verification of computational methods of modeling evaporative drops by abraham rosales andrew...

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