1. Miguel Ángel Sánchez Quintanilla Javier Pérez Vaquero
Measurement of electric charge in gas dispersed particles using Particle Tracking Velocimetry
Miguel Ángel Sánchez Quintanilla
Javier Pérez Vaquero
Grupo de Electrohidrodinámica y Medios Granulares Cohesivos.
Departamento de Electrónica y Electromagnetismo, Facultad de Física, Universidad de Sevilla

2. Motivation 𝐹 𝑐 ≃2𝜋𝛾𝑅 𝛾=73 mJ/m2 Capilary forces. Electric force.
𝐹 𝑒 ≃ 𝑄 16𝜋 𝜀 𝑜 𝑅 2
vdW forces
𝐹 𝑣𝑑𝑊 ≃2𝜋𝜔 𝑅 ∗
𝑅 ∗ =0.1 𝜇m
𝑊= 4 3 𝜋 𝑅 3 𝜌
Weight.
𝜌=1.5 g/cm3

3. Experimental set-up 𝐼 𝑡𝑢𝑏𝑒 (𝑡) A End of steel tube tribocharger
Venturi dispersion unit
Compressed air A
Material feeding
End of steel tube tribocharger
Fiberglass extension with glass window
High- intensity led
LED
High voltage (AC)
High speed camera and magnifying optics
High speed camera

4. Detection algorithm Background removal
Subtraction of average of all frames
Image segmentation by thresholding
Removes particles out of focus.
fr0
fr1
fr2
fr3
fr4
fr5
fr6
fr7
fr8
fr9
fr12
fr13
fr14
fr16
fr15
fr17
fr18
fr19
fr20
Particle identification
Own code based in nearest neighbours.
𝑧= 𝑧 𝑖𝑛𝑖 +𝑣 𝑧 𝑡
Trajectory linkage
ImageJ tracking tool by Sbalzarini & KoumoutSakos
Except 5-50 µm glass beads (example, the largest sample tested), other samples appear agglomerated in the images.
𝑥= 𝑥 𝑖𝑛𝑖 +𝑣 𝑥 𝑡+ 𝑥 𝑜 cos 𝜔𝑡+𝜃

5. Forces acting on a particle /agglomerate
Drag force opposing falling motion
𝐹 𝐷𝑥 =−6𝜋𝜇𝑅 𝑢 𝑧
Drag force opposing oscillatory motion
Force due to the electric field
𝐹 𝐷𝑥 =−6𝜋𝜇𝑅 1+ 𝑅 𝛿 𝑢 𝑥 −3𝜋 𝑅 𝜇𝜌 𝜔 𝑅 9𝛿 𝑑 𝑢 𝑥 𝑑𝑡
𝐹 𝐸 =𝑞 𝐸 𝑜 𝑒 𝑗𝜔𝑡
Weight
From Landau & Lifschizt, course of theoretical physics, vol 6, Fluid mechanics.
𝑊=𝑚𝑔
𝛿= 2𝜇 𝜌𝜔
Is the width of the vorticity layer due to the oscillatory motion

6. Equations and range of validity
For the vertical motion:
𝑚 𝑑 𝑢 𝑧 𝑑𝑡 =𝑚𝑔−6𝜋𝜇𝑅 𝑢 𝑧
𝑅 𝑒 𝑧 = 𝜌𝑅 𝑢 𝑧 𝜇 ≪1
Valid if
For the horizontal motion:
𝑚 𝑑 𝑢 𝑥 𝑑𝑡 =𝑞 𝐸 𝑜 𝑒 𝑗𝜔𝑡 −6𝜋𝜇𝑅 1+ 𝑅 𝛿 𝑢 𝑥 −3𝜋 𝑅 𝜇𝜌 𝜔 𝑅 9𝛿 𝑑 𝑢 𝑥 𝑑𝑡
Valid in each of these two cases:
𝑅 𝑒 𝑥 = 𝜌𝑅 𝑢 𝑥 𝜇 ≪1
Case 1:
Case 2:
𝑥 𝑜 ≪𝑅
and
𝛿≪𝑅
and
𝛿≫𝑅
Where xo is the amplitude of oscillation
For f=100 Hz in air 𝛿=223 𝜇𝑚

7. Materials      Glass beads 𝑑 𝑝 =33.9 µm
Resolution limit
Sipernat 320DS (hydrophylic)
𝑑 𝑝 =6.6 µm 
Resolution limit 
Regolith simulant 𝑑 𝑝 =9.7 µ𝑚
Resolution limit 
Sipernat D10 (hydrophobic)
𝑑 𝑝 =3.3 µm 
Milled sand 𝑑 𝑝 =4.0 µ𝑚
Resolution limit 
Resolution limit
𝑑 𝑝 is surface-weighed mean diameter.
Measured in Mastersizer Gas: air. Dispersion pressure 1 bar.

8. Relevant solutions For the vertical motion: 𝜏 𝑧 = 2 9 𝜌 𝑝 𝜇 𝑅 2
𝜏 𝑧 = 𝜌 𝑝 𝜇 𝑅 2
Velocity relaxation time:
𝑣 𝑧,𝑡𝑒𝑟𝑚 = 𝜌 𝑝 𝜇 𝑅 2
Terminal velocity:
For the horizontal motion:
𝜏 𝑥 = 𝜏 𝑧 𝜏 𝑧 𝜔 𝑅 𝛿 1+ 2𝑅 9𝛿 1+ 𝑅 𝛿
Velocity relaxation time:
Steady state phase lag with the electric field
𝜃= arctan 1 𝜔 𝜏 𝑥
Steady-state amplitude of oscillation
𝑥 𝑜 = 1 𝜔 𝑞 𝐸 𝑜 6𝜋𝜇𝑅 𝑅 𝛿 𝜔 2 𝜏 𝑥 2
An estimation of xo is needed to calculate the Reynolds number Rex. For that we need to know the typical charge per particle q.

9. Average charge per particle.
We assume the charge to mass ratio of a particle q/m is the same as that of the whole sample Q/M
Compressed air
𝐼 𝑡𝑢𝑏𝑒 (𝑡)
Venturi dispersion unit
𝑞= 4 3 𝜋 𝜌 𝑝 𝑅 3 𝑄 𝑀
𝑄= 𝑡 𝑖𝑛𝑖 𝑡 𝑒𝑛𝑑 𝐼 𝑡𝑢𝑏𝑒 (𝑡) A
Material feeding 𝑀
The largest uncertainty comes from the value of the dispersed mass M.
We use the value of the surface-volume mean diameter for R.

10. Average charge per particle vs. particle surface-mean diameter
Experiments with continuous flow
𝑞 𝑑 =4𝜋 𝜖 𝑜 𝑅 2 𝐸 𝑐
Ec=30 kV/cm
𝑞 𝑑 ≃6.67× 10 −6 𝑅 2
(qd in pC, R in µm)
𝑞 𝑑 ≃3.33× 10 −4 𝑅 2
(qd in pC, R in µm)
PTV experiments (pulsed flow)

11. Check on validity for the surface volume mean diameter.
Reynolds number
Typical times to achieve steady state.
Using the surface-volume mean diameter both conditions are met.
Plots for p=2.5 g/cm3 Eo=3.4 kV/cm

12. Relevant solutions Amplitude of oscillation Phase lag with the field
𝑥 𝑜 = 1 𝜔 𝑞 𝐸 𝑜 6𝜋𝜇𝑅 𝑅 𝛿 𝜔 2 𝜏 𝑥 2
𝜃= arctan 1 𝜔 𝜏 𝑥
Markers represent values for surface-mean diameter. Experiment yield a distribution of values.
Plots for p=2.5 g/cm3 Eo=3.4 kV/cm

13. Size determination from images
To evaluate the electric charge of each particle we need to know its radius R. Two options are possible:
Circular equivalent diameter.
Calculated from the number of pixels Np of each particle in the image.
𝑅 𝑐𝑒
𝑅 𝑐𝑒 =Δ 𝑥 𝑝 𝑁 𝑝 𝜋
𝐴=𝜋 𝑅 𝑐𝑒 2
xp = 7.4 µm/pixel is the resolution of our images
Aerodynamic diameter.
𝑅 𝑎𝑒
Terminal velocity assuming Stokes drag:
Calculated from the vertical velocity vz of the particle.
𝑣 𝑧,𝑡𝑒𝑟𝑚 = 𝜌 𝑝 𝜇 𝑅 𝑎𝑒 2
𝑅 𝑎𝑒 = 9𝜇 𝑣 𝑧 2𝑔 𝜌 𝑝
𝑣 𝑧,𝑡𝑒𝑟𝑚
𝑣 𝑧,𝑡𝑒𝑟𝑚

14. Sizing glass beads 5-50 µm
Vertical velocity vs. Circular equivalent diameter.
Size distributions
No. of particles analyzed: 708 (goodness of fit r2>0.6)
𝑑 𝑝 =33.9 µm, p = 2.5 g/cm3

15. Sizing Regolith simulant
Vertical velocity vs. Circular equivalent diameter.
Size distributions
No. of particles analyzed: --- (goodness of fit r2>0.6)
𝑑 𝑝 =9.7 µm, p=2.9 g/cm3

16. Sizing milled sand Vertical velocity vs. Circular equivalent diameter.
Size distributions
No. of particles analyzed: 2009 (goodness of fit r2>0.6)
𝑑 𝑝 =4.0 µm, p = 2.5 g/cm3

17. Sizing sipernat 320 DS
Vertical velocity vs. Circular equivalent diameter.
Size distributions
No. of particles analized: 305 (goodness of fit r2>0.6)
𝑑 𝑝 =6.6 µm, p = 2.5 g/cm3

18. Sizing sipernat D10
Vertical velocity vs. Circular equivalent diameter.
Size distributions
No. of particles analyzed: 3616 (goodness of fit r2>0.9)
𝑑 𝑝 =3.3 µm, p = 2.5 g/cm3

19. Election of the sizing procedure
For all samples, specially the ones with smaller particle size, the circular equivalent diameter measured from the images tends to overestimate the size of the particles.
PSD of the circular equivalent diameter appear shifted to larger sizes compared from PSD from Mastersizer and aerodynamic diameter.
The measured vertical velocity of the particles is always smaller than the value expected from their circular equivalent diameter.
For these reasons we use the aerodynamic radius to substitute in the calculations.

20. Glass beads 5-50 µm Amplitude of oscillation
Phase with respect to the field
No. of particles analyzed: 708 (goodness of fit r2>0.6)
𝑑 𝑝 =33.9 µm, p = 2.5 g/cm3

21. Regolith simulant Amplitude of oscillation
Phase with respect to the field
No. of particles analyzed: --- (goodness of fit r2>0.6)
𝑑 𝑝 =9.7 µm, p=2.9 g/cm3

22. Milled sand Amplitude of oscillation Phase with respect to the field
No. of particles analyzed: 2009 (goodness of fit r2>0.6)
𝑑 𝑝 =4.0 µm, p = 2.5 g/cm3

23. Sipernat 320DS Amplitude of oscillation
Phase with respect to the field
No. of particles analized: 305 (goodness of fit r2>0.6)
𝑑 𝑝 =6.6 µm, p = 2.5 g/cm3

24. Sipernat D10 Amplitude of oscillation Phase with respect to the field
No. of particles analyzed: 3616 (goodness of fit r2>0.9)
𝑑 𝑝 =3.3 µm, p = 2.5 g/cm3

25. Charge distributions
All materials show a charge distribution spanning of both polarities
5-50 glass beads
Regolith simulant
Milled sand
Sipernat 320DS (hydrophylic)
Sipernat D10 (hydrophobic)

26. Overall charge distribution
𝑞=6.67× 10 −3 × 𝑅 2

27. The following slides represent results vs. circular equivalent radius

28. Glass beads 5-50 µm Amplitude of oscillation
Phase with respect to the field
No. of particles analyzed: 708 (goodness of fit r2>0.6)
𝑑 𝑝 =33.9 µm, p = 2.5 g/cm3

29. Regolith simulant Amplitude of oscillation
Phase with respect to the field
No. of particles analyzed: --- (goodness of fit r2>0.6)
𝑑 𝑝 =9.7 µm, p=2.9 g/cm3

30. Milled sand Amplitude of oscillation Phase with respect to the field
No. of particles analyzed: 2009 (goodness of fit r2>0.6)
𝑑 𝑝 =4.0 µm, p = 2.5 g/cm3

31. Sipernat 320DS Amplitude of oscillation
Phase with respect to the field
No. of particles analized: 305 (goodness of fit r2>0.6)
𝑑 𝑝 =6.6 µm, p = 2.5 g/cm3

32. Sipernat D10 Amplitude of oscillation Phase with respect to the field
No. of particles analyzed: 3616 (goodness of fit r2>0.9)
𝑑 𝑝 =3.3 µm, p = 2.5 g/cm3

33. Charge distributions
5-50 glass beads
Milled sand
All the data show a distribution with particles of both polarities
Sipernat 320DS (hydrophylic)
Sipernat D10 (hydrophobic)
Regolith simulant