Numerical investigation of the dissolution mechanism of a freely oscillating CO_2 gas bubble by the method of lines

Abstract

The dissolution process of a CO 2 Károly CzáderDepartment of Fluid Dynamics, BME, H-1111 Budapest, Bertalan Lajos u. 4-6., Hungary Kálmán Gábor SzabóDepartment of Hydraulics and Water Resources Engineering, BME, H-1111 Budapest, Műegyetem rkp. 3., K ép. mf. 12., Hungary IntroductionThe importance of research on bubble dynamics coupled with mass transport originates mainly from the chemical and bioprocessing industry, since gas and fluid phases are present simultaneously in many operations. The efficiency of such processes can be optimized by increasing the interfacial density using bubbly mixtures of the reagents. Bubbles can be classified according to their content into two basic types. Vapor filled bubbles are mainly formed in boiling fluids in heat exchangers or rectification columns, while gas filled bubbles are mostly generated by external injection in technologies used for gas purification [1], wastewater treatment [2] or synthesis of chemical materials [3].External forcing of bubble oscillation can produce enhanced evaporation of liquid and release of dissolved gases, thus it expedites to the phenomena of boiling and cavitation. For instance, the ultrasonic excitation of bubbles, as a specific procedure, is widely applied in sonochemistry [3], metal production [4] and ultrasonic medicinal treatment [5]. However, the less frequently studied free oscillation of bubbles, which also affect the mass and heat transport processes, is also frequently encountered in many operational conditions (e.g. in cases of bubble detachment, sudden decrease in ambient pressure etc).The most typical mode of bubble oscillation is the volumetric one, which can be satisfactorily modeled by assuming spherical symmetry. This problem has been studied thoroughly in the literature. The well-known Rayleigh-Plesset equation [6] describes this system as a specific nonlinear oscillator. Minnaert [7] was the first one who, by neglecting the surface tension effect, determined the natural frequency of the bubble oscillation in the small amplitude linear range. Prosperetti [8] extended Minnaert's analysis to the nonlinear range by including the surface tension and dissipation effects. Lauterborn [9] provided detailed numerical results for the free oscillation with large amplitudes. Chang and Chen [10], using the Hamiltonian function proposed by Ma and Wang [11], provided complete evaluation to the various solutions of free oscillation problem. Vokurka [12] has released a comprehensive study on the evaluation methods of the physical parameters measured for free oscillation of a bubble. Recently, Hegedűs et al. [13] revealed in his work the effect of ambient temperature and pressure on the damping of free oscillation by both finite difference and spectral numerical methods.The mutual effects of the mass transfer rate of dissolved gases and the forced oscillation of bubbles have also been extensively studied. Epstein and Plesset [14] prepared an analytical derivation for the passive dissolution of a quiescent gas bubble. In the case o...