Numerical study on hydrodynamic characteristics of spherical bubble contaminated by surfactants under higher Reynolds numbers

Abstract

Evolution of Γ against t : (a) Re = 250 and C 0 = 2 mol∙m −3 ( θ ≈ 120°), (b) Re = 200 and C 0 = 6 mol∙m −3 ( θ ≈ 0°). The surfactant molecules diffuses in the whole domain first. When they diffuse to the bubble surface, the adsorption and desorption phenomena happen to it. As the surfactant molecules are adsorbed at the bubble interface, they will diffuses in the adsorption layer. The surfactant concentration at the bubble interface is correlated with the interfacial shear stress by the Langmuir nonlinear equation so that the interfacial shear stress can be obtained. It is investigated in detail on the influence of interfacial contaminated degrees on hydrodynamic characteristics of the spherical bubble when the bubble Reynolds number ( Re ) is larger than 200. • The contaminated bubble dynamics are studied by an improved stagnation cap model. • The interfacial parameter distribution at the bubble interface is analyzed. • The relationship between interfacial concentration and wake flow is analyzed. • The conditions of axisymmetric model are discussed at higher Reynolds numbers. It is of significance to investigate deeply the hydrodynamic features of the bubble contaminated by impurities in view of the fact that the industrial liquid is difficult to keep absolutely pure. On the basis of the finite volume method, the bubble interface contaminated by the surfactant (1-pentanol) is achieved through solving the concentration transport equations in liquid and along the bubble interface, and solving the absorption and desorption equation at the bubble interface. And the three-dimensional momentum equation is solved at the same time. It is investigated in detail on the influence of interfacial contamination degrees (described with the cap angle θ ) on hydrodynamic characteristics of the spherical bubble when the bubble Reynolds number ( Re ) is larger than 200. The θ is realized by changing the surfactant concentration ( C 0 ) in liquid. The present results show that the hydrodynamic characteristics, such as interfacial concentration, interfacial shear stress, interfacial velocity and wake flow, are related to both Re and C 0 for the contaminated bubble. When C 0 is relatively low in liquid ( i.e. , the contamination degree of the bubble interface is relatively slight), the hydrodynamic characteristics of the bubble can still keep the 2D features even if Re > 200. The decrease of θ or the increase of Re can promote the appearance of the unsteady wake flow. For the present investigation, when Re > 200 and θ ≤ 60°, the hydrodynamic characteristics of the bubble show the 3D phenomena, which indicates that axisymmetric model is no longer valid.