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