fly your thesis! 2012 final report - european space...

Fly Your Thesis! 2012 – Final Report 1

Fly your Thesis! 2012

Final Report

Team Name: Dustbrothers Experiment Name: Levitation of sintered glass plates by the

Knudsen Compressor Effect

1. Executive Summary If a porous solid is subject to a temperature gradient, gas flows from the cold to the warm side at low ambient pressure. This can lead to a pressure build-up at the warm side, called Knudsen compressor due his pioneering work on this at the beginning of the 20th century. The dynamic of this effect was not yet investigated, so we proposed and conducted this experiment during the 57th ESA parabolic flight campaign in October 2012 via the Fly Your Thesis! programme. A parabolic flight campaign consists of three flight days with 31 parabolas each day. Every parabola has 20 seconds of microgravity – so in total we had over 30 minutes of microgravity measurement time. In microgravity we have investigated the force induced by the Knudsen compressor effect on a sample plate consisting of sintered glass beads (see figure 1), thus being very porous.

Figure 1: Picture of a whole sintered glass plate next to a centimeter scale We quantified this force and especially the pressure dependence by measuring the residual gravity at the instant a plate begins to lift. We used samples of different total plate size (2.2 cm and 3.5 cm) and constituent bead size (150-200µm and 40-70µm) on the different flight days, and varied the ambient pressure in a range between 10-2 to 10 mbar between parabolas. The plates were initially in contact with a hot Peltier element with a temperature of 100 °C. A second Peltier element was set to a temperature of 0°C, providing the


necessary temperature gradient. Around the Peltier elements was a housing so that the sample could not escape the measurement area. The plates were observed by a video camera. The images for lift-off were correlated to the residual gravity. For two samples we found a significant force but not to a level which allows a pressure dependence to be seen within the uncertainties of the data. However, one sample clearly shows the pressure dependence and especially one as expected from theory. For the samples studied the maximum force induced by the Knudsen Compressor Effect was about 40 µN on a sample of 2.2 cm diameter. The force peaks at two values related to the total size of the plate (peak at ~1·10-2 mbar) and the size of the particles (peak at 1 mbar). The pores strongly increase the force on a plate in a temperature gradient field.

2. Student Team Description Our team – the Dustbrothers consisted of three physics students from the University of Duisburg-Essen: Caroline de Beule, Christoph Dürmann and Markus Küpper (from left to right on the picture below taken by ESA (J.Makinen).

Figure 2: Dust brother team: Caroline de Beule, Christoph Dürmann, Markus Küpper (left to right)

During selection Alexander Hesse was part of the team, but he had to pursue other goals and left the team. Gerhard Wurm was the endorsing professor with prior experience in parabolic flights. Caroline was the team leader as she was already a PhD student as the campaign began. Christoph and Markus finished their master thesis just before the flights. Christoph’s master thesis was on related measurements of the Knudsen compressor force on channel plates taken under gravity with a torsion pendulum. Markus took care on the technical documentation.


3. Project Description

3.1. Scientific Motivation

The process in which planets are formed is not understood with every detail. The Knudsen effect plays an important role in protoplanetary disks [6], where dust grows by coagulation to planetesimals and planets. Results of the experiment help for a better understanding of transport mechanisms in those disks, where porous material or dust is transported away from a (thermal) radiation source (see figure 3).

Figure 3: Transporting porous bodies in a protoplanetary disk by the Knudsen effect. The particles coagulate and sedimentate. Due to gas friction they experience an inward drift. Yet the Knudsen Compressor may be able to stop this drift or even to push the aggregates further out again.

A meter size body, for example, can drift 1 AU in 100 years inward. If it is accreted by the star, it is lost for further process of planet formation. Hence, the Knudsen effect of transporting porous material can prevent material from being accreted by star by diminishing the drift velocity or even pushing the body outwards again.

3.2. Scientific Objectives

In this experiment the Knudsen compressor effect on porous plates was investigated. Knudsen reported this effect first [1], as he found a pressure difference between two


chambers connected by a capillary smaller than the mean free path of the gas molecules if this capillary was heated on one side. This is due to the fact that gas in a short boundary layer of a solid surface moves from cold to warm. This effect was already used to levitate dust over a hot surface like a hovercraft (see figure 4). By this the quasi steady state is left and the dynamic of this process become important. The main aim of this experiment was to study the dynamics, the forces which occur due to the Knudsen compressor effects.

Figure 4: A dust aggregate is placed on a slightly concave heater placed in a vacuum chamber which is evacuated to pressures of 10 mbar. The heater is set to T2 > 400 K. Thermal radiation cools the surface of the aggregate to T1. The aggregate is levitated by a pressure difference Δp established through the Knudsen compressor effect. [2]

Figure 5: Levitation of a 1.2 mm SiO2 at 2 mbar and ~800 K heater temperature. The levitation height is about ~100 µm. [2]

3.3. Scientific Background

To understand these effects the mean free path is the important key. The gas molecules often collide, transferring energy and momentum with each collision. The mean distance they travel between these collisions is the mean free path. So if the capillary diameter gets smaller than the mean free path, it becomes likely that they only collide with the walls and not with other atoms. In a simple picture the Knudsen effect can be explained by the fact, that the molecules tend to leave the wall in a direction biased to the warmer side. If they collide during their flight this bias gets lost quickly, hence this effect is stronger at low pressures, where the molecules are further apart and collide less often.


A similar effect is seen in the famous light mill constructed by Crookes in 1874 [3] (see figure 5). Here, a macroscopic particle moves as reaction to the gas flow induced by illumination. This motion due to illumination is called photophoresis.

Figure 6: Light mill: Inside a glass bulb is a low pressure environment, where vanes can rotate on a spindle. One side of each vane is black, the other is silver or white. Illuminating the light mill leads to a rotation with the black sides in the back due to photophoresis.

Photophoresis is strongly pressure dependent and works best if the mean free path of the molecules is comparable to the object. Therefore, at high pressure in Earth atmosphere with a mean free path of 70 nm at 1 bar it is not important for macroscopic objects. However, as seen in the light mill at reduced pressure, it can be quite significant. In fact in low pressure protoplanetary disks – a motivation for this work – the photophoretic force can be orders of magnitude larger than stellar gravity. The pressure dependence of the photophoretic force for a spherical particle is given over the entire pressure range by Rohatschek [4] with a characteristic maximal force and a optimal pressure where the force is reached:

2

The Force becomes maximal when the characteristic size of the body equalls the mean free path. For a porous body it was not clear on which size the photophoretic force or Knudsen compressor force depends on, the overall size of the plate or the size off the individual pores. If the capillary (pore space) is on a comparable length scale as the mean free path of the surrounding gas, the effect on the pores become important. These effects were largely overlooked, but became more important again, as by the miniaturisation of devices the length scales employed there became comparable to the mean free path length, or in the context of astrophysics, where the conditions are often such that this effects may play a role. For example Wurm and Krauss [5] introduced photophoresis as a mechanism for size sorting material in the solar nebula.


The main aim was to study the force on porous solids as initial step to see how it influences our understanding of planet formation. By using a plate from sintered glass beads and examining the movement of this plate in microgravity the force of the Knudsen compressor effect was measured for a defined sample.

3.4. Experimental Set-up

a. 3.4.1 Overview

Figure 7: Schematic design of the rack. The main part is the vacuum chamber

(details in figure 8). It was placed in the plane with the lower side of the rack to the wall. Two operators could run the experiment from both sides.

The whole experiment was mounted on a single rack as it is shown in figure 7. To achieve the needed pressure, a vacuum system was implemented. Here a turbo molecular pump with a membrane pump was used to evacuate the chamber. To measure the temperatures of the Peltier elements and the surrounding system a Digital Multi Meter (DMM) was used. The pressure and g-data was recorded via a DAQ, which also was used to set the power supply voltage via an interface on the laptop. The laptop was also used to record the camera pictures of the chamber.

DAQ

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pump

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Chamber with cooling units


3.4.2 Inner Chamber The setup consisted mainly of a vacuum chamber, in which - by means of two Peltier elements – a temperature gradient could be set (figure 8). There was a housing around the area between the Peltier elements to confine the sample to that area and the sample and a tracer particle could be observed by a high speed camera outside the chamber. Around this the vacuum system was built to achieve different pressures down to 10-2 mbar. Furthermore a temperature control was added to measure the temperature of the Peltier elements and the cooling units the Peltier elements needed. All this was displayed at a laptop which was mounted on top of the experiment. The pressure could be changed by adding gas ballast at the pump to get to a static equilibrium pressure or switching the pump of at higher pressure and filling the chamber to a desired pressure. During the parabolas the plate was observed with a camera, at 60 frames per second. A sample frame is shown in figure 6.

Figure 8: Experimental setup. The sintered glass plate is additionally put on the warm Peltier element at the bottom of the chamber. There are also LED lights on the left and right of the camera, illuminating the inner part and making reflections on the inner window as seen in figure 9.


Figure 9: Picture of the first-flight-day sample inside the chamber. The plate is about

to leave the Peltier element below, which is heated. The upper Peltier element is cooled and in a distance of 50 mm to the other one. The bright marks on the window

are reflections of the LED lights.

3.5. Samples

We used three different samples, to see the influence of the overall size and the constituent bead size, all with the same thickness of 1.7 mm. The properties of the plates are displayed in table 1. The samples were sintered from sandblast material, which are µm sized glass beads. To get well defined sizes, templates of defined thickness and diameter were filled with the glass beads. The sinter temperature and time was experimentally adapted that the resulting samples were not prone to breaking, but still sintered well enough to have pores (see figure 11).

Flight day Ø [cm] sintered@ sphere Ø[µm] Mass [g] 1 3.5 700°C,3.5h 150-200 2.29 2 2.2 650°C,3.5h 150-200 0.72 3 2.2 650°C,3h 40-70 0.66

Table 1: The samples flown during the parabolic flight


Figure 10: Microscopic picture of the edge of a sintered glass sphere. Because

it becomes thinner at the edge, single glass spheres are visible.

3.6. Experimental Procedure During each parabola a different pressure was set and the movement of the plate was observed. As we had 31 parabolas with a middle break after 15 parabolas where we could change the sample – if needed, we choose to set 16 Pressures between 10-2 to 102 mbar – equally distributed on a logarithmic scale, so the measurement was complete at the middle break and could either be done again with a new sample or with the old sample for better statistics. (The highest pressure was recorded only at the first half, as there were only 15 parabolas after the middle break.) One operator had to set the pressures according to this schedule in between parabolas. The second operator was observing the temperatures and managing the saving of the camera stream. As the plate was solid enough to be used the whole flight we adapted our procedure and measured the range twice to get better statistics and to avoid changing the sample. Combining the acceleration of the plate with the residual g-data the force on the plate due to the Knudsen Compressor Effect could be calculated. We looked especially for the detachment of the plate from the surface, as this moment could easily be searched for automatically. The g-data and the camera frames had both the timestamp of our laptop - we didn’t have to synchronise our g-data, therefore we could precisely determine at which g-level the plate began to move. At this point the force due residual gravity and Knudsen compressor effect had to be equal, the force could be determined by multiplying the acceleration with the mass of the sample.


4. Parabolic Flight Campaign

4.1. Preparation Week

Our experiment worked well, and was in a ready to flight configuration on arriving at the side, as it was small enough to transport it in one piece. Only the regular safety tests and a quick check if all components had survived the journey had to be done – the DAQ had to be changed as it did not start up every time, but it was easily accessible and the spare one worked fine. This was followed by the normal procedure of cleaning the rack, protecting all edges with foam, and loading the rack. The experiment was loaded on Wednesday and all checks were repeated. Therefore the week dedicated for preparation was quite relaxed as all test showed that everything was working as expected and no changes were needed. As the sample preparation was done at our lab, we had an easy preparation week.

4.2. Flight Week

The flight week scheduled 3 consecutive flight days, a reserve flight day if the weather conditions or any problem should prohibit a flight and a day for unloading and departure. Each flight day had 31 parabolas with approx. 20 seconds of microgravity. Between the parabolas there were short breaks of 2 minutes. A 5 minute break after every 5 parabolas and an 8 minute break in the middle. Our worst case expectation was that a sample could break during the flights, as we would not be able to change the sample except in the long middle break, potentially loosing al the parabolas between the breaking and the opportunity to change. But all previous tests (dropping the plate in vacuum several times on a hard surface, dropping the plate from 1 m height at ambient pressure) on the ground suggested that the plates should be able to sustain the conditions they would experience during the flight, and they did. The flight procedure was as simple as possible: One operator had to monitor the temperatures and operate the laptop to save the video files. The other operator was responsible to monitor and set the pressures. All the work could be done during normal gravity, as working under 2g conditions may induce motion sickness and under zero-g fine handling is difficult due to the weightlessness and would interfere with our measurements. Because of this procedure no operator got motion sick. In the flight week we had three samples (and some backups) chosen to fly, one sample and 2 backups for each flight day. We kept the sample for the whole flight – as the plate was robust enough to withstand the flight without a sign of fatigue - and we were able to get better statistics for the measurement. On the first day it became clear that the large sample tended to be leaning to the walls instead of lying flat which gave less well defined temperatures and made the take-off harder to detect as the plate moved before taking off, because of this we flew the smaller samples on the following days, which proved to be better. The video data was recorded during the parabolas. The g-data, temperatures and pressures were recorded during the whole flight, as the temperatures had to be constantly monitored. As this data filled our solid state drive more than half, each day the laptop was taken home and the data was transferred to two external hard drives and then deleted from the laptop


for the following day. The first thing to do on arrival for the next flight day was of course to fix the laptop to the rack again, this was done by the team member not flying this day, as the other two got their flight medication and briefing.

5. Scientific Results

5.1. Collected Data

The experiment worked the whole flight, so we had 95 Parabolas (as there were two additional parabolas on the last day because of the bad weather conditions some of the others were out of the quality limits promised by Novespace) collected video-material. Additionally we had the pressure-, temperature- and g-data. As every parabola is about 20 seconds and we had 60 frames per second this were more than 100000 Images to evaluate.

5.2. Data Processing and Analysis

We first reduced the video data to the timespans when the plate started moving. This was done by a short algorithm which calculates differential pictures between two frames. If there is movement the brightness of the pixels will change when the white plate moves over the darker background. On difference images only this change will be visible as bright pixels. So by determining the mean grey level it can be seen whether something is moving. This is demonstrated in figure 12.


Figure 12: Example of the difference analysis. Two pictures were taken and the difference was calculated. The difference is shown in the 3rd picture with stretched contrast. The mean grey value of the first difference picture is 0.835 the second has a mean grey value of 1.18. This is enough difference to distinguish between a static phase and a moving phase. With an adapted threshold of 1 second without much movement and a mean grey value trigger of 1, the beginning of the new movement was recorded. These frames were then analysed manually to see if the plate was really detaching or if other influences induced a false triggering. If it detached the corresponding g-data and pressure at that time were taken as a data point. By this means we got 118 data points, 39 for the first sample 35 for the second and 44 for the third.

5.3. Results 5.3.1 Pressure dependence

We have measured the residual gravitation at the point the plate lifts off from the surface, this simply equals the force of the Knudsen compressor as there are only the Knudsen force and the gravity acting on the plate. The data was binned into pressure bins according to the pressures set – the pressure could be set with an accuracy of about 1%. This error was negligible, so we had several measurements with the same pressure. From these measurements at a single pressure we


calculated the mean acceleration. The variance in the acceleration was on the order of 0.01 g. This may come from the uncertainty of the exact time of the lift off and the correlation of this time to the residual gravity. Only for the sample on the second flight day the plate propulsion was large enough to see the pressure dependence clearly – this may be explained by the fact that on the first day the plate tended to lean to the wall and therefore only had a reduced temperature gradient. But for the last day one can only speculate whether the flight conditions or the small bead size or another issue reduced our signal. Along with the data a fit is shown. For simplicity reasons the error bars are left out, as the individual measurements consists from different amount of data and therefore the variation strongly depends on the small statistics. The fit is chosen due to the pressure dependence of the photophoretic force given by Rohatschek (1995), where p is the pressure and g the acceleration. There are two peaks corresponding to the plate but also the bead size, hence two force components were employed. The fit parameters a and c are the maximal accelerations and b and d are the optimal pressures for one of the components. The fit result is displayed in table 2, the parabolic flight data in figure 13-15.

2 2

Figure 13: Acceleration at detachment over pressure for sample #1 [7]

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Parameter value sdt. error a (max. acceleration) 0.057 g 0.007 g b (optimal pressure) 0.025 mbar 0.006 mbar c (max. acceleration) 0.040 g 0.005 g d (optimal pressure) 4.0 mbar 1.0 mbar

Table 2: Fit results for the fit depicted in figure 14 [7]

5.3.2 Optimal Pressure

The dependence of the optimal pressure on the pore size and depth was investigated. The dependence was fitted as a power law of thickness and size: , where r is the radius and l the length of the pore [8].

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The fit yielded . . , over a wide pressure range and different experiments, as can be seen in figure 16.

Figure 16: Optimal pressure over the characteristic length scale of a particle

or pore. The diamonds are the parabolic flight measurements [7] triangles from [9]. [8]

5.4. Fulfilment of Scientific Objectives

Our goal was to measure the strength of the Knudsen compressor effect and its pressure dependence only having an order of magnitude estimate on the force before. We measured a significant force of 43 µN at the optimal pressure plate and of 29 µN for the pores (though partially with low signal to noise ratio). However, we also could observe – for the first time ever – a force related to the porosity of the plate and being consistent with expected pressure dependence. The force due to the pores is nearly as strong as the force on the particle without pores. Hence, this experiment shows that this force has to be considered, too. Therefore the experiment was very successful. Sadly the signal to noise ratio and our measurement procedure did not allow seeing the pressure dependence for the other two samples, partly because they did not work this well and partly as the optimal pressures might be outside of the estimated pressure range. In fact the campaign was so successful that we are currently preparing one paper dedicated to this campaign [7] and the results have been included in a second paper [8], where also the results of the master thesis


by Christoph Dürmann have been incorporated. In this case “Fly your thesis” literally worked.

5.5. Future Work As the project idea turned out to be successful and absolute forces could be measured, parameter variations are now possible to be carried out in future experiments, i.e. particle size, particle material, thickness and shape of the plates etc. The data gathered on the parabolic flight are first step to a possible systematic study and applications to the motion of large porous bodies in protoplanetary disks during the planet formation process.

6. Conclusions

This experiment showed that the porous structure is important for the forces acting on a particle and cannot be neglected. Yet this is only for a plate of 22 mm diameter and 1.7 mm thickness, therefore one has to be cautious to extrapolate this effect to a spherical object. As a second result it seems, that Knudsen effect and Photophoresis show the same pressure dependence, which was not necessarily expected. If there is a hole in a body or if there is a body of this size with the same temperature, the resulting force is the same.

7. References

[1]Knudsen, M. (1910). Eine Revision der Gleichgewichtsbedingung der Gase. Thermische Molekularströmung, Analen der Physik, 336, P. 633-640.

[2] T. Kelling, G. Wurm, PRL 103, 215502 (2009) [3] Crookes, W. (1874). On Attraction and Repulsion acompanying Radiation,Philosophical

Magazine Series 4,48,P. 81-95 [4]Rohatschek. (1995). Semi-empirical model of photophoretic forces for the entire range

of pressures,Journal of Aerosol Science,26,P.717-734 [5]Wurm, G. and Krauss O. (2006). Concentration and sorting of chondrules and CAIs in

the late Solar Nebular. Icarus, 180, P. 487-495. [6]Blum, J. and Wurm, G. (2008). The growth mechanisms of macroscopic bodies in

protoplanetary disks. Annual Review of Astronomy and Astrophysics, 46, P. 21-56. [7]Küpper, M., de Beule, C. , Dürmann, C., Wurm, G., Propulsion of Porous Plates in Thin

Atmospheres and Temperature Fields, Microgravity Science and Technology, (in prep.)

[8] Duermann, C., Wurm, G. and Kuepper, M., Radiative Forces on Macroscopic Porous Bodies in Protoplanetary Disks: Laboratory Experiments, Astronomy and Astrophysics, 558, A70, 2013.

[9] Selden, N., Ngalande, C., Gimelshein, S., et al. Area and edge effects in radiometric forces, Phys. Rev. E, 79, 041201, 2009

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