! Generally Attractive ! Generally Attractive z ! Short Range ! - - PowerPoint PPT Presentation

SLIDE 1

1

Ahmadi ME 437/537 Ahmadi ME 437/537

! ! Features of van Features of van der der Waals Waals Force Force ! ! Sphere Near a Plane Sphere Near a Plane ! ! Cylinder near a Flat Plate Cylinder near a Flat Plate ! ! Interfaces Interfaces ! ! Hamaker Hamaker Constants Constants ! ! Hamaker Hamaker Constants for Dissimilar Constants for Dissimilar Materials Materials

Ahmadi ME 437/537

! ! Generally Attractive Generally Attractive ! ! Short Range Short Range ! ! Origin in Atomic Dipole Origin in Atomic Dipole

Ahmadi ME 437/537

Interaction Energy Interaction Energy

] x 1 x ln 2 x 1 1 x 1 [ 12 A + + + + − = φ

z 12 Ad − ≈ φ

z →

z d

d z x =

A=Hamaker Const. A=Hamaker Const.

d 2 . ~ kT 12 Ad z <

Range of Application Range of Application

SLIDE 2

2

Ahmadi ME 437/537

Particle Surface (air)

(water)

Poly- styrene Poly- stynne 1.2-1.8 70-100 0.2 12 Si Si 13.6-14.4 800-850 7 410 Cu Cu 17 1000 9.8 580 Ag Ag 18 1060 15.5 910

dU 3 F πµ

ν

dU 3 F πµ

ν

N 10 F

8

×

ν

N 10 F

8

×

ν

s / m 1 U =

• A

4 z =

Ahmadi ME 437/537

2

• 123

z 12 d A ~ Fν

d 2 ~ F

st

πγ

dt dV d ~ F

3 am

ρ

2 2 f D

V d ~ F ρ t V d ~ F

2 B

ν µ

v

F

8

10 3

−

×

5

10 9

−

×

18

10−

12

10−

15

10 4

−

×

7

10 3

−

×

4

10 9

−

×

15

10−

10

10−

13

10 4

−

×

6

10 3

−

×

3

10 9

−

×

12

10−

8

10−

11

10 4

−

×

van der Waals Surface Tension Added Mass Drag/Lift Basset Diameter d (µm)

0.2 2 20

Ahmadi ME 437/537

2

• 123

z 12 d A ~ Fν

d 2 ~ F

st

πγ

dt dV d ~ F

3 am

ρ

2 2 f D

V d ~ F ρ t V d ~ F

2 B

ν µ

v

F

van der Waals Surface Tension Added Mass Drag/Lift Basset Diameter d (µm)

0.2 2 20

9

10 2

−

×

8

10 2

−

×

7

10 2

−

×

16

10 8

−

×

13

10 8

−

×

10

10 8

−

×

10

10 8

−

×

8

10 8

−

×

6

10 8

−

×

12

10−

10

10−

8

10−

Ahmadi ME 437/537

zo d

2

• 132

z 12 d A F =

Sphere Near Sphere Near a Surface a Surface

SLIDE 3

3

Ahmadi ME 437/537 2 2 / 1 132

z 16 d A length F =

zo d Cylinder Near Cylinder Near a Surface a Surface

Ahmadi ME 437/537

Planar Surfaces Planar Surfaces zo

3 132

z 6 A area F π =

2 132

z 12 A π = φ

Surface Energy Surface Energy

Ahmadi ME 437/537 22 11 12

A A A ≈

22 11 22 11 12

A A A A 2 A + =

23 13 33 12 132

A A A A A − − + =

2 33 11 33 11 2 33 11 13 33 11 131

) A A ( ~ A A ) A A ( A 2 A A A − + − = − + =

Two Materials Two Materials Three Materials Three Materials

Ahmadi ME 437/537

J 10 / A

20 −

Materials Vacuum Water Polystyrene 7.9 1.3 Gold 40 30 Silver 50 40 Al2O3 16.75 4.44 Copper 40 30 Water 4.0

SLIDE 4

4

Ahmadi ME 437/537

) eV ( h

131

ω

Combinations Water Polystyrene Au-Cu 6.41 5.93 Au-Diamond 6.11 5.45 Au-Si 5.32 4.70 Au-Ge 6.50 5.93 Au-MgO 1.99 1.25

Ahmadi ME 437/537

R

d1

d2

s

] ) 2 d d ( R ) 2 d d ( R ln ) 2 d d ( R 2 / d d ) 2 d d ( R 2 / d d [ 6 A

2 2 1 2 2 2 1 2 2 2 1 2 2 1 2 2 1 2 2 1

− − + − + − − + + − − = Φ

s 2 d d R

2 1

+ + =

Ahmadi ME 437/537

d d d

2 1

= =

s d r + =

)] r d 1 ln( ) d r ( 2 d r 2 d [ 6 A

2 2 2 2 2 2 2

− + − + − = Φ

) A A ( A A A A

22 11 12 22 11 121

− ≈ − + =

For Equal Sizes For Equal Sizes

Ahmadi ME 437/537

! ! van van der der Waals Waals force is very large force is very large at short distances at short distances ! ! Short range force Short range force ! ! Can be computed for particles, Can be computed for particles, cylinders and plane interfaces cylinders and plane interfaces