A first order relaxation model for the prediction of the local interfacial area density in two-phase flows

Akita, 1974, Bubble size, interfacial area, and liquid-phase mass transfer coefficient in bubble columns, Ind. Eng. Chem. Process Des. Develop., 13, 84, 10.1021/i260049a016 Bensler, 1991, Determination of the volumetric interfacial area, volumetric void fraction and Sauter mean diameter in bubbly flow by means of ultrasound attenuation, 1096 Burgess, 1975, The measurement of bubble parameters in two-phase dispersions—I, Chem. Eng. Sci., 30, 743, 10.1016/0009-2509(75)85101-3 Burgess, 1975, The measurement of bubble parameters in two-phase dispersions—II, Chem. Eng. Sci., 30, 1107, 10.1016/0009-2509(75)87013-8 Burgess, 1975, The measurement of bubble parameters in two-phase dispersions—III, Chem. Eng. Sci., 30, 1511, 10.1016/0009-2509(75)85029-9 Calderbank, 1967, Gas absorption from bubbles, The Chem. Eng., 43, CE209 Chandrasekharan, 1981, Further observations on the scale-up aerated mixing vessels, Chem. Eng. Sci., 36, 819, 10.1016/0009-2509(81)85033-6 Chang, 1992, Determination of gas-liquid bubble column instantaneous interfacial area and void fraction by a real-time neutron radiography method, Chem. Eng. Sci., 47, 13, 10.1016/0009-2509(92)85080-U Chang, 1992, Determination of gas-liquid bubble column instantaneous interfacial area and void fraction by a real-time neutron radiography method, Chem. Eng. Sci., 47, 3639, 10.1016/0009-2509(92)85080-U Daly, 1992, Measurement of gas holdups and sauter mean bubble diameters in bubble column reactors by dynamic gas disengagement method, Chem. Eng. Sci, 47, 13, 10.1016/0009-2509(92)85081-L Daly, 1992, Measurement of gas holdups and sauter mean bubble diameters in bubble column reactors by dynamic gas disengagement method, Chem. Eng. Sci, 47, 3647, 10.1016/0009-2509(92)85081-L Deckwer, 1992 de Figueiredo, 1979, The scale-up of aerated mixing vessels for specified oxygen dissolution rates, Chem. Eng. Sci., 34, 1333, 10.1016/0009-2509(79)80025-1 Garncarek, 1991, A new method in investigations of bubble cluster shapes in two-phase flow, Chem. Eng. Process., 30, 107, 10.1016/0255-2701(91)80017-J Guido-Lavalle, 1993, A contribution to the kinetic formulation of gas-liquid flows, Chem. Eng. Communications, 120, 99, 10.1080/00986449308936127 Guido-Lavalle, 1994, A bubble number density constitutive equation, Nuclear Eng. Design, 152, 213, 10.1016/0029-5493(94)90086-8 Ishii, 1975 Ishii, 1984, Two-fluid model and hydrodynamic constitutive relations, Nucl. Eng. Des., 82, 107, 10.1016/0029-5493(84)90207-3 Ishii, 1992, Interfacial area in two-phase flow, HTD, Vol. 197, 1 Kalkach-Navarro, 1992, Two-fluid modeling of the bubbly/slug flow regime transition Kataoka, 1986, Local formulation and measurements of interfacial area concentration in two-phase flow, Int. J. Mult. Flow, 12, 505, 10.1016/0301-9322(86)90057-1 Kelly, 1993, A four-field approach towards developing a mechanistic model for multiphase flow, Pacific Northwest Laboratory Report PNL-SA-18878, DE93 006572 Lahey, 1992, Phase distribution and two-phase turbulence for bubbly flows in pipe, Vol. 6, 303 Levich, 1962 Lewis, 1983, Bubble sizes produced by shear and turbulence in a bubble column, Chem. Eng. Sci., 38, 161, 10.1016/0009-2509(83)80147-X Marrucci, 1967, Coalescence of gas bubbles in aqueous solutions of inorganic electrolytes, Chem. Eng. Sci., 22, 1257, 10.1016/0009-2509(67)80190-8 Mudde, 1992, Noise analysis of transmitted light beams for determining bubble velocity and gas holdup profiles in a bubble column, Chem. Eng. Sci., 47, 13, 10.1016/0009-2509(92)85079-Q Mudde, 1992, Noise analysis of transmitted light beams for determining bubble velocity and gas holdup profiles in a bubble column, Chem. Eng. Sci., 47, 3631, 10.1016/0009-2509(92)85079-Q Nagel, 1972, Stoffaustauschflache and Energiedissipationsdichte als Auswahlkriterien fur Gas/Fliissig-Reaktoren: Teil 1, Chem. Ing. Tech., 44, 367, 10.1002/cite.330440603 Nagel, 1972, Stoffaustauschflache and Energiedissipationsdichte als Auswahlkriterien fur Gas/Flüssigkeits-Reaktoren: Teil 2, Chem. Ing. Tech., 44, 899, 10.1002/cite.330441406 Nagel, 1973, Die Stoffaustauschflache in Gas/Flüssigkeits-Kontaktap-paraten Auswahlkriterien and Unterlagen zur VergrMerung, Chem. Ing. Tech., 45, 913, 10.1002/cite.330451402 Nagel, 1976, Untersuchungen zum Dispergieren im turbulenten Scherfeld, Chem. Ing. Tech., 48, 513, 10.1002/cite.330480604 Nagel, 1978, Kriterien fur die Auswahl and die Auslegung von Gas/Flussigkeits-Reaktoren, Chem. Ing. Tech., 50, 935, 10.1002/cite.330501208 Nagel, 1978, Design of gas/liquid reactors: mass transfer area and input of energy, 835 Oolman, 1986, Bubble coalescence in air-sparged bioreactors, Chemical Engng J., 32, B7 Park, 1992, Void wave propagation in two-phase flow Patel, 1989, holdup and interfacial area measurements using dynamic gas disengagements, AIChE J., 35, 931, 10.1002/aic.690350606 Prince, 1990, Transition electrolyte concentrations for bubble coalescence, AIChE J., 36, 1425, 10.1002/aic.690360915 Prince, 1990, Bubble coalescence and break-up in air sparged bubble columns, AIChE J., 36, 1485, 10.1002/aic.690361004 Schumpe, 1986, The gas desengagement technique for studying gas holdup structure in bubble columns, Can J. Chem. Eng., 64, 891, 10.1002/cjce.5450640602 Serizawa, 1990, Phase distribution in two-phase flow Stewart, 1993, A model for simultaneous coalescence of bubble clusters, Chem. Eng. Sci., 48, 3347, 10.1016/0009-2509(93)80151-F Thomas, 1983, Physical modelling of multi-phase flow, BHRA Fluid Engng, 169