M. Krzan

Profiles of local velocities of bubbles in n-butanol, n-hexanol and n-nonanol solutions

Abstract Local velocities, size and deformation of bubble were measured in distilled water and solutions of n -butanol, n -hexanol and n -nonanol as a function of distance from capillary at which the bubbles were formed. CCD camera and stroboscopic illumination were used for monitoring and video recording of the bubbles rising inside square glass column. Sequences of the recorded frames were digitized and analyzed using image analysis software. It was found that the bubbles were deformed immediately after departure from the capillary orifice. Degree of deformation (ratio of horizontal and vertical diameters) was the largest in clean water and dropped rapidly from 1.5 in distilled water to a level approximately 1.05–1.03 at n -alkanol solutions. At low concentrations of the solutions the profiles of the bubble local velocity showed maximum at distances approximately 5–50 mm from the capillary orifice, prior to reaching a value of the terminal velocity. Position, height and width of the maximum varied with solution concentration. No maximum was observed at distilled water and at high concentrations of n -butanol, n -hexanol and n -nonanol solutions. Degree of adsorption coverage at surface of the departing bubbles were calculated and the bubble velocities were analyzed in a function of the adsorption coverage at different concentrations of the solutions.

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

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 v(st)(ψ), the dependence of non-steady velocity on time is obtained by employing v(st)[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 βC0, while it is usually βC0(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.