The Equations of Tribocharging

1. The Equations of Tribocharging Brian Young 26 January 2009 Reference: “The Static Electrification of Particles in Gas-Solids Pipe Flow” – Komatsu, 1976

2. Fundamental Equation • Equation defines the average charge/mass ratio • Essentially linear when n(x) is much smaller than n0 • Asymptotically approaches maximum ratio • Previous work shows us our target is around 0.1-0.5 C/kg

3. Maximum Charge

4. Relaxation Collision Number Number of collisions representing the ‘knee’ in the curve. Defines the scale of collisions required to achieve maximum charge.

5. Simplified Form Assuming

6. Contact Potential (or Volta or Electrostatic Potential) Reference: “The Origin of the Thermoelectric Potential” – J. Jackle, University of Konstanz http://www.uni-konstanz.de/FuF/Physik/Jaeckle/papers/thermopower/node4.html

7. Surface Contact Area and Deformation

8. Time constants Assume travel time is around 4 times the required for particle to travel the deflection distance.

9. Velocities • System should be designed to create a large amount of turbulence, and also be dense enough to carry the particles • Gas velocity is a design variable • Assume all velocities equal to gas velocity • Equations in paper experimentally verified between 10 and 30 m/s

10. Impact Number • We must define the function n(x). • Assume a linear function, defining a number of bounces per meter • Assuming the particles move at 45 degree angles on average, this implies that dn/dx is approximately equal to 1/D. • Turbulence and inter-particle bounces may increase this to around 10/D. • Thus n(x)= 10x/D

11. Point Design Parameters • A 1-meter by 1mm tribotube • Nylon tube with 100-micron Teflon powder • Nitrogen Gas flowing at 20 m/s • 0.01 kg/s (approximately 1 pound/minute) mass flow rate • Assume e=0.3? • Assume z0 = 5e-10 meters

12. Material Properties • Nylon • 1150 kg/cubic meter density • 4.08 eV Work function • 45 MPa Yield stress • 1e12 ohm-meter specific resistance • 4.5 dielectric constant • Teflon • 6.04 eV work function • 1e16 ohm-meter specific resistance • 2.1 dielectric constant • 23 Mpa • 2200 kg/cubic meter density • Nitrogen • 1.251 kg/cubic meter density • 8.85e-12 F/m dielectric constant

13. Derived Quantities • Impact surface area: 1.38e-11 square meters • Impact distance: 7.6 microns • Impact time period: 2.9e-7 seconds • Relaxation time: 1.9e5 seconds • Contact potential: 2 Volts • Number of bounces: 10,000 • Powder/gas mass ratio: 314 • Maximum charge: 0.21 C/kg • Relaxation number: 1.426e11 bounces

14. Final results • Final charge ratio is 1.5e-8 C/kg • The final result is nowhere near the level we need • In order to get up to the desired level, we need 1000 km of travel

15. Alternative Design

16. Conclusions • Not perfect, but we have equations to work with to size to within an order of magnitude • Experiments required for further design • Teflon is not a good choice due to high specific resistivity • Instead consider Polypropelene (or something else from this region of the triboseries) • Work function: 5.8 eV • Density: 905 kg/cubic meter • Yield Stress: 25 Mpa • Specific Resistance: 8.5e12 ohm-meters • Dielectric constant: 2.2 • Max charge: .16 C/kg • Relaxation Number: 1.1e8 • Should require closer to 10-100 meters