Mathematical analysis of axisymmetric sessile drop: Application to the reduction of bromine in a two-phase electrolyte

• Published in: Journal of colloid and interface science 1983, Vol.92 (2), p.489-498
• Main Authors: Leach, Steven C, Ablow, Clarence M, Kinoshita, Kimio
• Format: Article
• Language: English
• ISSN: 0021-9797; 1095-7103
• DOI: 10.1016/0021-9797(83)90170-4

The profile of an axisymmetric sessile drop was mathematically analyzed to relate the drop height, H, and equatorial diameter, D, to the contact radius with 180° contact angle, R, and the ratio of buoyant to interfacial tension forces, β. The relationships between ( H D ) and ( R D ) or log 10 β, which are valid over 0.2 < H D < 0.9 , were derived from a numerical integration of the differential equations and fitting of the results to fifth-order polynomials. Asymptotic formulas were also obtained analytically for the cases where H D < 0.2 and H D > 0.9 and all contact angles. The results of the mathematical analysis were used to analyze the data on the enhancement in the bromine reduction current that was observed with a two-phase electrolyte consisting of sessile drops of bromine complexed with trimethylethylammonium bromide less than 0.2 cm high on a ruthenized titanium electrode in an aqueous electrolyte ( 2M ZnBr 2 1M ZnCl 2 3M KCl ) containing dissolved bromine.