Studying the Mass Transport Phenomena Associated with

EvaporationGreg Wassom & Taylor Piske

Advised by Dr. Peter Kelly-Zion, Dr. Chris Pursell, and Dr. Hoa Nguyen

Details of EvaporationApplications:• Coating• Spray cooling• Printing• Surface Patterning• DNA stretching and depositingVapor Transport Mechanisms:• Diffusion and Convection

Image take from: Lin, Zhiqun. Evaporative Self-Assembly of Ordered Complex Structures. World Scientific, 2012.

Image taken from http://fe867b.medialib.glogster.com/media/18/180d72257aa1a63672899016e3dfb937691298252f3e50416f3c04d10f9ca46a/diffusion-pic-1-gif.gif

• Molecular Transport

• Driven by Concentration gradients

Buoyancy Induced Convection

Video taken from Sharma, Vidit. “VOF in Ansys Fluent 14”. https://www.youtube.com/watch?v=wys3qiBQzYY

• Bulk Transport Phenomena

• Driven by a Density Gradient

• Gravity

Experimental Techniques• Gravimetric Analysis

• Shadowgraph

• Pressure Chamber

• Schlieren Imaging

• IR Spectral Analysis0 100 200 300 400 500 600 700 800

-10

0

10

20

30

40

50

60

f(x) = − 0.108458557679504 x + 53.4299931331544R² = 0.998986998326417

Mass vs. Time

Measured Data

Fitted Slope (evaporation rate)

Linear (Fitted Slope (evaporation rate))

Time (s)

Mas

s (m

g)

SpectraMethanol

IR Spectroscopic Measurements

0 5 10 15 20 25 30 35 400.0

0.2

0.4

0.6

0.8

1.0

Hexane Methanol

Radial Position (mm)

Conc

entr

ation

/Sat

. Con

c.

Z = 1mmZ = 2 mmZ = 3 mmZ = 4 mmZ = 5 mmZ = 6 mmZ = 8 mmZ = 10 mmZ = 15 mm

Using the Experimental Conc. Data with Gridfit

• MATLAB function Gridfit models the data with a surface

• Concentration gradients ( and ) are computed along a cylindrical control volume

• Flux through the control volume is calculated

• Flux Diffusion rate

-5 0 5 10 15 20 25 30 350

5

10

15

20

r-position (mm)

z-po

sitio

n (m

m)

Analytical Methanol Data from the Weber’s Disc Model Modeled by Gridfit

Methodology Check - Comparing Methanol Diffusion Rates of Different Control Volumes

0.75 0.95 1.15 1.35 1.55 1.75 1.95 2.15 2.35 2.55 2.755.5E-08

6.0E-08

6.5E-08

7.0E-08

7.5E-08

8.0E-08

8.5E-08

9.0E-08Diffusion Rates of Methanol Using Analytical Data

Methanol TheoryCV Radius = 8.5 mmCV Radius = 8 mmCV Radius = 7.5 mm

Height of Control Volume (mm)Di

ffusi

on R

ate

(kg/

s)

Theory

Experimental Methanol Data Modeled by Gridfit

Comparing Diffusion Rates of Different Control Volumes

(Experimental Data)

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.60.0E+00

5.0E-08

1.0E-07

1.5E-07

2.0E-07

2.5E-07

Control Volume Radius = 7 mm

3MP

3MP Theory

Hexane

Hexane Theory

Methanol

Methanol Theory

Control Volume Height (mm)

Diffu

sion

Rat

e (k

g/s)

5.5 6 6.5 7 7.5 8 8.5 90.0E+00

5.0E-08

1.0E-07

1.5E-07

2.0E-07

2.5E-07

3.0E-07

Control Volume Height = 1.5 mm

3MP

3MP Theory

Hexane

Hexane Theory

Methanol

Methanol Theory

Control Volume Radius (mm)Di

ffusi

on R

ate

(kg/

s)

Traditional Theory vs. Real Hexane Data

-25 -20 

-15 

-10 

-5 

0 

5 

10 

15 

20 

25 Radial Position, r [mm]

Elev

atio

n, z

[mm

]

0

5

10

15

20

25MeasuredComputed: Diffusion-Only

Summary• Vapor concentration data measured for methanol, hexane, and 3-methylpentane

• Data modeled by Gridfit

• Gridfit model used to compute gradients, calculate diffusion rates

• Diffusion rates and theory compared

• Evidence of convection found

Acknowledgments• Petroleum Research Fund• Dr. Peter Kelly-Zion• Dr. Chris Pursell• Dr. Hoa Nguyen• Chemistry Department, Trinity University• Engineering Department, Trinity University• Mathematics Department, Trinity University