ХІМІЯ, ФІЗИКА ТА ТЕХНОЛОГІЯ ПОВЕРХНІ

ISSN 2518-1238 (Online), ISSN 2079-1704 (Print)

Характеристика змочуваності поверхні має вирішальне значення у багатьох галузях науки і технології, від видобувної промисловості до створення сучасних функціональних матеріалів і виробів біомедичного призначення. Зростаючий інтерес до явищ, пов’язаних зі змочуваністю, стимулює стрімке зростання дослідницької діяльності в цьому напрямку. Метою представленого огляду є послідовне висвітлення низки питань, пов’язаних з природою змочуваності та методами її дослідження. В ньому розглядаються базові концепції змочуваності як фізичного явища, методи для кількісного визначення її характеристик та сучасний рівень приладів для визначення характеристик змочуваності.

У першому розділі розглядаються фізичні основи змочуваності. Міжмолекулярні взаємодії, якими обумовлюється змочуваність, класифікуються залежно від їхньої природи. Так, обговорення міжмолекулірних взаємодій, у яких беруть участь полярні молекули, охоплює взаємодії між молекулами, які мають постійний дипольний момент, включаючи особливий механізм взаємодії між молекулами, який виникає, коли молекули можуть вільно обертатися. Розгляд взаємодій, що відбуваються в результаті поляризації молекул, включає взаємодії між іонами та незарядженими молекулами, взаємодії Дебая та дисперсійні сили Лондона. Водневі зв’язки розглядаються як окремий тип взаємодій.

У другому розділі розглядаються питання, які стосуються поверхневого натягу та його впливу на форму поверхні рідини, яка знаходиться у контакті з твердим тілом. Обговорюється взаємозв’язок між величиною поверхневого натягу та значенням контактного кута змочування. Розглядається рівняння Юнга-Лапласа, яке визначає форму краплі рідини, яка лежить на твердій поверхні.

Третій розділ присвячений експериментальному визначенню характеристик змочуваності поверхні та теоретичним засадам відповідних методів вимірювання. Особлива увага приділяється методу, відомому в англомовній літературі як метод ADSA, який засновується на аналізі  форми краплі, що лежить на поверхні. Коротко розглядаються чисельні методи виявлення геометричних структур на оцифрованих зображеннях, які призначені для отримання кількісних даних про силу поверхневого натягу та значення крайового кута змочування.

У четвертому розділі наводиться огляд приладів для дослідження змочуваності та вимірювання крайового кута, які серійно випускаються приладобудівельними підприємствами у різних країнах світу. Представлений також прототип приладу аналогічного призначення, створений у ІФН НАНУ.

Nogalska A., Trojanowska A., Tylkowski B., Garcia-Valls R. Surface characterization by optical contact angle measuring system. Phys. Sci. Rev. 2019. 5(2): 20190083. https://doi.org/10.1515/psr-2019-0083

Woodruff D.P. Modern techniques of surface science. 3rd ed. (Cambridge: Cambridge University Press, 2016). https://doi.org/10.1017/CBO9781139149716

Yun W., Chang S., Cogswell D.A., Eichmann S.L., Gizzatov A., Thomas G., Al-Hazza N., Abdel-Fattah A., Wang W. Toward reservoir-on-a-chip: rapid performance evaluation of enhanced oil recovery surfactants for carbonate reservoirs using a calcite-coated micromodel. Sci. Rep. 2020. 10: 782. https://doi.org/10.1038/s41598-020-57485-x

Tajmiri M., Zallaghi M., Roozbehani B. A comprehensive review of chemically induced reservoir wettability alteration: characterization and EOR aspects. Am. J. Oil Chem. Technol. 2018. 6(2): 151.

Mohammed M., Babadagli T. Wettability alteration: A comprehensive review of materials/methods and testing the selected ones on heavy-oil containing oil-wet systems. Adv. Colloid Interface Sci. 2015. 220: 54. https://doi.org/10.1016/j.cis.2015.02.006

Erzuah S., Fjelde I., Omekeh A.V. Wettability characterization using the flotation technique coupled with geochemical simulation. In: European Symposium on Improved Oil Recovery (IOR 2017). Proc. 19th Int. Conf. (Apr. 24, 2017, Stavanger, Norway). P. 1. https://doi.org/10.3997/2214-4609.201700309

Chi J., Zhang X., Wang Y., Shao C., Shang L., Zhao Y. Bio-inspired wettability patterns for biomedical applications. Mater. Horiz. 2021. 8(1): 124. https://doi.org/10.1039/D0MH01293A

Xue M., Ji Y., Ou J., Wang F., Li C., Lei S., Li W. Surface wettability and strong adhesion of medical polyurethane elastomer porous films by microphase separation. AIP Adv. 2019. 9(7): 075309. https://doi.org/10.1063/1.5107459

Nychka J.A., Gentleman M.M. Implications of wettability in biological materials science. JOM. 2010. 62(7): 39. https://doi.org/10.1007/s11837-010-0107-6

Menzies K.L., Jones L. The impact of contact angle on the biocompatibility of biomaterials. Optometry and Vision Science. 2010. 87(6): 387. https://doi.org/10.1097/OPX.0b013e3181da863e

Campbell D., Carnell S.M., Eden R.J. Applicability of contact angle techniques used in the analysis of contact lenses, part 1: comparative methodologies. Eye Contact Lens. 2013. 39(3): 254. https://doi.org/10.1097/ICL.0b013e31828ca174

Read M.L., Morgan P.B., Kelly J.M., Maldonado-Codina C. Dynamic contact angle analysis of silicone hydrogel contact lenses. J. Biomater. Appl. 2011. 26(1): 85. https://doi.org/10.1177/0885328210363505

Cai S., Wu C., Yang W., Liang W., Yu H., Liu L. Recent advance in surface modification for regulating cell adhesion and behaviors. Nanotechnol. Rev. 2020. 9(1): 971. https://doi.org/10.1515/ntrev-2020-0076

Cai Q., You H., Guo H., Wang J., Liu B., Xie Z., Chen D., Lu H., Zheng Y., Zhang R. Progress on AlGaN-based solar-blind ultraviolet photodetectors and focal plane arrays. Light. Sci. Appl. 2021. 10: 94. https://doi.org/10.1038/s41377-021-00527-4

Motmaen A., Rostami A., Matloub S. Ultra high-efficiency integrated mid infrared to visible upconversion system. Sci. Rep. 2020. 10: 9325. https://doi.org/10.1038/s41598-020-66392-0

Rogalski A., Antoszewski J., Faraone L. Third-generation infrared photodetector arrays. J. Appl. Phys. 2009. 105(9): 091101. https://doi.org/10.1063/1.3099572

Law K.Y., Zhao H. Contact angle measurements and surface characterization techniques. In: Surface Wetting: Characterization, Contact Angle, and Fundamentals. (Cham: Springer, 2016). https://doi.org/10.1007/978-3-319-25214-8_2

De Wijs W.J.A., Laven J., de With G. Wetting forces and meniscus pinning at geometrical edges. AIChE J. 2016. 62(12): 4453. https://doi.org/10.1002/aic.15341

Zimon A.D. Fluid adhesion and wetting. (Moscow: Chemistry, 1974). [in Russian].

Padday J.F., Uffindell N.D. The calculation of cohesive and adhesive energies from intermolecular forces at a surface. J. Phys. Chem. 1968. 72(5): 1407. https://doi.org/10.1021/j100851a002

Kumar G., Prabhu K.N. Review of non-reactive and reactive wetting of liquids on surfaces. Adv. Colloid Interface Sci. 2007. 133(2): 61. https://doi.org/10.1016/j.cis.2007.04.009

Weltsch Z. Wetting of non-reactive and reactive metallic substrates by brazing liquids. IOP Conf. Ser.: Mater. Sci. Eng. 2020. 903(1): 012035. https://doi.org/10.1088/1757-899X/903/1/012035

Eustathopoulos N. Wetting by liquid metals - application in materials processing: the contribution of the Grenoble Group. Metals. 2015. 5(1): 350. https://doi.org/10.3390/met5010350

Young T. An Essay on the Cohesion of Fluids. Philosophical Transactions of the Royal Society of London. 1805. 95: 65. https://doi.org/10.1098/rstl.1805.0005

Israelachvili J.N. Intermolecular and surface forces. 3rd ed. (Amsterdam: Elsevier, 2011). https://doi.org/10.1016/B978-0-12-391927-4.10001-5

Barash Yu.S. Van der Waals forces. (Moscow: Nauka. 1988). [In Russian].

Prigogine I. The molecular theory of solutions. (Amsterdam: North-Holland publishing company, 1957).

Rimai D.S., Quesnel D.J. Particle adhesion. In: Adhesion science and engineering. V. 2. (Amsterdam: Elsevier B.V., 2002). https://doi.org/10.1201/9781482298161

Margenau H., Kestner N.R. Theory of intermolecular forces. (Oxford: Pergamon. 1971).

Israelachvili J.N. Van der Waals forces in biological systems. Q. Rev. Biophys. 1974. 6(4): 341. https://doi.org/10.1017/S0033583500001566

Mahanty J., Ninham B.W. Dispersion forces. (New York: Academic Press. 1976).

Parsegian V.A. Van der Waals forces: a handbook for biologists, chemists, engineers, and physicists. (New York: Cambridge University Press, 2006). https://doi.org/10.1017/CBO9780511614606

Pauling L. The nature of the chemical bond and the structure of molecules and crystals; an introduction to modern structural chemistry. 3rd ed. (Ithaca (NY): Cornell University Press, 1960).

Coulson C.A. Valence. 2nd ed. (New York: Oxford University Press, 1961).

Joesten M.D., Schaad L.J. Hydrogen bonding. (New York: Dekker, 1974).

Jeffrey G.A. An introduction to hydrogen bonding (topics in physical chemistry). (USA: Oxford University Press, 1997).

Schuster P., Zundel G., Sandorfy C. The hydrogen bond. (Amsterdam: North-Holland Publ., 1976).

Steiner T. The hydrogen bond in the solid state. Angew. Chem. Int. Ed. 2002. 41(1): 48. https://doi.org/10.1002/1521-3773(20020104)41:1<48::AID-ANIE48>3.0.CO;2-U

Larson J.W., McMahon T.B. Gas-phase bihalide and pseudobihalide ions. An ion cyclotron resonance determination of hydrogen bond energies in XHY- species (X, Y = F, Cl, Br, CN). Inorg. Chem. 1984. 23(14): 2029. https://doi.org/10.1021/ic00182a010

Emsley J. Very strong hydrogen bonds. Chem. Soc. Rev. 1980. 9(1): 91. https://doi.org/10.1039/cs9800900091

Needham P. Hydrogen bonding: Homing in on a tricky chemical concept. Studies in History and Philosophy of Science. Part A. 2013. 44(1): 51. https://doi.org/10.1016/j.shpsa.2012.04.001

Inoue M. Structural integrity of metal-polymer adhesive interfaces in microelectronics. In: Advanced Adhesives in Electronics. Materials, Properties and Applications. (Sawston, Cambridge: Woodhead Publishing, 2011). https://doi.org/10.1533/9780857092892.2.157

Hutchins K.M. Functional materials based on molecules with hydrogen-bonding ability: applications to drug co-crystals and polymer complexes. R. Soc. Open Sci. 2018. 5(6): 180564. https://doi.org/10.1098/rsos.180564

Zhang J., Zeng H. Intermolecular and Surface Interactions in Engineering Processes. Engineering. 2021. 7(1): 63. https://doi.org/10.1016/j.eng.2020.08.017

Dzialoshinskii I.E., Lifshiz E.M., Pitaevskii L.P. General theory of van der Waals forces. Uspekhi Fizicheskih Nauk. 1961. LXXIII(3): 381. [in Russian]. https://doi.org/10.3367/UFNr.0073.196103b.0381

Hermann J., Robert A., DiStasio Jr. R.A., Tkatchenko A. First-principles models for van der Waals interactions in molecules and materials: Concepts, theory, and applications. Chem. Rev. 2017. 117(6): 4714. https://doi.org/10.1021/acs.chemrev.6b00446

Leite F.L., Bueno C.C., Da Róz A.L., Ziemath E.C., Oliveira Jr.O.N. Theoretical models for surface forces and adhesion and their measurement using atomic force microscopy. Int. J. Mol. Sci. 2012. 13(10): 12773. https://doi.org/10.3390/ijms131012773

Singla S., Jain D., Zoltowski C.M., Voleti S., Stark A.Y., Niewiarowski P.H., Dhinojwala A. Direct evidence of acid-base interactions in gecko adhesion. 2021. Sci. Adv. 7(21): eabd9410. https://doi.org/10.1126/sciadv.abd9410

Whitesides G.M., Biebuyck H.A., Folkers J.P., Prime K. Acid-base interactions in wetting. J. Adhes. Sci. Technol. 5(1): 57. https://doi.org/10.1163/156856191X00828

Casimir H.B.C. On the attraction between two perfectly conducting plates. Proc. K. Ned. Akad. Wet. 1948. 51(7): 793.

Drosdoff D., Woods L.M. Casimir forces and graphene sheets. Phys. Rev. B. 2010. 82(15): 155459. https://doi.org/10.1103/PhysRevB.82.155459

Bordag M., Fialkovsky I.V., Gitman D.M., Vassilevich D.V. Casimir interaction between a perfect conductor and graphene described by the Dirac model. Phys. Rev. B. 2009. 80(24): 0245406. https://doi.org/10.1103/PhysRevB.80.245406

Fialkovsky I.V., Marachevsky V.N., Vassilevich D.V. Finite temperature Casimir effect for graphene. Phys. Rev. B. 2011. 84(3): 035446. https://doi.org/10.1103/PhysRevB.84.035446

Adamson A.W., Gast A.P. Physical chemistry of surfaces. 6th ed. (New York: A Wiley Interscience Publication, 1997).

Hebbar R.S., Isloor A.M., Ismail A.F. Contact Angle Measurements. In: Membrane Characterization. (Amsterdam: Elsevier, 2017). https://doi.org/10.1016/B978-0-444-63776-5.00012-7

Ebnesajjad S., Landrock A.H. Surface Tension and Its Measurement. In: Adhesives Technology Handbook. 3rd ed. (Amsterdam: Elsevier Inc., 2015). https://doi.org/10.1016/B978-0-323-35595-7.00002-4

Van Oss C.J. Chapter Two - The apolar and polar properties of liquid water and other condensed-phase materials. Interface Science and Technology. Book series. 2008. 16: 13. https://doi.org/10.1016/S1573-4285(08)00202-0

Dupré A. Theorie mécanique de la chaleur. (Paris: Gauthier-Villars, 1869).

Durand M. Mechanical approach to surface tension and capillary phenomena. American Journal of Physics. 2021. 89(3): 261. https://doi.org/10.1119/10.0002411

Adam N.K. The physics and chemistry of surfaces. 3rd ed. (London: Oxford University Press, 1941).

Bangham D.H., Razouk R.I. Adsorption and wettability of solid surfaces. Trans. Faraday Soc. 1937. 33: 1459. https://doi.org/10.1039/tf9373301459

Zisman W.A. Relation of the equilibrium contact angle to liquid and solid constitution. In: Contact angle, wettability, and adhesion. (Washington: American Chemical Society, 1964). https://doi.org/10.1021/ba-1964-0043.ch001

Good R.J. Contact angle, wetting, and adhesion: a critical review. J. Adhes. Sci. Technol. 1992. 6(22): 1269. https://doi.org/10.1163/156856192X00629

Bikerman J.J. Surface Chemistry. 2nd ed. (New York: Academic Press, 1958). https://doi.org/10.1016/B978-1-4832-2937-9.50003-8

Bikerman J.J. Surface energy of solids. Top. Curr. Chem. 1978. 77: 1. https://doi.org/10.1007/BFb0048037

Ivanov I.B., Kralchevsky P.A., Nikolov A.D. Film and line tension effects on the attachment of particles to an interface: I. Conditions for mechanical equilibrium of fluid and solid particles at a fluid interface. J. Colloid Interface Sci. 1986. 112 (1): 97. https://doi.org/10.1016/0021-9797(86)90072-X

Johnson R.E.Jr. Conflicts between Gibbsian thermodynamcis and recent treatments of interfacial energies in solid-liquid-vapor systems. J. Phys. Chem. 1959. 63(10): 1655. https://doi.org/10.1021/j150580a021

Gao L., McCarthy T.J. Wetting 101. Langmuir. 2009. 25(24): 14105. https://doi.org/10.1021/la902206c

Makkonen L. Faulty intuitions of wetting. International Journal of Wettability Science and Technology. 2018. 1(1): 13.

Hui C.Y., Jagota A. Deformation near a liquid contact line on an elastic substrate. Proc. Math. Phys. Eng. Sci. 2014. 470(2167): 20140085. https://doi.org/10.1098/rspa.2014.0085

Makkonen L. Young's equation revisited. J. Phys.: Condens. Matter. 2016. 28(13): 135001. https://doi.org/10.1088/0953-8984/28/13/135001

Frumkin A.N. On wetting and sticking phenomena. Zhurnal Fizicheskoi Khimii. 1938. 12(4): 337. [in Russian].

Derjaguin B.V. Theory of capillary condensation and other capillary phenomena accounting for the disjoining pressure of polymolecular liquid films. Acta Physicochimia. 1940. 12(2): 181. [in Russian].

Derjaguin B.V., Zorin Z.M. Study of the surface condensation and adsorption of vapors near saturation by the optical micropolarization method. Zhurnal Fizicheskoi Khimii. 1955. 29(10): 1755. [in Russian].

Lubarsky G.V., Davidson M.R., Bradley R.H. Particle-surface capillary forces with disjoining pressure. Phys. Chem. Chem. Phys. 2006. 8(21): 2525. https://doi.org/10.1039/b602005d

Van Honschoten J.W., Brunets N., Tas N.R. Capillarity at the nanoscale. Chem. Soc. Rev. 2010. 39(3): 1096. https://doi.org/10.1039/b909101g

Popescu M.N., Oshanin G., Dietrich S., Cazabat A.M. Precursor films in wetting phenomena. J. Phys.: Condens. Matter. 2012. 24(24): 243102. https://doi.org/10.1088/0953-8984/24/24/243102

Indekeu J.O. Line tension at wetting. Int. J. Mod. Phys. B. 1994. 8(3): 309. https://doi.org/10.1142/S0217979294000129

Hirasaki G.L. Wettability: Fundamentals and Surface Forces. SPE Form Eval. 1991. 6(02): 217. https://doi.org/10.2118/17367-PA

Boruvka L., Neumann A.W. Generalization of the classical theory of capillarity. J. Chem. Phys. 1977. 66(12): 5464. https://doi.org/10.1063/1.433866

Saini D., Rao D.N. Line Tension-Based Modification of Young's Equation for Rock-Oil-Brine Systems. SPE Reservoir. Eval. Eng. 2009. 12(05): 702. https://doi.org/10.2118/113321-PA

Li D., Neumann A.W. Determination of line tension from the drop size dependence of contact angles. Colloids Surf. 1990. 43(2): 195. https://doi.org/10.1016/0166-6622(90)80288-F

Koshoridze S.I. Calculating Line Tension for a Simple Model of a Surface Nanobubble. Tech. Phys. Lett. 2020. 46(5): 416. https://doi.org/10.1134/S1063785020050089

Das S.K., Egorov S.A., Virnau P., Winter D., Binder K. Do the contact angle and line tension of surfaceattached droplets depend on the radius of curvature? J. Phys.: Condens. Matter. 2018. 30(25): 255001. https://doi.org/10.1088/1361-648X/aac363

Weijs J.H., Marchand A., Andreotti B., Lohse D., Snoeijer D.J. Origin of line tension for a Lennard-Jones nanodroplet. Phys. Fluids. 2011. 23(2): 022001. https://doi.org/10.1063/1.3546008

Drelich J.W., Boinovich L., Chibowski E., Della Volpe C., Hołysz L., Marmur A., Siboni S. Contact angles: history of over 200 years of open questions. Surf. Innovations. 2020. 8(1-2): 3. https://doi.org/10.1680/jsuin.19.00007

Tadmor R. Line energy and the relation between advancing, receding, and young contact angles. Langmuir. 2004. 20(18): 7659. https://doi.org/10.1021/la049410h

Swain P.S., Lipowsky R. Contact angles on heterogeneous surfaces: A new look at Cassie's and Wenzel's laws. Langmuir. 1998. 14(23): 6772. https://doi.org/10.1021/la980602k

Cassie A.B.D., Baxter S. Wettability of porous surfaces. Trans. Faraday Soc. 1944. 40: 546. https://doi.org/10.1039/tf9444000546

Cassie A.B.D. Contact angles. Discuss. Faraday Soc. 1948. 3: 11. https://doi.org/10.1039/df9480300011

Wenzel R.N. Resistance of solid surfaces to wetting by water. Ind. Eng. Chem. 1936. 28(8): 988. https://doi.org/10.1021/ie50320a024

Wolansky G., Marmur A. Apparent contact angles on rough surfaces: the Wenzel equation revisited. Colloids Surf. A. 1999. 156(1-3): 381. https://doi.org/10.1016/S0927-7757(99)00098-9

Marmur A. Soft Contact: Measurement and Interpretation of Contact Angles. Soft Matter. 2006. 2: 12. https://doi.org/10.1039/B514811C

Kung C.H., Sow P.K., Zahiri B., Mérida W. Assessment and interpretation of surface wettability based on sessile droplet contact angle measurement: challenges and opportunities. Adv. Mater. Interfaces. 2019. 6(18): 1900839. https://doi.org/10.1002/admi.201900839

Eral H.B., Oh J.M. Contact angle hysteresis: A review of fundamentals and applications. Colloid Polymer Sci. 2013. 291(2): 247. https://doi.org/10.1007/s00396-012-2796-6

Moradi S., Englezos P., Hatzikiriakos S.G. Contact angle hysteresis: surface morphology effects. Colloid Polymer Sci. 2013. 291(2): 317. https://doi.org/10.1007/s00396-012-2746-3

Bormashenko E.Y. Physics of wetting. Phenomena and applications of fluids on surfaces. (Boston: Cengage Learning - Gale, 2017). https://doi.org/10.1515/9783110444810

Mugele F., Heikenfeld J. Introduction to capillarity and wetting phenomena. In: Electrowetting: Fundamental Principles and Practical Applications. 1st ed. (Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA, 2019). https://doi.org/10.1002/9783527412396.ch1

Siqveland L.M., Skjæveland S.M. Derivations of the Young-Laplace equation. Capillarity. 2021. 4(2): 23. https://doi.org/10.46690/capi.2021.02.01

Yuan Y., Lee T.R. Contact Angle and Wetting Properties. In: Surface Science Techniques. (Berlin Heidelberg: Springer-Verlag, 2013). https://doi.org/10.1007/978-3-642-34243-1_1

Volpe C.D., Siboni S. The Wilhelmy method: a critical and practical review. Surf. Innovations. 2018. 6(3): 120. https://doi.org/10.1680/jsuin.17.00059

Lu C., Wang J., Lu X., Zheng T., Liu Y., Wang X., Zhang D., Seveno D. Wettability and Interfacial Properties of Carbon Fiber and Poly(ether ether ketone) Fiber Hybrid Composite. ACS Appl. Mater. Interfaces. 2019. 11(34): 31520. https://doi.org/10.1021/acsami.9b09735

Yum K., Yu M.-F. Measurement of Wetting Properties of Individual Boron Nitride Nanotubes with the Wilhelmy Method Using a Nanotube-Based Force Sensor. Nano Lett. 2006. 6(2): 329. https://doi.org/10.1021/nl052084l

Bruel C., Queffeulou S., Darlow T., Nick Virgilio N., Tavares J.R., Patience G.S. Experimental Methods in Chemical Engineering: Contact Angles. Can. J. Chem. Eng. 2018. 97(4): 832. https://doi.org/10.1002/cjce.23408

Hebbar R.S., Isloor A.M., Ismail A.F. Contact Angle Measurements. In: Membrane Characterization. (Amsterdam: Elsevier, 2017). https://doi.org/10.1016/B978-0-444-63776-5.00012-7

Law K.Y., Zhao H. Surface Wetting. Characterization, Contact Angle, and Fundamentals. (Cham: Springer International Publishing, 2016).

Shimokawa M., Takamura T. Relation between interfacial tension and capillary liquid rise on polished metal electrodes. J. Electroanal. Chem. Interfacial Electrochem. 1973. 41(3): 359. https://doi.org/10.1016/S0022-0728(73)80414-0

Budziak C.J., Vargha-Butler E.I., Neumann A.W. Temperature dependence of contact angles on elastomers. J. Appl. Polym. Sci. 1991. 42(7): 1959. https://doi.org/10.1002/app.1991.070420720

Jordan D.D., Lane J.E. A thermodynamic discussion of the use of a vertical-plate balance for the measurement of surface tension. Austral. J. Chem. 1964. 17(1): 7. https://doi.org/10.1071/CH9640007

Budziak C.J., Neumann A.W. Automation of the capillary rise technique for measuring contact angles. Colloids Surf. 1990. 43(2): 279. https://doi.org/10.1016/0166-6622(90)80293-D

Restagno F., Poulard C., Cohen C., Vagharchakian L., Léger L. Contact angle and contact angle hysteresis measurements using the capillary bridge. Langmuir. 2009. 25(18): 11188. https://doi.org/10.1021/la901616x

Vagharchakian L., Restagno F., Léger L. Capillary bridge formation and breakage: A test to characterize antiadhesive Surfaces. J. Phys. Chem. B. 2009. 113(12): 3769. https://doi.org/10.1021/jp807698s

Cohen C., Restagno F., Poulard C., Léger L. Wetting and dewetting transition: An efficient toolbox for characterizing low-energy surfaces. Langmuir. 2010. 26(19): 15345. https://doi.org/10.1021/la102545z

Adam N.K., Jessop G.J. Angles of contact and polarity of solid surfaces. J. Chem. Soc., Trans. 1925. 127: 1863. https://doi.org/10.1039/CT9252701863

Extrand C.W., Moon S.I. Indirect Methods to Measure Wetting and Contact Angles on Spherical Convex and Concave Surfaces. Langmuir. 2012. 28(20): 7775. https://doi.org/10.1021/la301312v

Bigelow W.C., Pickett D.L., Zisman W.A. Oleophobic Monolayers. I. Films adsorbed from Solution in Non-Polar. Liquids. J. Colloid Sci. 1946. 1(6): 513. https://doi.org/10.1016/0095-8522(46)90059-1

Neumann A.W., Good R.J. Methods of measuring contact angles. In: Surface and Colloid Science: Experimental Methods. V. 11. (New York: Plenum Publishing, 1979). https://doi.org/10.1007/978-1-4615-7969-4_2

Hunter R.J. Foundations of Colloid Science. 2nd ed. (Oxford: Clarendon Press, 2001).

Quincke G.H. Ueber der capillaritats-erscheinungen an der gemeinschaftlichen Oberfläche von Flüssigkeiten. Annu. Phys. Chem. 1870. 215: 1. https://doi.org/10.1002/andp.18702150102

Magie W.F. The contact angle of liquids and solids. Philos. Mag. 1888. 26: 162. https://doi.org/10.1080/14786448808628250

de Gennes P.G., Brochard-Wyart F., Quere D. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. (New York: Springer, 2004). https://doi.org/10.1007/978-0-387-21656-0

Behroozi F. Determination of contact angle from the maximum height of enlarged drops on solid surfaces. Am. J. Phys. 2012. 80(4): 284. https://doi.org/10.1119/1.3678306

Williams D.L., Kuhn A.T., Amann M.A., Hausinger M.B., Konarik M.M., Nesselrode E.I. Computerized Measurement of Contact Angles. Galvanotechnik. 2010. 101(11): 2502.

Behroozi F., Behroozi P.S. Reliable determination of contact angle from the height and volume of sessile drops. Am. J. Phys. 2019. 87(1): 28. https://doi.org/10.1119/1.5078512

Bunday B.D. Basic optimisation methods. (London: Edward Arnold, 1984).

Rotenderg Y., Boruvka L., Neumann A.W. Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces. J. Colloid Interface Sci. 1983. 93(1): 169. https://doi.org/10.1016/0021-9797(83)90396-X

Bashforth F., Adams J.C. An attempt to test the theories of capillary attraction. (Cambridge: Cambridge University Press, 1883).

Euler L. Recherches sur la courbure des surfaces. Mémoires de l'Académie des Sciences de Berlin. 1767. 16: 119.

Eisenhart L.P. A treatise on the differential geometry of curves and surfaces. (Boston: Ginn and Company, 1909).

Glaeser G., Stachel H., Odehnal B. The Universe of Conics: From the ancient Greeks to 21st century developments. (Berlin Heidelberg: Springer Spektrum, 2016). https://doi.org/10.1007/978-3-662-45450-3

Yates R.C. Analytic geometry with calculus. (New Jersey: Englewood Cliffs, 1961).

Muskhelishvili N.I. Analytic Geometry Course, 4th edition. (Moskow: Vysshaya shkhola, 1967). [in Russian].

Protter M.H., Morrey C.B. College calculus with analytic geometry. (Boston: Addison-Wesley, 1970).

Kishan H. Differential calculus. (New Dehli: Atlantic Publishers and Distributors, 2007).

Zhang Y., Chatain D., Anna S.L., Garoff S. Stability of a Compound Sessile Drop at the Axisymmetric Configuration. J. Colloid Interface Sci. 2016. 462: 88. https://doi.org/10.1016/j.jcis.2015.09.043

Zhu Z.Q., Wang Y., Liu Q.S., Xie J.C. Influence of Bond number on behaviors of liquid drops deposited onto solid substrates. Microgravity Sci. Technol. 2012. 24(3): 181. https://doi.org/10.1007/s12217-011-9294-1

Hartland S., Hartley R.W. Axisymmetric fluid-liquid interfaces. (Amsterdam: Elsevier, 1976).

Ferguson R. An easier derivation of the curvature formula from first principles. Australian senior mathematics journal. 2018. 32(2): 16.

Saad S.M.I., Neumann A.W. Axisymmetric Drop Shape Analysis (ADSA): An outline. Adv. Colloid Interface Sci. 2016. 238: 62. https://doi.org/10.1016/j.cis.2016.11.001

Del Río O.I., Neumann A.W. Axisymmetric Drop Shape Analysis: Computational Methods for the Measurement of Interfacial Properties from the Shape and Dimensions of Pendant and Sessile Drops. J. Colloid Interface Sci. 1997. 196: 136. https://doi.org/10.1006/jcis.1997.5214

Bateni A., Susnar S.S., Amirfazli A., Neumann A.W. A high-accuracy polynomial fitting approach to determine contact angles. Colloids Surf. A. 2003. 219(1-3): 215. https://doi.org/10.1016/S0927-7757(03)00053-0

Atefi E., Mann J.A., Tavana H. A Robust Polynomial Fitting Approach for Contact Angle Measurements. Langmuir. 2013. 29(19): 5677. https://doi.org/10.1021/la4002972

Cabezas M.G., Bateni A., Montanero J.M., Neumann A.W. A new drop-shape methodology for surface tension measurement. Appl. Surf. Sci. 2004. 238(1-4): 480. https://doi.org/10.1016/j.apsusc.2004.05.250

Stalder A.F., Melchior T., Müller M., Sage D., Blu T., Unser M. Low-bond axisymmetric drop shape analysis for surface tension and contact angle measurements of sessile drops. Colloids Surf. A. 2010. 364(1-3): 72. https://doi.org/10.1016/j.colsurfa.2010.04.040

Kalantarian A., David R., Chen J., Neumann A.W. Simultaneous measurement of contact angle and surface tension using axisymmetric drop-shape analysis-no apex (ADSA-NA). Langmuir. 2011. 27(7): 3485. https://doi.org/10.1021/la104155x

Hussain R., Vogt S.J., Honari A., Hollingsworth K.G., Sederman J., Mitchell J., Johns M.L. Interfacial tension measurements using MRI drop shape analysis. Langmuir. 2014. 30(6): 1566. https://doi.org/10.1021/la404635x

Marchuk I.V., Cheverda V.V., Strizhak P.A., Kabov O.A. Determination of surface tension and contact angle by the axisymmetric bubble and droplet shape analysis. Thermophys. Aeromech. 2015. 22(3): 297. https://doi.org/10.1134/S0869864315030038

Heib F., Schmitt M. Statistical contact angle analyses with the high-precision drop shape analysis (HPDSA) approach: Basic principles and applications. Coatings. 2016. 6(4): 57. https://doi.org/10.3390/coatings6040057

Yang J., Yu K., Zuo Y.Y. Accuracy of axisymmetric drop shape analysis in determining surface and interfacial tensions. Langmuir. 2017. 33(6): 8914. https://doi.org/10.1021/acs.langmuir.7b01778

Vuckovac M., Latikka M., Liu K., Huhtamäki T., Ras R.H.A. Uncertainties in contact angle goniometry. Soft Matter. 2019. 15: 7089. https://doi.org/10.1039/C9SM01221D

Ma W.Y., Manjunath B.S. Edgeflow: a technique for boundary detection and image segmentation. IEEE Trans. Image Process. 2000. 9(8): 1375. https://doi.org/10.1109/83.855433

Somkantha K., Theera-Umpon N., Auephanwiriyakul S. Boundary detection in medical images using edge following algorithm based on intensity gradient and texture gradient features. IEEE Trans. Biomed. Eng. 2011. 58(3): 567. https://doi.org/10.1109/TBME.2010.2091129

Senthilkumaran N., Vaithegi S. Image segmentation by using thresholding techniques for medical images. Comput. Sci. Eng. 2016. 6(1): 1. https://doi.org/10.5121/cseij.2016.6101

Sharma N., Aggarwal L.M. Automated medical image segmentation techniques. J. Med. Phys. 2010. 35(1): 3. https://doi.org/10.4103/0971-6203.58777

Danielsson P.E., Seger O. Generalized and separable sobel operators. In: Machine vision for three-dimensional scenes. (Cambridge: Academic Press, 1990). https://doi.org/10.1016/B978-0-12-266722-0.50016-6

Davis L.S. A survey of edge detection techniques. Computer Graphics and Image Processing. 1975. 4(3): 248. https://doi.org/10.1016/0146-664X(75)90012-X

Mlsna P.A., Rodríguez J.J. Chapter 19 - Gradient and Laplacian Edge Detection. In: The essential guide to image processing. 2nd ed. (Cambridge: Academic Press, 2009). https://doi.org/10.1016/B978-0-12-374457-9.00019-6

Adlakha D., Adlakha D., Tanwar R. Analytical Comparison between Sobel and Prewitt Edge Detection Techniques. International Journal of Scientific & Engineering Research (IJSER). 2016. 7(1): 1482.

Hoorfar M., Neumann A.W. Axisymmetric drop shape analysis (ADSA) for the determination of surface tension and contact angle. The Journal of Adhesion. 2004. 80(8): 727. https://doi.org/10.1080/00218460490477684

Hoorfar M., Neumann A.W. Recent progress in axisymmetric dop shape analysis (ADSA). Adv Colloid Interface Sci. 2006. 121(1-3): 25. https://doi.org/10.1016/j.cis.2006.06.001

Canny J.F. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1986. 8(6): 769. https://doi.org/10.1109/TPAMI.1986.4767851

Biole D., Wang M., Bertola V. Assessment of direct image processing methods to measure the apparent contact angle of liquid drops. Exp. Therm. Fluid Sci. 2016. 76: 296. https://doi.org/10.1016/j.expthermflusci.2016.04.006

Zakariah M., AlShalfan K., Li D., Huang W., Xu G., Zhang T., Shahnasser H. Image boundary, corner, and edge detection: past, present, and future. International Journal of Computer Electrical Engineering. 2020. 12(2): 39. https://doi.org/10.17706/IJCEE.2020.12.2.39-57

Teja V.S.M., Rao K.D.G. Moore contour tracing algorithm. Int. Res. J. Eng. Technol. 2019. 6(9): 1330.

Mirzaei M. A new method for measuring the contact angles from digital images of liquid drops. Micron. 2017. 102: 65. https://doi.org/10.1016/j.micron.2017.09.001

Sonka M., Hlavac V., Boyle R. Image Processing, Analysis, and Machine Vision. 4th ed. (Stamford: Cengage Learning, 2015).

Szeliski R. Computer Vision: Algorithms and Applications. (New York: Springer, 2011). https://doi.org/10.1007/978-1-84882-935-0

Ramé-hart Model 90 Goniometer / Tensiometer. http://ramehart.com/pdf/90_Series.pdf

Ramé-hart Model 790. http://ramehart.com/pdf/790.pdf

The KRÜSS Scientific Drop Shape Analyzer DSA100 model. https://www.kruss-scientific.com/en/products-services/products/dsa100m

The KRÜSS Scientific Drop Shape Analyzer DSA30 model (Datasheet). https://www.kruss-scientific.com/en/products-services/products/dsa30b

Owens D.K., Wendt R.C. Estimation of the surface free energy of polymers. J. Appl. Polym. Sci. 13 (8): 1741. https://doi.org/10.1002/app.1969.070130815

Palencia M. Surface free energy of solids by contact angle measurements. J. Sci. Technol. Appl. 2017. 2: 84. https://doi.org/10.34294/j.jsta.17.2.17

Cabezas M.G., Bateni A., Montanero J.M., Neumann A.W. A new drop-shape methodology for surface tension measurement. Appl. Surf. Sci. 2004. 238(1-4): 480. https://doi.org/10.1016/j.apsusc.2004.05.250

Cabezas M.G., Bateni A., Montanero J.M., Neumann A.W. A new method of image processing in the analysis of axisymmetric drop shapes. Colloids Surf. A. 2005. 255(1): 193. https://doi.org/10.1016/j.colsurfa.2004.12.049

Eral H.B., 't Mannetje D.J.C.M., Oh J.M. Contact angle hysteresis: a review of fundamentals and applications. Colloid Polym. Sci. 2013. 291(2): 247. https://doi.org/10.1007/s00396-012-2796-6

Makkonen L. A thermodynamic model of contact angle hysteresis. 2017. J. Chem. Phys. 147(6): 064703. https://doi.org/10.1063/1.4996912

Chibowski E., Jurak M. Comparison of contact angle hysteresis of different probe liquids on the same solid surface. Colloid Polym. Sci. 2013. 291(2): 391. https://doi.org/10.1007/s00396-012-2777-9

Huhtamäki T., Tian X., Korhonen J.T., Ras R.H. A. Surface-wetting characterization using contact-angle measurements. Nature Protocols. 2018. 13(7): 1521.https://doi.org/10.1038/s41596-018-0003-z