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Department of Chemistry and Physics
Georgia Regents University
Determining Surface Tension Using
The Pendant Drop Method
Camille Miller, Jaleel Bolden, Zane Corder, Charlene Higdon
Faculty Advisor: Dr. Guerrero-Millan
Applications
Surface Tension
The energy required to decrease the surface area of a fluid
Y. Yuan, T. R. Lee. Surface science techniques. Springer Berlin Heidelberg, 2013. 3‐34.
Surface Tension
Sessile drops
lg cos (θC) = γsg− γsl
Experimental Setup
Image Processing
Original image
Edge Detected
Edge Plotted
A. Egatz‐Gomez, et al. RSC Advances 2(30) (2012)
Fitting
Literature: 38.6o Our code: 38.5o
Concentration
VSoap/VWater
Contact Angle
5mL/5mL
15.7
5mL/10mL
5mL/20mL
34.7
43.5
Droplet
Other Methods of Determination
Some instruments to measure surface tension:
Du Noüy Ring
Wilhelmy plate
Pendant drop method
Young Laplace Equation
Gravity
P  P0  ( ) gz
 1 sin   2
 
   ( )gz
x  R0
 R1
Capillarity
1
1 

P     
 R1 R2 
Young Laplace Equation
In dimensionless parametric form:
sin 
d
 2  Z 
dS
X
dX
 cos 
dS
dZ
 sin 
dS

( ) gR02
Boundary conditions:

X ( 0)  Z ( 0)   ( 0)  0

( ) gR02

Shape factor
Young Laplace Equation
In dimensionless parametric form:
sin 
d
 2  Z 
dS
X
dX
 cos 
dS
dZ
 sin 
dS

( ) gR02
Boundary conditions:

X ( 0)  Z ( 0)   ( 0)  0

( ) gR02

Shape factor
Young Laplace Equation
In dimensionless parametric form:
sin 
d
 2  Z 
dS
X
dX
 cos 
dS
dZ
 sin 
dS

( ) gR02
Boundary conditions:

X ( 0)  Z ( 0)   ( 0)  0

( ) gR02

Shape factor
Image Enhancement
Edge Detection
Finding Ro

How did we choose the number of
points at the bottom of the drop?
( ) gR02

Radius of curvature Ro (pixels)
Finding Ro
Number of points
Finding Ro
Needle diameter: 0.9 mm
Ro = 1.5 mm
Determining the shape factor
CC
Method 1:
Two diameters at
different heights

( ) gR02

Method 2:
Fitting the profile
Method 1: Measuring two diameters within the drop (DE and DS)
DE: Largest diameter in the drop
DS: Diameter DE to the drop apex
CC
DS = 56 px
DE = 85 px
2
 DS 
 DS 
DS
  0.5426 

 1.7713 
  0.12836  0.7577
DE
 DE 
 DE 
3
F. K. Hansen and G. Rødsrud, J. Colloid Interface Sci. 141 (1991)
Method 2: Fitting the whole profile
= 0.05 : 0.01 : 0.5
Method 2: Fitting the profile
Surface Tension Values γ (mN/m)
From
Literature
First Method
(DS DE)
Second Method
(fitting the profile)
72.75
73.18
73.47
Water /10 cSt Silicone oil
-
40.83
40.87
Glycerol /
10 cSt Silicone oil
-
29.19
29.40
Ethylene glycol /
10 cSt Silicone oil
-
18.98
15.74
Water / Air
Measuring the flow rate in electro-coflow
Experimental setup
Drop size measurement
If the same drop appears in several frames…
Monitoring the centroid position
Results
Thank you!