3 = JKR F W d Pull- -Off Force Off Force Pull Contact - - PowerPoint PPT Presentation

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3 = JKR F W d Pull- -Off Force Off Force Pull Contact - - PowerPoint PPT Presentation

! Static Equilibrium ! Static Equilibrium ! Hydrodynamic Forces and Torque ! Hydrodynamic Forces and Torque ! Adhesion Forces for Bumpy Particles ! Adhesion Forces for Bumpy Particles ! Electrostatic Forces ! Electrostatic Forces ! Capillary


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! ! Static Equilibrium Static Equilibrium ! ! Hydrodynamic Forces and Torque Hydrodynamic Forces and Torque ! ! Adhesion Forces for Bumpy Particles Adhesion Forces for Bumpy Particles ! ! Electrostatic Forces Electrostatic Forces ! ! Capillary Forces Capillary Forces ! ! Rolling and Sliding Removal Rolling and Sliding Removal ! ! Critical Detachment Shear Velocity Critical Detachment Shear Velocity

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⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π + π + π + =

2 A A A 3

2 d W 3 dP W 3 2 d W 3 P K 2 d a

( ) ( )

1 2 2 2 1 2 1

E 1 E 1 3 4 K

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ν − + ν − =

Contact Radius Contact Radius

Spherical Particles Spherical Particles

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Pull Pull-

  • Off Force

Off Force Contact Radius Contact Radius at Separation at Separation

d W 4 3 F

A JKR po

π =

3 1 2 A

K 8 d W 3 a ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ π =

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SLIDE 2

2

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Schematics of a Schematics of a Bumpy Particle Bumpy Particle

d

β 2

N n n d

b u

= β

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Adhesion Force Adhesion Force Per contact Bump Per contact Bump

β π =

A JKR po

W 2 3 f

β π =

A c JKR ad

W N 2 3 F

Total Total Adhesion Adhesion Force Force

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Capillary Force Capillary Force Per Contact Bump Per Contact Bump Total Capillary Total Capillary Force Force

πσβ = 4 fc

c c

N 4 F πσβ =

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Boltzmann Boltzmann Charge Charge Distribution Distribution

∞ + −∞ = − −

=

n dkT e n dkT e n

2 2 2 2

e e f(n)

d 37 . 2 n ≈

Average Number Average Number

  • f Charge
  • f Charge
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SLIDE 3

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Diameter Neutral Fraction Average Absolute Number of Charges d (µm) f(0) 5 0.0606 5.29 10 0.0428 7.46 15 0.0349 9.17 20 0.03 10.55

Boltzmann Boltzmann Charge Distribution Charge Distribution

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Diffusion Charging Diffusion Charging

) t N e kT 2 c d 1 ln( e 2 dkT n

i 2 i 2 diff

π + =

Field Field Charging Charging

e 4 Ed 2 3 n

2 field

+ ε ε =

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Diameter Number of Charges

d (µm) Diffusion Field Combined 5 407 4340 4747 10 874 17361 18235 15 1365 39062 40427 20 1870 69444 71314

Diffusion and Field Charging Diffusion and Field Charging

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{

4 43 4 42 1 3 2 1 4 3 4 2 1

  • n

Polarizati 4 2 6

  • horetic

dielectrop 3 3 age Im 2

  • 2

Coulomb e

y E d 128 3 y 16 qEd y 16 q qE F πε − + πε − =

Spherical Particles Spherical Particles

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SLIDE 4

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Charge Charge

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2 2

  • 2

/ 3 2 b 2 2 2 b 2 2

  • 2

e

E 72 ) 1 n 4 ( 3 ) N / 3 )( 1 n 4 [( d ) N / 3 1 ( 4 q qE 5 . 1 F β πε − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + β + + − πε − − =

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V C dC f 3 F

c d t

µ π =

Drag Force Drag Force

687 . d

Re 15 . 1 C + =

( )

2 1 2 1 2 l

dy dV dy dV V d 61 . 1 F ρµ =

Lift Force Lift Force

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Hydrodynamic Hydrodynamic Torque Torque

c 2 m t

C V d f 2 M πµ = + + =

y 72 . 1 uM

Near Wall Near Wall Peak Velocity Peak Velocity

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t

F

a

F

e

F

c

F

l

F

t

M

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Electrostatic Electrostatic Rolling Rolling

β + + ≥ +

b c e ad h h

)0.58n F F (F 2 d F M

) F F k(F F

e c ad h

+ + ≥

Sliding Sliding

c ep ei ad ed ec

F F F F F F + + + ≥ +

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+ + + + + + + +

β = ≤ β − = = z y 2 w 85 . 1 y , y v y u

  • 2

01085 .

  • =

β

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Saturation Saturation Charge Charge

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SLIDE 6

6

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q=20 q=20 µ µC/g C/g

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Neutral Neutral Particles Particles

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Boltzmann Boltzmann Charge Charge

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Saturation Saturation Charge Charge

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SLIDE 7

7

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q=20 q=20 µ µC/g C/g

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Saturation Saturation Charge Charge

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Boltzmann Boltzmann Charge Charge

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Saturation Saturation Charge Charge

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SLIDE 8

8

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t

F

a

F

e

F

l

F

t

M

a

2 / d

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β 2

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. E N 24 ) N N 13 . d ) N N 1 ( ( 4 q qE 5 . 1 F

2 2

  • 2

c 2 2 3 c 2 2 c

  • 2

r e

ε β π − β + − πε − − =

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SLIDE 9

9

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Boltzmann Boltzmann Charge Charge Rough Rough Particles Particles

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Saturation Saturation Charge Charge Rough Rough Particles Particles

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Rough Rough Particles Particles

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SLIDE 10

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  • Rolling detachment is the dominant mechanism

Rolling detachment is the dominant mechanism for bumpy particle removal in turbulent flows. for bumpy particle removal in turbulent flows.

  • Drag and hydrodynamic torque are dominant for

Drag and hydrodynamic torque are dominant for particle detachment from the wall. particle detachment from the wall.

  • Electrical

forces contribute significantly to Electrical forces contribute significantly to particle particle adhesion. adhesion.

  • increasing the number of bumps reduces the

increasing the number of bumps reduces the adhesion force. adhesion force.

  • Patch charge model presents a more realistic

Patch charge model presents a more realistic picture picture

  • f surface charge distribution.
  • f surface charge distribution.

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