Sessile drops pinned on a horizontal superhydrophobic coating of steel. The cotangent formula

• M. Vigdorowitsch^1,2, L.D. Rodionova³, Dar Ali Al Saadi⁴, L.E. Tsygankova³, M.G. Shcherban⁵ and M.N. Uryadnikova³

¹ Mousson GmbH, Zum Gottschalkhof 8, 60594 Frankfurt am Main, Germany
² All-Russian Scientific Research Institute for the Use of Machinery and Oil Products in Agriculture, Novo-Rubezhnyj side str. 28, 392022 Tambov, Russian Federation
³ The G.R. Derzhavin Tambov State University, Internatsyonal’naya str. 33, 392000 Tambov, Russian Federation
⁴ Al Salam University College, district Al-Siddiyyah adjacent to Al-Waleed Center, Baghdad, Iraq
⁵ Perm State University, Bukirev str. 15, 614068 Perm, Russian Federation

Abstract: We have studied the dependence of apparent contact angles on water drop size on a steel superhydrophobic coating positioned horizontally. The cotangent formula introduced earlier to link contact angles of drops of different sizes (masses) on a horizontal flat substrate has been subjected to verification. Drops with volumes 0.64 up to 30.53 μL have been pinned on samples of carbon steel St3, possessing a superhydrophobic coating. Pinning has been arranged in 6 series, each with 11 drops. Every next drop had a bigger volume, covering the previous drop so that their centres coincided. The contact line of a bigger drop has thereby subtended the substrate’s dry circumferential fragment. Every new series has begun on a new dry surface fragment. The Young–Laplace method has been employed to basically determine the apparent contact angles. Based on the cotangent formula, the deviation of contact angles calculated with the power law on the basis of statistically processed data, from those given by the cotangent formula with the theoretical power magnitude 1/6, has constituted within 0.30%. Employment of the cotangent formula has been aimed to computationally determine hydrophobic and superhydrophobic features of a metal coating what is, in general, essential to prognosticate its durability.

Keywords: wetting, contact angle, superhydrophobicity, drop shape, cotangent formula

Int. J. Corros. Scale Inhib., 2024, 13, no. 2, 930-934
doi: 10.17675/2305-6894-2024-13-2-15

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