1 Introduction
2 Materials and experimental setup
Label | Description | Manufacturer/model/properties |
---|---|---|
P | Particle | Cospheric LLC; PMMA spheres; \(\rho _{\mathrm{p}} = 1200 \, {\mathrm{kg/m}}^3\) |
D | Droplet | Demineralized water |
S | Substrate | PMMA |
SL1/2 | Strobe light | GS Vitec; MultiLED R100; \(P=150 \,\)W |
D1/2 | Diffusor | |
HS1/2 | High-speed camera | Phantom; VEO 410L; \(400 \, \times \, 512 \, {\mathrm{px}}\); \(20\,{\mathrm{k}} \, {\mathrm{fps}}\) |
M1/2 | Macro lens | Qioptiq; Magnification 7 : 1 |
DN | Dosing needle | Vieweg; Discrete \(d_N\) |
C | Cartridge | |
CM | Cartridge adjustment | Operating displacement 50 mm |
Sync | Synchronizer | ILA; 5150 |
PT | Pressure transducer | Gonano Dosiertechnik; \(0.5-3 \,\)bar |
PC | Computer | \(2 \, \times \,\)GPU at \(2.4 \, {\mathrm{GHz}}\); \(64 \,\)GB RAM |
PD1/2 | Positioning device | Owis; XY Stages MKT 300; \(s = 5 \,\)mm |
3 Methodology
We | \([-]\) | 13 | \(\le {\mathrm{We }} \le\) | 94 |
---|---|---|---|---|
\({\mathrm{Ca}}\) | \([-]\) | 90 | \(\le {\mathrm{Ca}} \le\) | 140 |
\({\mathrm{Re}}\) | \([-]\) | 740 | \(\le {\mathrm{Re }} \le\) | 3420 |
\(\Phi\) | \([-]\) | 0.4 | \(\le \Phi \le\) | 1.1 |
\(C_{\mathrm{I}}\) | \([\%]\) | 0 | \(\le C_{\mathrm{I}} \le\) | 100 |
3.1 Image processing
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The greyscale image is transformed into a binary black and white image by a threshold which is based on a sensitivity analysis of the possible threshold range. The images are depicted in 8 bit grey scale. The pixels of the contour of the droplet-particle system are stored in a list.
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The CG of the droplet (\({\mathrm{CG}}_{\mathrm{d}}\)) before impact is determined by a function for the calculation of the center of a contour. The diameter of the droplet is determined by the maximum distance of white pixels in x- and y-direction. The velocity is determined by the displacement of \({\mathrm{CG}}_{\mathrm{d}}\) between sequential images and the frame rate of the high-speed camera. Droplet velocity and diameter are both averaged from three images before the impact, to reduce the influence of the oscillation of the droplet surface.
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The determination of the particle diameter is similar to the droplet diameter, but only with one image before impact.
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To determine the CG of the particle (\({\mathrm{CG}}_{\mathrm{p}}\)) for all images of an experiment it is necessary to mask its shape before the impact with an ideal circle (gray circle in the figure). For later images the position of this circle is adjusted to accurately map the bottom rows of the particle (red pixels in the figure). \({\mathrm{CG}}_{\mathrm{p}}\) is set equal to the CG of this mapped circle.
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The CG of the particle-droplet system (\({\mathrm{CG}}_{\mathrm{s}}\)) after the impact is determined similarly to the \({\mathrm{CG}}_{\mathrm{d}}\) before the impact. The x-value the centroid is used to split the image into a left and a right part.
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An overlap of the masked circle and the detected contour of the particle-droplet system is used to detect the pixel of the three-phase-point (3PP).
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To quantify the movement of the particle-droplet system, the flight height and time of flight are tracked. The code calculates the current lift-off state by identifying the number of pixels between the bottom of the particle and the substrate (bottom edge of the image). If there is at least one pixel inbetween, lift-off state is detected. The time of flight is determined by summing up the number of images with lift-off state and multiplication with the inverse of the frame rate.
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The half-spread angle is determined based on the coordinates of the \({\mathrm{CG}}_{\mathrm{p}}\) and the two 3PPs.
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The contact angles are calculated between the tangent of the particle surface and the tangent of the droplet contour at the 3PPs. The tangent of the particle is determined by the grey circle and the 3PP using a python function. The tangent of the droplet is determined by the 3PP and the coordinates of a pixel of the droplet contour near the 3PP. The selection of the second pixel is subject to a case distinction depending on the wetted particle area and some test studies.
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All calculated values are averaged based on both camera views.