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Statistical characteristics of coefficients of a cubic approximation of isotherms of surface active substance films; pp. 417–427

Full article in PDF format | doi: 10.3176/proc.2014.4.07

Elena L. Averbukh, Tatyana G. Talipova, Andrey A. Kurkin, Tarmo Soomere


We explore possibilities for polynomial approximation of the isotherms (the dependence of the pressure, exerted by the film, on the concentration of the substance per unit area) of films of surface active substances in marine environment. The analysis is based on isotherms for samples from the nearshore of the Black Sea and the coasts of the USA. The isotherms are approximated using cubic polynomials. The constant term and the coefficients of this polynomial have a reasonable scatter: their average values are comparable with their standard deviation. The standard deviations of the coefficients at the quadratic and the cubic term exceed the relevant average values by two orders of magnitude. This property signals that it is evidently not possible to approximate the isotherms of surface active films using one universal polynomial function even for one location and that it is necessary to account for the described scatter in estimates of the properties and impact of surface films. We provide cumulative distributions of the coefficients of the cubic approximation for the use in probabilistic express models of properties of surface films in the marine environment.


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