Measurements had to be done first. As an example for the results of our measurements we want to show you two diagrams. The measurements were quite difficult, because there were lots of fluctuations. So the results are only average values.
This diagram shows the dependence of the current from the horizontal distance of the electrodes.
This diagram shows another example of our measurements.
After our measurements we drew the following conclusions:
Now we want to show you, what we found out about the influence of these parameters.
Let's start with the gas flow:
For our research on gas flow, we "recycled" a theory and measurement results from the previous year. For those who can't remember: In the 12th IYPT the problem no. 13 "Gas flow" concerned the gas flow in the flame of a candle. So we now show you what we found out one year ago:
This sketch shows you, how we measured the gas flow:
left mass: 2g; right mass: 1g; connected with a circular Al - plate (in the flame: Fe - plate); Temperature measurement with Pt-100 or thermocouple
The streaming force FStr is an upward force on the right mass which produces an additional downward force on the electronic scales. This causes the scales to show a higher weight, so FStr can be calculated using this "mass difference".
With the streaming force we are able to calculate the velocity of the gas flow using this formula:
|Cw = 1,1 (for circular plates)
A = r2.p (area of the circular plate)
FStr ... has been measured
rho ... density of air: calculated (see following)
Calculation of air density: using the ideal gas equation
calculation of the molecular weight M:
values from literature: air at 0°C, 1 bar: r = 1,293 [kg/m3]
This diagram finally shows the result of the gas flow measurements: Velocity of the flow versus the vertical distance from the flame:
Furthermore we considered some theory about plasma. Useful statements can only be given about a balance plasma. For a balance plasma, 3 distributions have to be fulfilled:
We wanted to find out, how many molecules are ionised. In order to calculate the minimum velocity for ionisation through hits, we set the ionisation energy equal to the kinetic energy of a molecule.
After having calculated the minimum velocity, we used the Maxwell distribution to calculate the fraction x of molecules which are faster than the minimum speed.
It is possible to calculate this for each kind of molecules in the plasma. Here are two results for example:
results: e.g. for O2: x = approx. 3.10-64; for N2: x = approx. 9.10-91
As you can see the fraction of ionised molecules is so small that it is possible to neglect it.
The Saha equation indicates the ionisation balance between the electrons and the ions versus neutral particles:
Also this equation proofs that there are actually no ions in the plasma.
The electric field causes electrons to drift through the plasma with a current density j:
Moreover we used some formulas which we found in literature.
|Ne||number of electrons|
|E||electric field strength|
|me||mass of the electron|
|t||average time between 2 hits|
|µ||mobility of the electrons|
|lambdae||free distance between 2 hits|
|ve||average speed of the electrons (Maxwell distribution)|
Using the shown formula, we can proof that the conductivity is proportional to one divided by squareroot of the mass.
By taking an element with an average mass from the periodic system of the elements we can show that the share of ions of the current is smaller than 0,4 %.
So we can restrict ourselves to the consideration of drifting electrons only.
The Richardson-Dushman equation indicates, how many electrons are emitted by the electrodes.
The Richardson-Dushman equation shows only the influence of the temperature and does not consider the point effect!
The electric field also causes the electrodes to emit electrons, as it is indicated by the Fowler-Nordheim equation.
It shows that the current density is proportional to the electric field strength squared times Euler's number to the minus one divided by the field strength.
To determine the electric field strength we made a computer simulation. The following plots shall give you an idea how the field depends on the shape and arrangement of the electrodes.
Click on a thumbnail to enlarge...
|Field between a point electrode and a spherical electrode.|
|Field on the surface of a spherical electrode.|
|Potential distribution on the surface of two needel electrodes.|
|Field between two spherical electrodes (quarter of the symmetry)|
In conclusion the following things have to be said: The connection between our experiments and our theory is not possible. The current is determined by so many parameters which correlate so much that it is not possible to measure the dependence of the current from one single parameter. Therefore there can be no real connection between theory and experiments. Moreover, the phenomenon is much too complex so that there can be no final solution formula which describes the behaviour of the current.