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 Chen Kroum Stoev

Geometry Highest point on line of sight Tube Diameter: D T = 2.5 cm D T >> 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 DTDT

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 contour Result: 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 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

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

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