detailed measurement of interface shapes for static and dynamic contact angles geometry optics data...

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