An alternative method for computing contact angle from the dimensions of a small sessile drop

Ehrlich, R. B.

doi:10.1016/s0021-9797(68)80001-3

Cited by 16 publications

(13 citation statements)

References 3 publications

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“…First use of perturbation theory in this context has been made by Ehrlich [16]. Using surface energy minimisation, Shanahan obtained a first-order solution to the profile of an axisymmetric drop [17].…”

Section: Analytical Approximation Solutionmentioning

confidence: 99%

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Low-bond axisymmetric drop shape analysis for surface tension and contact angle measurements of sessile drops

Stalder¹,

Melchior²,

Müller³

et al. 2010

Colloids and Surfaces A: Physicochemical and Engineering Aspect

604

400

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a b s t r a c tA new method based on the Young-Laplace equation for measuring contact angles and surface tensions is presented. In this approach, a first-order perturbation technique helps to analytically solve the Young-Laplace equation according to photographic images of axisymmetric sessile drops. When appropriate, the calculated drop contour is extended by mirror symmetry so that reflection of the drop into substrate allows the detection of position of the contact points. To keep a wide range of applicability, a discretisation of the drop's profile is not realised; instead, an optimisation of an advanced image-energy term fits an approximation of the Young-Laplace equation to drop boundaries. In addition, cubic B-spline interpolation is applied to the image of the drop to reach subpixel resolution. To demonstrate the method's accuracy, simulated drops as well as images of liquid coal ash slags were analysed. Thanks to the high-quality image interpolation model and the image-energy term, the experiments demonstrated robust measurements over a wide variety of image types and qualities. The method was implemented in Java and is freely available [A.F. Stalder, LBADSA, Biomedical Imaging Group, EPFL,

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Section: Analytical Approximation Solutionmentioning

confidence: 99%

“…Introducing the first and second derivative of (17) with respect to˛into (16) and factoring out b, we obtain:…”

Section: Small-perturbation Theorymentioning

confidence: 99%

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Low-bond axisymmetric drop shape analysis for surface tension and contact angle measurements of sessile drops

Stalder¹,

Melchior²,

Müller³

et al. 2010

Colloids and Surfaces A: Physicochemical and Engineering Aspect

604

400

View full text Add to dashboard Cite

show abstract

“…In this case, we have, as may be seen from Figure 15, (23) i.e., the liquid surface remains horizontal up to the cylinder, and the contact angle may be obtained from equation (18). The depth of immersion h may be obtained using a cathetometer equipped with a high-power telescope (see above).…”

Section: Determination From the Equilibrium Meniscus Near A Floating mentioning

confidence: 99%

“…(64) In this case, the contact angle may be established in a manner identical to the one used when the particle is cylindrical, employing equation (18).…”

Section: Spherical Bodiesmentioning

confidence: 99%

Techniques of Measuring Contact Angles

Neumann

Good

1979

Surface and Colloid Science

274

164

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Bestimmung des Randwinkels bei der Benetzung von durch Koronaentladungen vorbehandelten Polyethylenfolien

Żenkiewicz

1989

Acta Polymerica

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Die Methoden zur Bestimmung des Benetzungswinkels von Polymeren werden analysiert. Die Randwinkel einer mit Koronaentladungen unterschiedlicher Intensitat vorbehandelten Polyethylenfolie wurden nach drei verschiedenen Verfahren gemessen. Die Homogenitat der Folienoberflache in bezug auf die freie Oberflachenenergie hangt von der IntensitPt der Entladung ab. Der Vergleich indirekter Bestimmungsmethoden mit der direkten Messung des Randwinkels rnit Hilfe eines Goniometers zeigt, daR die Genauigkeit der direkten Messung zur Beurteilung der Folien ausreicht . Onpedeaenue l~paesoeo y z~a npu cMaltueauuu nnenok u3 noamrnunena, 06pa60mannb&x Eoponnbw p a a p d o w npOaHaJIH3RpOBaHbl MeTORbI AJIR OIIpeAeJIeHMR yrna CMaqHBaHRH IIOJIRMepOB. KpaeBOfi IIJleHOK R 3 IIOJIH-3THJIeHa, 06pa60TaHHHX KOPOHHbIM pa3PRAOM pa3JIHqHOfi HHTeHCMBHOCTH, H3MePHJICR TpeMR Pa3JlHYHbIMH MeTO-AaMH. OJ(H0POAHOCTb IIOBepXHOCTH IIJIeHOK OTHOCHTeJIbHO CBO6OAHOfi IIOBepXHOCTHOfi 3HeprHH 3aBHCRT OT HHTeH-CRBHOCTH paspaga. CpasHeme KocBeHHbIx MeToAoB onpeAeneHm KpaeBoro yrna c nocpeAcTseHHbIM m~e p e~e x e~ C IIOMOwbIO r0HHOMeTpa yKa3bIBaeT H a TO, 'iT0 TOZIHOCTb IIpRMOrO R3MepeHRR AOCTaTOZIHa AJIH OUeHHH CMaWiBae-MOCTM IIJIeHOK. Determination of the contact angle at wetting of polyethylene foils treated by cornna dischargeMethods for the determination of the contact angle of polymers are analyzed. The contact angles of a polyethylene foil which had been treated by corona discharges of different intensities were determined by three methods. The homogeneity of the foil surface referring to the free surface energy depends on the intensity of the corona discharge. By comparing the direct measurement of the contact angle by means of a goniometer with the indirect determination methods it is shown that the accuracy of the direct method is sufficient for the evaluation of the wettability of the foils. I . EinleitungDer Wert der Oberflachenenergie (ys) und die Werte ihrer Komponenten y t und yep ( y t -Dispersionskomponente, ysP -Polarkomponente) bilden eine Grundlage fur die Einschatzung der Oberflacheneigenschaften der Polymere, die fur das Bedrucken, Schmucken, Kleben und Laminieren vorgesehen sind [l]. Die Zunahme von ys und insbesondere der Komponente ysP bei einer Vorbehandlung der Polymere [a] beeinfluat direkt die Verbesserung der Benetzungsbedingungen dieser Stoffe. Dies ist die Grundbedingung fur eine ausreichende Haftung des Druckes und eine entsprechende Haltbarkeit der Klebeverbindungen. Die Zunahme von ys hangt von der Intensitat und von der Zeitdauer der Vorbehandlungsprbzesse und von den Eigenschaften des Polymers ah. Die Vorbehandlungsprozesse erfordern bedeutende Energiemengen (Vorbehandlung mit Koronaentladungen oder Flammen) oder bedeutende Mengen chemischer Substanzen, hauptsachlich Losungsmittel und Sauren (Vorbehandlung rnit chemischen Methoden). ErfahrungsgemaR gibt es bestimmte Grenzwerte der Zeitdauer und der Intensitat der Vorbehandlungsprozesse. Wenn diese iiherschritten werden, kommt es zu keiner Verbesserung der Oberflacheneigen...

show abstract

An alternative method for computing contact angle from the dimensions of a small sessile drop

Cited by 16 publications

References 3 publications

Low-bond axisymmetric drop shape analysis for surface tension and contact angle measurements of sessile drops

Low-bond axisymmetric drop shape analysis for surface tension and contact angle measurements of sessile drops

Techniques of Measuring Contact Angles

Bestimmung des Randwinkels bei der Benetzung von durch Koronaentladungen vorbehandelten Polyethylenfolien

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