Marizeh Lotfi

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.

Adsorption of Proteins at the Solution/Air Interface Influenced by Added Nonionic Surfactants at Very Low Concentrations for Both Components. 3. Dilational Surface Rheology

The influence of the addition of the nonionic surfactants C12DMPO, C14DMPO, C10OH, and C10EO5 at concentrations between 10(-5) and 10(-1) mmol/L to solutions of β-casein (BCS) and β-lactoglobulin (BLG) at a fixed concentration of 10(-5) mmol/L on the dilational surface rheology is studied. A maximum in the viscoelasticity modulus |E| occurs at very low surfactant concentrations (10(-4) to 10(-3) mmol/L) for mixtures of BCS with C12DMPO and C14DMPO and for mixtures of BLG with C10EO5, while for mixture of BCS with C10EO5 the value of |E| only slightly increased. The |E| values calculated with a recently developed model, which assumes changes in the interfacial molar area of the protein molecules due to the interaction with the surfactants, are in satisfactory agreement with experimental data. A linear dependence exists between the ratio of the maximum modulus for the mixture to the modulus of the single protein solution and the coefficient reflecting the influence of the surfactants on the adsorption activity of the protein.