2024-06-11 –, Olav Tryggvason 2+3
Bubble hydrodynamics, bubble column, Marangoni flow, liquid-gas flow, computational fluid dynamics
The accurate prediction of mass, momentum, and heat transfer across the liquid-gas interface is a fundamental concern in a great variety of industrial applications. Thereby, concentration gradients occurring in hydrometallurgy, chemical or biological industry towards the complex hydrodynamics are not fully understood, but play a major role for the final design. To overcome this, in-depth analysis for single bubble hydrodynamics is required. The Marangoni effect assumes significance in bubbly flows when temperature or concentration gradients exist in the domain. This study investigates the hydrodynamics of single bubbles under the influence of the Marangoni force induced by stratified fields of dissolved sugar, providing a numerical framework to examine these phenomena. A lab-scale bubble column and high-speed imaging were utilized to analyze the bubble behavior. An OpenFOAM-based geometric volume of fluid solver is extended by incorporating the solutocapillary Marangoni effect and a passive scalar transport equation for the sugar concertation was solved. To reproduce the sugar concentration gradient field in water, the passive scalar field of c is initialized with a linear rate in the vertical direction, and the physical properties of the continuous phase are accordingly linked to the concentration value. It is worth mentioning that an OpenFOAM function object called phaseScalarTransport is adopted to prevent the penetration of contamination into the bubble during the simulation, i.e., the contamination field is only transported inside the water phase. The dependency of surface tension on the concentration (β) is a unique value for each system, which is equal to 0.0038 in the case of an aqueous sugar solution (c ≤ 0.4 w/w). To obtain an insight into the influence of β on the bubble behavior with the aid of CFD, three different values were assigned to this parameter (β=0.2,0.02,0.0038 and 0); among which, the 0.2, 0.02 and zero values are artificial values. In order to exclusively study the influence of Marangoni force on the bubble behavior, the artificial cases of β=0, in which the gradient of concentration is applied but the Marangoni force is set to zero manually, was considered. Results reveal that small bubbles entering regions of elevated sugar concentration experience deceleration, transitioning into linear paths, while those departing high sugar concentration areas exhibit fluctuation and meandering. Furthermore, the concentration gradient leads larger bubbles to meander throughout the entire column, without a notable increase in their velocity. The intensity of these behaviors is governed by the magnitude of the Marangoni force. In fact, regarding the influence of β magnitude, this study reveals that it increases the aspect ratio of the bubble throughout the column and enhances the zigzag behavior in cases with positive concentration gradients where impurity concentration is below 20%w/w. Consequently, it elevates the velocity when the impurity concentration exceeds 20%w/w. Therefore, impurities causing a substantial increase in surface tension result in higher average bubble velocities, potentially unfavorable for prolonging contact time between the two phases.
Department of Particulate Flow Modelling, Johannes Kepler University, Austria
Sadra Mahmoudi1, Mahdi Saeedipour2, Mark W. Hlawitschka1
1 Institute of Process Engineering, Johannes Kepler University
2 Department of Particulate Flow Modelling, Johannes Kepler University
E-mail: mark.hlawitschka@jku.at and sadra.mahmoudi@jku.at