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Verification of Computational Methods of Modeling Evaporative Drops
ByAbraham RosalesAndrew Christian
Jason Ju
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Abstract
This project presents theoretical, computational, and experimental aspects of mass-loss of fluid drops due to evaporation.
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Overview
• Applications• Experimental Setups and Procedures• Experimental Results• Derivation of Methodology• Numerical Results• Discussion of Disparities
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Evaporation Process
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Applications
• Manufacturing computer chips– Influence conductivity of electrons
• Lubrication or cleaning of machinery– Duration of the fluid
• Printing process– Spreading and drying time.
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Experimental Setup
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software
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Video of 100% IPA Evaporation
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Experimental Results for 100% Isopropyl Alcohol
ACTUAL VOLUME vs. TIME
0
5
10
15
20
25
30
35
0 100 200 300 400 500 600 700 800 900 1000
Time (s)
VO
LU
ME
(mm
^3
)
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Video of Water Evaporation
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Experimental Results for WaterACTUAL VOLUME vs. TIME
0
2
4
6
8
10
12
14
16
18
0 1000 2000 3000 4000 5000 6000
Time (s)
VO
LU
ME
(mm
^3
)
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Experimentally Determined Evaporation Constant
-6100% 2
-72
2.28012 10
5.64225 10
surface
IPA
water
mJtA
gJ
s mmg
Js mm
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Conceptual and Theoretical Derivations
3 2 3 3 0
surface tension Van Der Waals Forceviscous dissipation
3 ( ) [ ( )] ( )evaporationgravity
hh h h h g h h EJ
t
: cos :
: : tan
: :
vis ity fluid density
g gravity J evaporation cons t
h fluid thickness surface tension
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Conceptual and Theoretical Derivations
• Reduce Navier stokes equation (lubrication approximation)• Re << 1, ignore inertia term• Incompressible fluid.• For detail derivations see (instabilities in Gravity driven flow
of thin fluid films by professor Kondic)2
2 22
0
0
1: =( , )
2 :
by laplace young boundary condition solve equation 2
z=h(x,y) p(h)=- +p
( )
veq p x y
zp
eq pgz
p g z h p
P gh
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Conceptual and Theoretical Derivations
2
2
( , )
2
2
2
2
0
solve equation 1 by boudary conditon of no slip and 0
1v= ( )
2
by average over the short direction to remove the z-dependce of v
1v*= ( )
h 3
by conservation of mass:
z h x y
h
v
z
zP hz
hvdz P
h
t
2
3 2 3
surface tensionviscous dissipation
( *) 0 =
03 ( ) ( )gravity
hv h
hh h g h h
t
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Derivations: Van Der Waal Forces
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Van Der Waal Approximation:Lennard Jones Potential
In our use:
( )
1 3, 2
n mh h
V h hh h
for n m n m
, , 1 cos
1 1
n mSwhere M S
Mh m n
16
min, 2r
33 0dh
h V hdt
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Derivations: Evaporation
3
2 2
2
2
0
: ,
dhEJ
dt
kg m mgiven J kg V
m t m t t
m area differential areaE
m height function f h K
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Numerical Scheme:Forward Time, Central Space
1
1 1
1 12
, ,
2
2
t tr r
t tr r
r
t t tr r r
rr
h hf derivatives t r XStep
TStep
h hh
XStep
h h hh
XStep
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Numerical Scheme:All Together + CoOrdinate Foolishness
3 3 3
2 2 3 2 3
3 3 0
3 33t x xx xxx x xxxx
dhh h h V h g h h EJ
dt
TSteph g h h h h h h h h h VdW EJ
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Results: 100% Alcohol
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Results: 100% Alcohol
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Disparities:
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Results: 100% Alcohol
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Disparities:
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Disparities:
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Water Issues:
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Mixology Issues:
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Conclusion
• Mass loss fits for fluids which behave within lubrication approximation.
• Surface tension term keeps area similar regardless of intermolecular forces.
• Things not within approximation:Combinations of liquidsHigh contact angles
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Questions and Answers