= Pull- -Off Force Off Force JKR Pull- -Off Off Pull Pull - - PowerPoint PPT Presentation

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! ! van van der der Waals Waals/Pull /Pull-

• off Force for
• ff Force for

Rough Surfaces Rough Surfaces ! ! Rolling and Sliding Removal of Rolling and Sliding Removal of Rough Particles Rough Particles ! ! Hydrodynamic Forces and Torque Hydrodynamic Forces and Torque ! ! Critical Shear Velocity for Critical Shear Velocity for Detachment Detachment

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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 =

3 1 Po

K 2 d F a ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ =

( ) ( )

1 2 2 2 1 2 1

E 1 E 1 3 4 K

−

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ν − + ν − =

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Pull Pull-

• Off

Off Force Force Contact Contact Radius Radius

c

/ 6 . Po 2 M

e Nf a F

∆ −

π =

3 1 M

K 2 d F a ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = σ δ = ∆

c c Number of Number of Asperities per Asperities per Unit Area Unit Area Pull Pull-

• Off Force

Off Force for each for each Asperity Asperity Max Asperity Max Asperity Extension Extension Roughness Height Roughness Height Standard deviation Standard deviation Estimated

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3 / 1 2 2 Po c

K 3 f ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ β = δ 0.1 N ≈ σβ

JKR JKR Model Model Greenwood Greenwood-

• Williamson

Williamson

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σ = 5.9 k r

r

0.53k e =

Average Roughness Height Average Roughness Height Displaced Origin of Velocity Profile Displaced Origin of Velocity Profile Equilibrium Separation Distance Equilibrium Separation Distance

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V C d f 3 F

c t

µ π =

Drag Force Drag Force

( )

2 / 1 2 / 1 2 l

dy / dV dy / dV V d 61 . 1 F ρµ = Lift Force Lift Force Hydrodynamic Hydrodynamic Torque Torque

c 2 m t

C V d f 2 M πµ =

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+ + + + + + + +

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

• 2

01085 .

• =

β

3

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+ + + + + +

= α − + σ + = L H 76 . 2 2 d u

) H 76 . 2 2 d ( 2 w

+ + + + + +

α − + σ + Λ β =

α − + σ + = H 76 . 2 2 d L

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C L du 8 . 5 F

2 * t

πρ =

ν ρ = L u d 95 . 1 F

3 * 2 L

C L d u 14 . 2 M

2 2 * t

πρ =

Drag Force Drag Force Lift Force Lift Force Hydrodynamic Hydrodynamic Torque Torque

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t

F

M

F

l

F

t

M

O

a

d

L

mg

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t

F

a

F

l

F

t

M

a

2 / d

mg

4

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MOMENT DETACHMENT MOMENT DETACHMENT

a F a ) mg F ( ) 2 d ( F M

M L t t

≥ − + α − +

SLIDING DETACHMENT SLIDING DETACHMENT

) F mg F ( k F

L M t

− + ≥

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Rolling Rolling Sliding Sliding

2 / 1 * c 2 2 c po 2 * c

) aCu 95 . 1 04 . 5 ( Ld ] mg ] ) /( 6 . exp[ Nf a [ aC u ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ν + π ρ + ∆ − π =

. ) kCdu 95 . 1 8 . 5 ( Ld ] mg ] ) D /( 6 . exp[ Nf a [ kC u

2 / 1 * c 2 c po 2 * c

⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ν + π ρ + − π =

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Rolling Rolling Sliding Sliding

( )

2 / 1 2 / 1 * c * c * c 2 2 c po 2 * c

) L u 2 . 72 . 1 ( aCu 95 . 1 04 . 5 ) L u 1 . 72 . 1 ( Ld mg ] ) /( 6 . exp[ Nf a aC u ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ν + ν + π ν + ρ + ∆ − π =

2 / 1 2 / 1 * c * c * c 2 c po 2 * c

) L u 2 . 72 . 1 ( kCdu 95 . 1 8 . 5 ) L u 1 . 72 . 1 ( dL ] mg ] ) /( 6 . exp[ Nf a [ kC u ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ν + ν + π ν + ρ + ∆ − π =

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• Rolling detachment is the dominant mechanism

Rolling detachment is the dominant mechanism for detachment of rough spherical particles. for detachment of rough spherical particles.

• Roughness significantly reduces the adhesion

Roughness significantly reduces the adhesion pull pull-

• off force.
• ff force.
• Turbulence near wall flow structure plays an

Turbulence near wall flow structure plays an important role in particle detachment process. important role in particle detachment process.

• Accounting for surface roughness improves the

Accounting for surface roughness improves the agreement between the model prediction and agreement between the model prediction and experimental data experimental data

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