Verification of Computational Methods of Modeling Evaporative Drops

ByAbraham RosalesAndrew Christian

Jason Ju

Abstract

This project presents theoretical, computational, and experimental aspects of mass-loss of fluid drops due to evaporation.

Overview

• Applications• Experimental Setups and Procedures• Experimental Results• Derivation of Methodology• Numerical Results• Discussion of Disparities

Evaporation Process

Applications

• Manufacturing computer chips– Influence conductivity of electrons

• Lubrication or cleaning of machinery– Duration of the fluid

• Printing process– Spreading and drying time.

Experimental Setup

software

Video of 100% IPA Evaporation

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

)

Video of Water Evaporation

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

)

Experimentally Determined Evaporation Constant

-6100% 2

-72

2.28012 10

5.64225 10

surface

IPA

water

mJtA

gJ

s mmg

Js mm

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

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

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

Derivations: Van Der Waal Forces

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

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

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

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

Results: 100% Alcohol

Results: 100% Alcohol

Disparities:

Results: 100% Alcohol

Disparities:

Disparities:

Water Issues:

Mixology Issues:

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

Questions and Answers