van der waals/pull-off force for - web space - oit6 me 437/537 ahmadi me 437/537 ahmadi rolling...
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AhmadiME 437/537 AhmadiME 437/537
!! van van derder WaalsWaals/Pull/Pull--off Force for off Force for Rough SurfacesRough Surfaces
!! Rolling and Sliding Removal of Rolling and Sliding Removal of Rough ParticlesRough Particles
!! Hydrodynamic Forces and TorqueHydrodynamic Forces and Torque
!! Critical Shear Velocity for Critical Shear Velocity for DetachmentDetachment
AhmadiME 437/537
PullPull--Off Force Off Force
Contact RadiusContact Radius
at Separationat Separation
dW43F A
JKRpo π=
31
2A
K8dW3a ⎟⎟
⎠
⎞⎜⎜⎝
⎛ π=
31
Po
K2dFa ⎟⎠⎞
⎜⎝⎛=( ) ( ) 1
2
22
1
21
E1
E1
34K
−
⎥⎦
⎤⎢⎣
⎡ ν−+
ν−=
AhmadiME 437/537
PullPull--Off Off Force Force
Contact Contact RadiusRadius
c/6.0Po
2M eNfaF ∆−π=
31
M
K2dFa ⎟⎠⎞
⎜⎝⎛=
σδ
=∆ cc
Number of Number of Asperities per Asperities per
Unit AreaUnit Area
PullPull--Off Force Off Force for each for each AsperityAsperity
Max Asperity Max Asperity ExtensionExtension
Roughness Height Roughness Height Standard deviationStandard deviation
Estimated
2
AhmadiME 437/537
3/1
2
2Po
c K3f
⎥⎦
⎤⎢⎣
⎡β
=δ
0.1N ≈σβ
JKR JKR ModelModel
GreenwoodGreenwood--WilliamsonWilliamson
AhmadiME 437/537
σ= 5.9kr r0.53ke =Average Roughness Height Average Roughness Height Displaced Origin of Velocity Profile Displaced Origin of Velocity Profile
Equilibrium Separation Distance Equilibrium Separation Distance
AhmadiME 437/537
VC
df3Fc
tµπ
=Drag ForceDrag Force
( ) 2/12/12
l dy/dVdy/dVVd61.1F ρµ=Lift ForceLift Force
Hydrodynamic Hydrodynamic Torque Torque
c
2m
t CVdf2M πµ
=
AhmadiME 437/537
+++
+++
++
β=
≤β−=
=
zy2w
85.1y,yv
yu
o
o
2
01085.0o =β
3
AhmadiME 437/537
+++++
+ =α−+σ+= LH76.22du 0
)H76.22d(
2w 0
+++++
+ α−+σ+Λ
β=
α−+σ+= 0H76.22dL
AhmadiME 437/537
CLdu8.5F
2*
tπρ
=
νρ
=Lud95.1F
3*2
L
CLdu14.2M
22*
tπρ
=
Drag ForceDrag Force
Lift ForceLift Force
Hydrodynamic Hydrodynamic Torque Torque
AhmadiME 437/537
tF
MF
lFtM
O
a
d
Lmg
AhmadiME 437/537
tF
aF
lFtM
a
2/d
mg
4
AhmadiME 437/537
MOMENT DETACHMENTMOMENT DETACHMENT
aFa)mgF()2d(FM ML0tt ≥−+α−+
SLIDING DETACHMENTSLIDING DETACHMENT
)FmgF(kF LMt −+≥
AhmadiME 437/537
RollingRolling
SlidingSliding
2/1
*c2
2cpo
2*c
)aCu95.104.5(Ld
]mg])/(6.0exp[Nfa[aCu
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
ν+πρ
+∆−π=
.)kCdu95.18.5(Ld
]mg])D/(6.0exp[Nfa[kCu
2/1
*c
2cpo
2*c
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
ν+πρ
+−π=
AhmadiME 437/537
RollingRolling
SlidingSliding
( )2/1
2/1*c
*c
*c2
2cpo
2*c
)Lu2.072.1(aCu95.104.5)Lu1.072.1(Ld
mg])/(6.0exp[NfaaCu
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛ν
+ν
+πν
+ρ
+∆−π=
2/1
2/1*c
*c
*c
2cpo
2*c
)Lu2.072.1(kCdu95.18.5)Lu1.072.1(dL
]mg])/(6.0exp[Nfa[kCu
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛ν
+ν
+πν
+ρ
+∆−π=
AhmadiME 437/537
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AhmadiME 437/537 AhmadiME 437/537
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AhmadiME 437/537 AhmadiME 437/537
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 pullpull--off force.off 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 dataexperimental data
AhmadiME 437/537
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