Dynamics of rear stagnant cap formation at the surface of rising bubbles in surfactant solutions at large Reynolds and Marangoni numbers and for slow sorption kinetics

Autor: Volodymyr I. Kovalchuk, Stanislav S. Dukhin, Reinhard Miller, Dariush Bastani, Marzieh Lotfi
Rok vydání: 2016
Předmět:
Zdroj: Colloids and Surfaces A: Physicochemical and Engineering Aspects. 492:127-137
ISSN: 0927-7757
DOI: 10.1016/j.colsurfa.2015.12.028
Popis: In spite of the high level in the theory of steady rear stagnant caps (RSC) and its influence on steady rising, its practical application is mostly impossible because the coefficients for the adsorption and desorption rates are separately unknown. The determination of k a and k d separately is an actual task for the adsorption dynamics as whole. While steady RSC and steady rising retardation by surfactants are described in literature in details, only few papers are devoted to the modeling of the decelerated rising. Moreover, steady rising depends on the ratio k a / k d and its investigation is not helpful for the determination of k d . In contrast a possibility to determine k d (or k a independently) from measurements of decelerated rising was shown by Zholkovskij et al. (2000). However, experimental applications of this theory is difficult because of the condition Re Re = 100. However, direct application of this research is possible for a few surfactants, corresponding to the Marangoni number Ma = 61, as assumed in this simulation work. An equation is obtained for the determination of k d in a broad range of large Ma numbers from measurements of decelerated rising at Re = 200 (bubble radius 400 μm) in this work. This equation is obtained on the basis of an equation for slow adsorption kinetics, a quasi-steady approximation and an equation for surfactant accumulation derived by Zholkovskij et al. (2000) as well as due to incorporation in this theory the vorticity distribution, as calculated by Fdhila and Duineveld (1996) for Re = 200. For the determination of k d it is sufficient to measure the time required for the onset of maximal surface retardation for the concentrations above the critical concentration, i.e. the minimum concentration required for the onset of the minimum rising velocity.
Databáze: OpenAIRE
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