Computational analysis of single rising bubbles influenced by soluble surfactant

Abstract

This paper presents novel insights about the influence of soluble surfactants on bubble flows obtained by Direct Numerical Simulation (DNS). Surfactants are amphiphilic compounds which accumulate at fluid interfaces and significantly modify the respective interfacial properties, influencing also the overall dynamics of the flow. With the aid of DNS local quantities like the surfactant distribution on the bubble surface can be accessed for a better understanding of the physical phenomena occurring close to the interface. The core part of the physical model consists in the description of the surfactant transport in the bulk and on the deformable interface. The solution procedure is based on an Arbitrary Lagrangian-Eulerian (ALE) Interface-Tracking method. The existing methodology was enhanced to describe a wider range of physical phenomena. A subgridscale (SGS) model is employed in the cases where a fully resolved DNS for the species transport is not feasible due to high mesh resolution requirements and, therefore, high computational costs. After an exhaustive validation of the latest numerical developments, the DNS of single rising bubbles in contaminated solutions is compared to experimental results. The full velocity transients of the rising bubbles, especially the contaminated ones, are correctly reproduced by the DNS. The simulation results are then studied to gain a better understanding of the local bubble dynamics under the effect of soluble surfactant. One of the main insights is that the quasi-steady state of the rise velocity is reached without ad-and desorption being necessarily in local equilibrium.

Experimental and numerical investigation of reactive species transport around a small rising bubble

“…In the tested parameter range, the rise velocity never changed more than ±3 % around the mean of all test-cases. This observation is supported by the fact that in most of the literature concerned with the rise of single bubbles in a contaminated liquid (see for example [25,1,20]) the hydrodynamic drag is comparable to the one of a rising solid particle. No strong dependency on the specific surfactant is observed or included in correlations for the drag coefficient.…”

“…On the other hand, interface tracking solvers are expensive (iterative inter-phase coupling, mesh motion) and less robust than other approaches. The main modifications are a sorption-library [18,19] to simulate the effect of soluble surfactant and a subgrid-scale model to approximate the convection-dominated transport of surfactant in the boundary layer forming at the bubble interface [20]. The sorption-library contains models for fast (diffusion-controlled) and slow (kinetically controlled) sorption as well as corresponding models for the sorption-isotherm.…”

“…The initial surfactant bulk concentration was set to c 0 = 0.05 mol/m 3 , a very high value which causes the bubble to reach quickly a "fully contaminated" state (a state in which the Marangoni forces remain approximately constant). For a more comprehensive discussion of the properties in table 1 and the sorption model, the reader is referred to the sections 2-4 in [20]. Table 1.…”

“…The local Marangoni forces associated with the fully contaminated state are distributed over the entire upper bubble hemisphere. A more detailed discussion of the forces acting on the bubble can be found in [20].…”

“…A very sensitive way to investigate the adsorption of a chemical species onto the interface is the measurement of the bubble rise velocity over time (so-called local velocity profiles [19]). Under the influence of soluble surfactant, the rise velocity will show three very distinct stages of acceleration, deceleration, and steady state [20]. Of course, such experiments would have to be carried out using ultra-purified water and a fluorescent tracer with higher purity.…”