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Detailed Measurement of Interface Shapes for Static and Dynamic
Contact Angles•Geometry•Optics•Data analysis•Extracting contact angle and surface tension•Recommendations: when, where...
Main students doing the technique development:John A. Marsh
Qun ChenKroum Stoev
Geometry
Highest point on line of
sight
•Tube Diameter: DT = 2.5 cm•DT >> Cap Length (1.5 mm):
–Azimuthal curvature small effect on shape and flow
•Easy to focus, sharp meniscus seen on meridian plane(unlike flat plate) •Unlike spreading drop, outer length scale very large•Cylinder: No "end effects"
Cap Length
DT
Optics: Kohler Illumination
•Image of light source forms at condenser aperture
Condenser Focal plane
Optics: Kohler Illumination
•Image of source aperture forms at object plane
•Condenser aperture: controls cone angle•Source aperture: controls illuminated spot size
•Uniform illumination key to making physical edge parallel to equi-intensity contourResult: uniformly illuminated, in-
focus image of source aperture
Imaging System Schematic
Image Quality
•80° ≤ Contact angles ≤ 100°: Can’t measure because contact line hidden•Usually meniscus edge sharp out to >1.4 mm
Highest curvature in line of sight:Sharpest Image
Uniformly flat surface:
•Lowest curvature along line of sight
•Fuzzier image
Image Quality - 2
•Interfaces meeting at the contact line:–Diffraction patterns interfere & cause distortion
Contact angle < 5°:•No problem•Can get interface all the way through contact line
Larger contact angles:• Safely down to 15µm to 20µm from contact line
• Best conditions can get closer
Menisci in Depression
•Can be measured•Light path through liquid•PIV possible
•Question: do "equal intensity levels" follow physical edge?–A: Calibration
•Edge finder output: interface slope vs. position•Slope: One derivative closer to curvature than x-y data
Calibration•Needed due to small distortions near edges•Mechanical shapes (e.g., straight edge) not good enough– How straight is the edge?
•Use static capillary shape:– Known exact theoretical form: Young-Laplace Eq.– Use Static Contact Angle and Surface Tension as fitting parameter
– Two-parameter fit: contact angle & surface tension uncoupled
65
60
55
50300250200150100500
( )r µm
-4
-2
0
2
4
300250200150100500 ( )r µm
•Difference (Data-Fit):– No systematic deviation from zero– Strict criterion imposed – cloud of data does not move more than 1/3 width off zero line
Fitting Details
• Fitting AWAY from contact line crucial• Why
–All surfaces have contact angle hysteresis–With hysteresis comes contact line brokenness–...which leads to interface shape fluctuations–Fluctuations die out: scale larger than contact line waviness!
• Need to fit beyond folding to get “contact angle” & surface tension
• Global contact angle: boundary condition for meniscus beyond folds
Analysis
•We fit theoretical models to the interface data– Young-Laplace (static theory)
– Cox-Dussan composite asymptotics (Newtonian, viscous theory)
•Extract:– Static contact angle & surface tension from fit to Young-Laplace
– "Dynamic" apparent contact angle from fit to Cox-Dussan
•Requirements–(Best fit - Exptal data) free of systematic deviation
65
60
55
503002001000
( )r µm
70
65
60
553002001000
(r μ )m
-3
-2
-1
0
1
2
3
3002001000 (r μ )m
•Data cloud ~2° thick (but ~1° RMS)
•Contact angle accuracy ~1°or less•Mostly Run-to-Run variation•Good accuracy due to calibration with static shape•High precision in local interface angle from fitting to large number of data points to determine one interface angle
•Very accurate (~0.25deg) measurement of interface shape
Accuracy
70
65
60
553002001000
(r μ )m
Recommendations
•Kohler illumination less important than uniform illumination •Good resolution from 15µm to 1500µm from contact line•Perhaps not strictly necessary for static unless detailed shape needed (i.e., could use "2-point" for statics...)•Necessary when detailed interface shapes needed•Necessary for dynamic contact angle
Back Ups
Optics: Kohler Illumination
Settings:•Source aperture: just large enough to illuminate entire field of view
•Larger condenser aperture: more fuzzy, less contrast, more depth of focus
•Smaller condenser aperture: more contrast, more diffraction fringing around contact line
•Cylindrical geometry requires not-too-large depth of focus Result: uniformly illuminated, in-
focus image of source aperture