ASPHALT WETTING DYNAMICS
Troy Pauli, Fran Miknis, Appy Beemer, Julie Miller,Mike Farrar, and Will Wiser
5TH Annual Pavement Performance Prediction SymposiumAdhesion & Cohesion of Asphalt PavementsCheyenne, Wyoming June 22nd and 24th, 2005
Comments on WettingContact Angle HysteresisDynamic Wetting (Current Theories)
Asphalt Adhesive PropertiesLubrication Theory (Translational Dynamic Contact-line Wetting)Water Interactions (Rotational Dynamic Contact-line Wetting)Adhesion Hysteresis, Friction and Aggregate Surface Roughness
A Look at Stripping
OVERVIEW
Wetting Drop Experiment
rθaθ
rθaθ
alsls θγγγ cos+=
Advancing Contact Angle, θa
rθaθ rlsl
fs θγγγ cos+=
Receding Contact Angle, θr
rθaθ
rlslfs θγγγ cos+=alsls θγγγ cos+=
sfs γγπ −=
cos( )arl θθγπ cos−=
Film Pressure, π
[ ] [ ] ( )sl
a LLvt ln9)0()( 33
γηθθ +=
[ ] [ ] ( )sl
r LLvt ln9)0()( 33
γηθθ −=
Dynamic Wetting Hydrodynamic Model
Ranabothu, S. R., et al. (2005) J. Colloid Inter. Sci., (ARTICLE IN PRESS)
Advancing DCA
Receding DCA
[ ] [ ] ( )sl
a LLvt ln9)0()( 33
γηθθ +=
[ ] [ ] ( )sl
r LLvt ln9)0()( 33
γηθθ −=
gL l
ργ2=
Dynamic Wetting Hydrodynamic Model
Ranabothu, S. R., et al. (2005) J. Colloid Inter. Sci., (ARTICLE IN PRESS)
sL
Advancing DCA
Capillary length
Slip length
Receding DCA
[ ] [ ] ( )sl
a LLvt ln9)0()( 33
γηθθ +=
[ ] [ ] ( )sl
r LLvt ln9)0()( 33
γηθθ −=
gL l
ργ2=
sL
Capillary length
Dynamic Wetting Hydrodynamic Model
Ranabothu, S. R., et al. (2005) J. Colloid Inter. Sci., (ARTICLE IN PRESS)
Advancing DCA
Slip length
Receding DCA
lCa
vNγη
=
Capillary number
[ ] [ ] ( )λγλ
θθ wl
B KvTkt 2arcsinh2)0(cos)(cos 2m=
Dynamic Wetting Molecular-kinetic Model
Ranabothu, S. R., et al. (2005) J. Colloid Inter. Sci., (ARTICLE IN PRESS)
v: velocity
λ: distance between adsorption/desorption sites
Kw: quasi-equilibrium rate constant
Lubrication Theory(Translational Dynamic Contact-line Wetting)
Roto-Film™Solution Spin
Casting Device
Initial Solution Concentration-0.167g/mL
Spin Rate-600 to 800 rpm
Volume Deposited to slide-2.0μL
Filmetrics™ Thin-film Measurement System
r
θzω
r
θzω
)t,,r(hh θ=
3
3
rhh
t)t,,r(h n
∂∂
=∂
∂ θ
Transverse Wave Equation
ω
rρωzη 22
2
=∂∂
−υ
∫∫−
=⎟⎠⎞
⎜⎝⎛
∂∂
dzrz
dη
ρωυ 2
crzz
+−
=∂∂
ηρωυ 2
ηρωυ )hz(r
zc
=+⎟
⎠⎞
⎜⎝⎛ =
∂∂
=2
0
∫∫ ⎟⎟⎠
⎞⎜⎜⎝
⎛+
−=zv
dzrhrzd0
22
0 ηρω
ηρωυ
Lubrication TheoryTranslational Dynamic Wetting
Viscous Force/Centrifugal Force Balance (per unit Volume)
⎟⎠⎞
⎜⎝⎛ −= 222
211 rzrhz ρωρω
ηυ
ηρωρωρω
ηυ
3211 32
0
222
0
rhdzrzrhzdzQhh
=⎟⎠⎞
⎜⎝⎛ −== ∫∫
( )rrQ
thr
∂∂−
=∂∂
⎟⎟⎠
⎞⎜⎜⎝
⎛∂∂−
=∂∂
ηρω3hr
rr1
th 322
Lubrication Theory (cont.)Translational Dynamic Wetting
Continuity Equation in terms ofRadial Flow per unit Circumference, Q
Radial Velocity of Film
( )322
311 hH
rrr
rrtH
−⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
∂∏∂
+∂∂
−⎟⎠⎞
⎜⎝⎛
∂∂
+−=∂
∂ κγρωη
ω
υ
hH
Neat AAD-1 at constant concentration
Increasing angular velocity 666
Angular Velocity, ω, rpm
200 300 400 500 600 700 800 900
Film
Thi
ckne
ss, h
, nm
300
400
500
600
700
800
900
1000
Neat AAD-1 at constant concentration
Neat AAD-1 at 4 concentrations
Increasing angular velocity 666
Asphalt Designation
AAA-
1
AAB-
1
AAC-
1
AAD-
1
AAF-
1
AAG
-1
AAK-
1
AAM
-1
Film
Thi
ckne
ss (h
), nm
0
200
400
600
800
1000
1200
1400 c3-600 c3-700 c3-800 Average
Asphalt Designation
AAA-
1
AAB-
1
AAC-
1
AAD-
1
AAF-
1
AAG
-1
AAK-
1
AAM
-1
Film
Thi
ckne
ss, n
m
400
500
600
700
800
900
1000
1100
1200c4-600 c4-700 c4-800
Neat AAD-1 at constant concentration
Increasing angular velocity 666
AAD-1 PAV-Aged at 60EC, 240-hr
Increasing angular velocity 666
AAD-1 PAV-Aged at 60EC, 480-hr
Increasing angular velocity 666
Angular Velocity, ω (RPM)
300 400 500 600 700 800
Film
Thi
ckne
ss, h
(nm
)
400
600
800
1000
1200
1400
1600
Neat AAD-1AAD-1, 60°C Aged, 240hr AAD-1, 60°C Aged, 480hr h = a2ω2 + a1ω +a0
AAD-1(w/1.5%ppa) PAV Aged at 60EC, 96-hr
Increasing angular velocity 666
Increasing angular velocity 666
AAD-1(w/1.5%ppa) PAV Aged at 60EC, 184-hr
Increasing angular velocity 666
AAD-1(w/1.5%ppa) PAV Aged at 60EC, 260-hr
Angular Velocity, ω (RPM)
300 400 500 600 700 800
Film
Thi
ckne
ss, h
(nm
)
400
600
800
1000
1200
1400
1600Neat AAD-11.5%ppa AAD-1-60°C Aged, 96hr 1.5%ppa AAD-1-60°C Aged, 184hr 1.5%ppa AAD-1-60°C Aged, 260hr 1.5%ppa AAD-1-60°C Aged, 326hr h = a2ω2 + a1ω + a0
Angular Velocity, ω (RPM)
300 400 500 600 700 800
Film
Thi
ckne
ss, h
(nm
)
400
600
800
1000
1200
1400
16001.5% ppa-AAD-1. 0hr 1.5% ppa AAD-1-60°C Aged, 96hr 1.5% ppa AAD-1-60°C Aged, 184hr 1.5% ppa AAD-1-60°C Aged, 260hr 1.5% ppa AAD-1-60°C Aged, 326hr h = a2ω2 + a1ω + a0
Angular Velocity, ω (RPM)
300 400 500 600 700 800
Film
Thi
ckne
ss, h
(nm
)
400
600
800
1000
1200
1400
16001.5% ppa-AAD-1. 0hr 1.5% ppa AAD-1-60°C Aged, 96hr 1.5% ppa AAD-1-60°C Aged, 184hr 1.5% ppa AAD-1-60°C Aged, 260hr 1.5% ppa AAD-1-60°C Aged, 326hr h = a1ω + a0
Lubrication Theory(Rotational Dynamic Contact-line Wetting)
θ = 0
β
wa ρρ >
α = 0
wρ
awγ
wγ
aγ
Water Drop
Asphalt
θ
β
wa ρρ >α
wρ
awγ
wγ
aγ
2w
aCaawb z
S2VF)(gVFρρρρ ≡=−≡
Buoyancy Force Balances Capillary Force
aawaa zgS γρ −= 2
21
awwww zgS γγρ −−= 2
21
a
waw
zz
ρρ−
=
( )a
waw
zz
ρρρ −
=
z
Derivation of Half-Space for Spreading Coefficient
Szgz
g awwawa
wa ≡−−=−⎟⎟
⎠
⎞⎜⎜⎝
⎛ −γγγρ
ρρ
ρ 22
21
21
awwaS γγγ −−=
At pseudo-equilibrium, Sw = Sa
Spreading Coefficient
)(),()( awbawb Fg ρρρρ <↑+=−−= kkF
)(,0)( awawb g ρρρρ ==−−= kF
)(),()( awbawb Fg ρρρρ >↓−=−−= kkF
r
Buoyancy Force Balances Viscous Force
VFr
gVF viswa
waaawb =⎟⎟
⎠
⎞⎜⎜⎝
⎛++±
=−−=ηηηηηυρρ 32
23)( 2
kk
r
wa
wa
a
aw )(grηη
ηηη
ρρυ
3232 2
++−
=
r
Terminal Velocity of “falling” Liquid Drop In a Second Liquid (ρdrop < ρliquid)
2
223223
zr
S w
a
wa
waa ρ
ρηηηηηυ
=⎟⎟⎠
⎞⎜⎜⎝
⎛++
⎟⎠⎞
⎜⎝⎛
wa
awa
waaa ,332
23'
ηη
ηηη
ηηηη
>>
≈⎟⎟⎠
⎞⎜⎜⎝
⎛++
⎟⎠⎞
⎜⎝⎛=
Viscous Force Balances Capillary Force For Water Drop Traversing the Asphalt-Air Interface
)(,0)( awawb g ρρρρ ≈=−−= kF
2
22'zrN
S w
aCa
a
ρρυη
==2
32
⎟⎠⎞
⎜⎝⎛≅zrS
aηυ
Hydrodynamic and Geometric Definitions of Capillary Number & Terminal Velocity For Water Drop Traversing an Interface
z 2/Dr =
Time, Hours
0 100 200 300 400 500
Ang
le-α
°
0
20
40
60
80
100
120
140
160
180
AAA-1AAB-1AAC-1AAD-1AAF-1AAG-1AAK-1AAM-1
α
Time, hours
0 50 100 150 200
Ang
le-β
°
0
10
20
30
40
50
60
70
80
90
AAA-1AAB-1AAC-1AAD-1AAF-1AAG-1AAK-1AAM-1
β
Rate of Change in Angle-α, dα/dt, t = 0 to 24hr
-180 -160 -140 -120 -100 -80 -60 -40 -20 0
Nat
ural
Log
of D
ynam
ic V
isco
sity
, ln(
η a)
10.0
10.5
11.0
11.5
12.0
12.5
13.0
AAG-1
AAC-1
AAF-1AAM-1
AAK-1
AAB-1
AAD-1
AAA-1
Spreading Coefficient, Saw (dyne/cm)
-10 -8 -6 -4 -2 0
Film
Thi
ckne
ss, h
(nm
)
500
600
700
800
900
1000 AAM-1
AAK-1
AAF-1
AAA-1
AAG-1
AAC-1
AAB-1
AAD-1
Lubrication TheoryFriction and Aggregate Surface Roughness
⎟⎟⎠
⎞⎜⎜⎝
⎛++
=θνθ 22
2
sin)1(2cos34 l
kk
n
t
⎟⎟⎠
⎞⎜⎜⎝
⎛++⎟⎟
⎠
⎞⎜⎜⎝
⎛=
θνθ 22
2
3
3
sin)1(2cos34
4l
lwEtkt
3
3
4lwEtkn =
Model of a Lateral-Action Cantilever Measurement(Frictional Force Microscopy)
zkF tΔ=Hookian Force
Bliznyuk, V.N., J.L. Hazel, J. Wu, and V. Tsukruk, Quantitative Probing in Atomic Force Microscopy of Polymer Surfaces (1998). Chapter 15 in Scanning
Normal Force Constant
Torsional/NormalForce Constant Ratio
Probe Microscopy of Polymers, Ratner, B.D. and V.V. Tskruk, editors, American Chemical Society Symposium Series 694, Oxford University Press, Oxford.
Digital Digital Instruments, Instruments, Inc.Inc.
Scan Rate Frequency, νc (Hz)
0 2 4 6 8
Fric
tion
Forc
e R
espo
nse,
ξ (v
olts
)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
AAK-1, k1
AAG-1, k1
AAF-1, k1
AAC-1, k2
Frictional “traces” of four SHRP asphalts measured at different cantilever scan rates.
FRICTION IMAGE OF SHRP ASPHALT AAC-1
50 μm
Frictional Force Response ξ(@ νc = 4.0 Hz)
0.16 0.20 0.24 0.28 0.32 0.36Asp
halte
ne M
ass
Perc
ent,
( χa X
100)
0
5
10
15
20
25
30
Derived from n-heptane asphaltene precipitation
Derived from iso-octane asphaltene precipitation
Asphaltene Yield versus Frictional Force
Spreading Coefficient, Saw (dyne/cm)
-10 -8 -6 -4 -2 0
Film
Thi
ckne
ss, h
(nm
)
500
600
700
800
900
1000 AAM-1
AAK-1
AAF-1
AAA-1
AAG-1
AAC-1
AAB-1
AAD-1
Decreasing asphalt friction
Granite SurfaceLimestone Surface
Aggregate Sliding-Plates: 20-μm X 20-μm (length X width) X 4.0-μm (height), @ 25% color-contrast scaling of image
(AFM TappingModeTM)
AAB-1 on an RA Granite Plate
AAM-1 on an RD Limestone PlateBefore and After Sonication in water bath
Before After
AAD-1 on an RD Limestone PlateBefore and After Sonication in water bath
Before After
AAB-1 on an RA Granite AggregateAfter Sonication
