Dynamics of Rear Stagnant Cap formation at the surface of spherical bubbles rising in surfactant solutions at large Reynolds numbers under conditions of small Marangoni number and slow sorption kinetics
Document Type
Article
Publication Date
8-12-2015
Abstract
On the surface of bubbles rising in a surfactant solution the adsorption process proceeds and leads to the formation of a so called Rear Stagnant Cap (RSC). The larger this RSC is the stronger is the retardation of the rising velocity. The theory of a steady RSC and steady retarded rising velocity, which sets in after a transient stage, has been generally accepted. However, a non-steady process of bubble rising starting from the initial zero velocity represents an important portion of the trajectory of rising, characterized by a local velocity profile (LVP). As there is no theory of RSC growth for large Reynolds numbers Re « 1 so far, the interpretation of LVPs measured in this regime was impossible. It turned out, that an analytical theory for a quasi-steady growth of RSC is possible for small Marangoni numbers Ma » 1, i.e. when the RSC is almost completely compressed, which means a uniform surface concentration Γ(θ) = Γ∞ within the RSC. Hence, the RSC angle ψ(t) is obtained as a function of the adsorption isotherm parameters and time t. From the steady velocity vst(ψ), the dependence of non-steady velocity on time is obtained by employing vst[ψ(t)] via a quasi-steady approximation. The measurement of LVP creates a promising new opportunity for investigation of the RSC dynamics and adsorption kinetics. While adsorption and desorption happen at the same localization in the classical methods, in rising bubble experiments desorption occurs mainly within RSC while adsorption on the mobile part of the bubble surface. The desorption flux from RSC is proportional to αΓ∞, while it is usually αΓ. The adsorption flux at the mobile surface above RSC can be assumed proportional to β C0, while it is usually β C0(1 - Γ/Γ∞). These simplifications may become favorable in investigations of the adsorption kinetics for larger molecules, in particular for globular proteins, which essentially stay at an interface once adsorbed.
Identifier
84938900812 (Scopus)
Publication Title
Advances in Colloid and Interface Science
External Full Text Location
https://doi.org/10.1016/j.cis.2014.10.002
ISSN
00018686
First Page
260
Last Page
274
Volume
222
Grant
MAP AO-99-052
Fund Ref
European Space Agency
Recommended Citation
Dukhin, S. S.; Kovalchuk, V. I.; Gochev, G. G.; Lotfi, M.; Krzan, M.; Malysa, K.; and Miller, R., "Dynamics of Rear Stagnant Cap formation at the surface of spherical bubbles rising in surfactant solutions at large Reynolds numbers under conditions of small Marangoni number and slow sorption kinetics" (2015). Faculty Publications. 6843.
https://digitalcommons.njit.edu/fac_pubs/6843
