographs of Revised Setup: The top picture shows a side view of the whole apparatus, which rests on a granite surface plate. The lower photos are top and side close-ups of the level tube, nichrome wire and associated supports. The descriptions that follow refer to numbers on the photos: (1) Granite table. (2) Base beam. Three screw-legs allow coarse leveling. (3) Tilt beam. The micrometer on the left allows fine adjustment of tilt relative to the base beam. Those two beams are connected by a sheet metal flex-hinge at the right, and tilt motion is guided by a screw at the left that goes through the tilt beam into the base beam. (4) Load beam. Pivoting on a left-end crossbar that rests on the tilt beam, the weight of this narrow board applies a constant load to the nichrome wire that crosses over the level tube. (5) Level support. This structure rests on the tilt beam, arches over the load beam without touching it, and supports the level tube at both ends. Clay blobs hold the tube firmly without clamps. Independent movement of this support and the load beam allows the nichrome wire to be positioned anywhere along most of the level tube. (6) The board cantilevered behind the level tube can hold a wristwatch to add automatic date and time information to photos or videos.
The results of these investigations are displayed in the graphs in Figures 7 and 8. Figure 7 confirms the prediction about minimum delay. The absolute minimum time for the bubble to respond appears to occur when the right bubble edge is about 2.25 mm to the right of the heating wire, but the curve has a very broad minimum. Response is rapid when 1) the heat is introduced close to an air liquid interface and 2) not far from the end of the bubble. The tube surface around the bubble is entirely wetted so that first condition is satisfied when the heat source is anywhere on or close to the bubble. Then the second condition also is satisfied when the heat source is much closer to one end of the bubble than to the other. For the situation depicted in Figure 7, rapid response is observed when the right end of the bubble is anywhere from one mm left to six mm right of the heating wire.
Maximum movement is quite different from quick response, as figure 8 reveals. When the bubble end starts further to the left of the heating wire, it takes longer for the heat pulse to reach the liquid air interface. Once it does, though, the force of excess evaporation acts longer (and probably stronger) to accelerate the system and produce an inertial overshoot beyond where the gravitational restoring force would balance the evaporative force. With our experimental parameters, maximum displacement occurs when the bubble end starts seven or eight mm left of the heating wire. At smaller distances not as much inertia is developed, and at larger distances the heat reaching the bubble interface is insufficient to keep the movement accelerating.
Note that "inertial overshoot" does not refer to the inertia of the bubble, but to the inertia of the liquid moving under the bubble in the opposite direction. When the bubble end starts to the left of the heating wire, some of the liquid moving under the bubble is already heated, and assists in producing evaporative forces; however, if too much warmed liquid moves, it could cause evaporation at the far end of the bubble that would somewhat counteract evaporation at the heated end.
Figure 7 – A constant current of 250 mA was applied to the heating wire. The time delay before the bubble started to move was carefully measured. It is graphed here as a function of the initial bubble position with respect to the position of the heating wire.
Figure 8 – A constant current of 250 mA was applied to the heating wire for one minute and then shut off. Maximum bubble displacement after the heat was applied was carefully measured. It is graphed here as a function of the initial bubble position with respect to the position of the heating wire.
During our investigations we made the discovery that the bubble could be made to oscillate with a constant heat input if the current and initial location of the heating wire were in the correct range. The oscillations have been observed to cover a distance as large as 5 millimeters. They have been sustained for longer than an hour at a time, and can likely be sustained indefinitely. These oscillations were non sinusoidal and asymmetric, but definitely periodic (see Figure 9).
Figure 9 – A graph of the oscillatory motion of the bubble when the applied heating current was in the proper range.
In the discussion that follows, the bubble started entirely to the left of the heating wire. The position of the bubble is indicated throughout this discussion as the position of the right edge of the bubble relative to the wire. Our investigations showed that the oscillations are caused by an interesting combination of fluid flow and heat flow. Small currents yielded stable bubble positions to the left of the heating wire. (The bubble moved toward the wire, but did not reach it.) Large currents led to stable bubble positions to the right of the heating wire. However, if the amount of current applied to the heating wire was in the proper range, the bubble could be forced into oscillation, thus becoming a heat engine. (See Figure 10.)
Figure 10 – A graph showing the final position of the bubble versus the heating current when the bubble started seven millimeters away from the heating wire. Note that for a range of currents (approximately 240 – 260 mA) the bubble never reached a stable position, but rather oscillated like a heat engine.
In the range of oscillation, there was initially a delay in the motion as the heat from the wire flowed through the fluid toward the edge of the bubble. Then the bubble would start to move. It moved slowly at first, then it would accelerate rapidly to the right and, due to the fluid inertia, overshoot the wire. The gravitational force would cause the bubble to slide quickly back to the left where the bubble would pause briefly just to the right of the heating wire. Then it would begin moving slowly to the left, then at a more moderate rate. As the bubble moved back toward its starting position it would slow and eventually return approximately to its starting point. After a small delay, the bubble would repeat this motion. The periodic motion could be maintained for long periods of time with a constant heat input.
CONCLUSIONS
The bubble in an ultra sensitive “spirit level” has been observed to move significantly as a result of simply shining a flashlight on the level. This surprising phenomenon seems to have an explanation that may be even more surprising: a pressure differential between the two ends of a two centimeter long bubble.
When energy is introduced at one end of the bubble level, it will be distributed to the environment in multiple directions by multiple mechanisms. Some portion of that energy will pass along the length of the level tube toward the cooler end. Of the energy passing along the tube, some portion will be transferred thru the bubble by the “heat pipe” principle – evaporation at the warmer end and condensation along the sides or at the cooler end. Our experiments and calculations show that the thermally caused bubble shift can be explained by a pressure differential within the bubble if just 9% of the total applied energy is transported by methanol evaporation.
Experiments detailing bubble response to very localized heating are entirely consistent with our hypothesis that evaporation at one end of the bubble causes a pressure differential within the bubble that results in bubble movement.
ACKNOWLEDGEMENTS
We are grateful to Penn State York students, Jennifer Diver and Zachary Miller, for their contributions to this project. We also acknowledge the assistance of Todd Hoy, lab technician at Penn State York, for providing assorted lab equipment and chemicals as needed.
REFERENCES
CRC Handbook of Chemistry and Physics (51 st Ed) pg. F 3 methyl alcohol density = 0.810 g/cm 3 pg. D 151 methyl alcohol heat of vaporization = 8978.8 cal/g mole
Ducourret SA 11 Rue de Chenival BP 29 95690 Nesles la Vallée (France) Tel : 33 1 30 34 74 50 Fax : 33 1 30 34 74 ( www.ducourret.com )
Halliday, Resnick, and Walker, Fundamentals of Physics Extended (5 th Ed.) , pg. 489 Oxygen – 483 m/s at 300 K
Jewell Instruments 850 Perimeter Road, Manchester, NH 03103 Tel: 800 227 5955 ( www.jewellinstruments.com )
Level Developments Limited Spencer Place, 97 99 Gloucester Road, Croydon, Surrey, CR0 2DN, England Tel : +44 (0)20 8684 1400 Fax: +44 (0)20 8684 1422 ( www.leveldevelopments.com )
The Merck Index (12 th Ed.) pg. 1018 methyl alcohol molecular weight = 32.04 grams