Bubble size, interfacial area, and liquid-phase mass transfer coefficient in bubble columns, Industrial & Engineering Chemistry Process Design and Development, vol.13, issue.1, pp.84-91, 1974. ,
Influence of coalescence behaviour of the liquid and of gas sparging on hydrodynamics and bubble characteristics in a bubble column, Chemical Engineering and Processing, vol.38, pp.329-344, 1999. ,
Hydrodynamics and mass transfer in bubble column: Influence of liquid phase surface tension, Chemical Engineering Science, vol.62, pp.7378-7390, 2007. ,
, Bubbles, Drops, and Particles, 1978.
Effect of surface-active agents on the phase holdups of three-phase fluidized beds, Chemical Engineering and Processing, vol.45, pp.764-772, 2006. ,
Numerical study of bubble formation from submerged orifice under reduced gravity condition, Procedia IUTAM, vol.18, pp.8-17, 2015. ,
Hydrodynamics scale-up of slurry bubble columns, 2003. ,
On the surfactants and interfacial motion, Z. Fizicheskoi Khimii, vol.21, pp.1183-1204, 1947. ,
Bubble column reactors, Process Biochemistry, vol.40, pp.2263-2283, 2005. ,
A scale-up strategy for a commercial scale bubble column slurry reactor for Fischer-Tropsch synthesis, Oil & Gas Science and Technology, vol.55, issue.4, pp.359-393, 2000. ,
URL : https://hal.archives-ouvertes.fr/hal-02054048
Bubble formation and bubble rise velocity in gas-liquid systems: A review, Industrial & Engineering Chemistry Research, vol.44, pp.5873-5931, 2005. ,
DOI : 10.1021/ie049131p
, Physicochemical Hydrodynamics, 1962.
Effects of orifice orientation and gas-liquid flow pattern on initial bubble size, Chinese Journal of Chemical Engineering, vol.21, issue.11, pp.1206-1215, 2013. ,
Flow of fluid in gas-bubble columns, Chemical engineering, vol.34, issue.9, pp.958-964, 1970. ,
Local gas hold-up measurements in fluidized bed and slurry bubble column, Chemical Engineering Science, vol.56, issue.3, pp.1103-1110, 2001. ,
DOI : 10.1016/s0009-2509(00)00327-4
Design parameters estimations for bubble column reactors, American Institute of Chemical Engineering Journal, vol.28, issue.3, pp.353-379, 1982. ,
DOI : 10.1002/aic.690280302
Numerical study of dynamics of single bubbles and bubble swarms, Applied Mathematical Modelling, vol.32, issue.5, pp.641-659, 2008. ,
Flow Patterns in Bubble Columns, 1969. ,
Bubble velocity, size and interfacial area measurements in bubble columns, 2004. ,
DOI : 10.1002/aic.11386
The effect of electrolytes on bubble coalescence and gas hold-up in bubble column reactors, Chemical Engineering Research and Design, vol.73, pp.341-346, 1995. ,
, Duality of the gas-liquid flow regimes in bubble column reactors, vol.52, pp.3811-3826, 1997.
Scalar mixing in bubbly flows: Experimental investigation and diffusivity modelling, Chemical Engineering Science, vol.140, pp.114-122, 2016. ,
Mixing by bubble-induced turbulence, Journal of Fluid Mechanics, vol.776, pp.458-474, 2015. ,
, Computational Fluid Dynamics for Engineers, 2012.
The effect of aspect ratio in counter-current gas-liquid bubble columns: Experimental results and gas holdup correlations, International Journal of Multiphase Flow, vol.94, pp.53-78, 2017. ,
On the scale-up criteria for bubble columns, 2018. ,
Transport Phenomena, revised second edn, 2007. ,
Théorie de l'écoulement tourbillonnant et tumultueux des liquides dans les lits rectilignes à grande section, 1897. ,
The mechanics of vertical gasliquid fluidized system i: Countercurrent flow, American Institute of Chemical Engineering Journal, vol.10, issue.6, pp.819-826, 1964. ,
DOI : 10.1002/aic.690100610
Modeling and simulation of turbulent polydisperse gas-liquid systems via the generalized population balance equation, Reviews in Chemical Engineering, vol.30, pp.73-126, 2014. ,
The favre averaged drag model for turbulent dispersion in eulerian multi-phase flows, 5th International Conference on Multiphase Flow, 2004. ,
Circulation in bubble columns, American Institute of Chemical Engineering Journal, vol.43, issue.6, pp.1390-1402, 1997. ,
Simulation of heterogeneous flow in large bubble column with mixing of species, 2016. ,
, Bubbles, Drops, and Particles, 1978.
On the gradient diffusion hypothesis and passive scalar transport in turbulent flows, Industrial & Engineering Chemistry Research, vol.50, issue.15, pp.8817-8823, 2011. ,
, CFD simulations of bubble column reactors: 1D, 2D and 3D approach, vol.60, pp.6733-6746, 2005.
A two-equation turbulence model for two-phase flows, Physics of Fluids, vol.26, pp.931-938, 1983. ,
CFD simulation of industrial bubble columns: Numerical challenges and model validation successes, Applied Mathematical Modelling, vol.44, pp.25-42, 2017. ,
Hydrodynamics scale-up of slurry bubble columns, 2003. ,
Hydrodynamics and bubble size in bubble columns: Effects of contaminants and spargers, Chemical Engineering Science, vol.184, pp.93-102, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01899599
Shapes and velocities of single drops and bubbles moving freely through immiscible liquids, Transactions of the Institution of Chemical Engineers, vol.54, pp.167-173, 1976. ,
Prediction of gas-liquid flow in an annular gap bubble column using a bi-dispersed eulerian model, Chemical Engineering Science, vol.161, pp.138-150, 2017. ,
Investigations and modelling of slurry bubble columns, Chemical Engineering Science, vol.49, issue.6, pp.837-843, 1994. ,
Simulation and experimental validation of reactive bubble column reactors, Chemical Engineering Science, vol.170, pp.306-319, 2017. ,
Drag coefficient and relative velocity in bubbly, droplet or particulate flows, American Institute of Chemical Engineering Journal, vol.25, issue.5, pp.843-855, 1979. ,
Modeling of bubble column reactors: Progress and limitations, Industrial & Engineering Chemistry Research, vol.44, issue.14, pp.5107-5151, 2005. ,
Computational flow modelling and design of bubble column reactors, Chemical Engineering Science, vol.56, issue.21, pp.5893-5933, 2001. ,
Basic equation of turbulence and modelling of interfacial transfer terms in gas-liquid two-phase flow, Chemical Engineering Communications, vol.118, pp.221-236, 1992. ,
Turbulence intensity in bubble columns, The Chemical Engineering Journal, vol.40, issue.1, pp.55-58, 1989. ,
, Lectures in Mathematical Models of Turbulence, 1972.
CFD simulation of effects of the configuration of gas distributors on gas-liquid flow and mixing in a bubble column, Chemical Engineering Science, vol.64, issue.24, pp.5104-5116, 2009. ,
Hydrodynamics and mixing in airlift contactors: Experimental work and CFD modelling, Chemical Engineering Research and Design, vol.127, pp.154-169, 2017. ,
Development of a CFD model of bubble column bioreactors: Part one-A detailed experimental study, Chemical Engineering & Technology, vol.36, issue.12, pp.2065-2070, 2013. ,
Experimental investigation into the drag volume fraction correction term for gas-liquid bubbly flows, Chemical Engineering Science, vol.170, pp.91-97, 2017. ,
Validation of a computationally efficient computational fluid dynamics (CFD) model for industrial bubble column bioreactors, Industrial & Engineering Chemistry Research, vol.53, issue.37, pp.14526-14543, 2014. ,
Flow of fluid in gas bubble columns, Kagaku Kogaku, vol.34, issue.9, pp.958-964, 1970. ,
Modeling and simulation of the dynamic flow behavior in a bubble column, Chemical Engineering Science, vol.56, pp.1737-1747, 2001. ,
Multiphase flow and mixing in dilute bubble swarms, American Institute of Chemical Engineering Journal, vol.56, pp.2421-2445, 2010. ,
Analysis and modelization of local hydrodynamics in bubble columns, 2015. ,
URL : https://hal.archives-ouvertes.fr/tel-01267349
Modelling of turbulent flow in a bubble column reactor, Process and Product Development, vol.75, pp.1-23, 1997. ,
On the drag force of bubbles in bubble swarms at intermediate and high reynolds numbers, Chemical Engineering Science, vol.66, pp.3204-3211, 2011. ,
, The effect of voidage on the drag force on particles, droplets and bubbles in dispersed two-phase flow, in '2nd Japanese European Two-Phase Flow Meeting, 2000.
CFD modeling of bubble-induced turbulence, International Journal of Multiphase Flow, vol.55, pp.138-155, 2013. ,
Effects of liquid height on gas holdup in air-water bubble column, Experimental Thermal and Fluid Science, vol.72, pp.67-74, 2016. ,
One-dimensional two-phase flow, 1969. ,
Turbulence modeling for CFD, 1998. ,
Design parameters estimation for scale-up of high pressure bubble column, American Institute of Chemical Engineering Journal, vol.38, pp.544-554, 1992. ,
Renormalization group analysis of turbulence i basic theory, Journal of scientific computing, vol.1, issue.1, pp.1-51, 1986. ,
Volumetric interfacial area prediction in upward bubbly two-phase flow, International Journal of Heat and Mass Transfer, vol.47, pp.307-328, 2004. ,
Eulerian modeling of reactive gas-liquid flow in a bubble column, 2007. ,
Numerical simulation of dynamic flow behavior in a bubble column: A study of closures for turbulence and interface forces, Chemical Engineering Science, vol.61, pp.7593-7608, 2006. ,
Simulation of the population balances for liquid-liquid systems in a nonideal stirred tank. part 2-parameter fitting and the use of the multiblock model for dense dispersions, Chemical Engineering Science, vol.57, issue.10, pp.1815-1825, 2002. ,
, Computational Fluid Dynamics for Engineers, 2012.
Transition criteria for two-phase flow patterns in vertical upward flow, International Journal of Multiphase Flow, vol.13, pp.283-298, 1987. ,
Multivariate population balance for turbulent gas-liquid flows, 2012. ,
Simplified volumeaveraged models for liquid-liquid dispersions: Correct derivation and comparison with other approaches, Chemical Engineering Science, vol.153, pp.382-393, 2016. ,
Multivariate Quadrature-Based Moments Methods for turbulent polydisperse gas-liquid systems, International Journal of Multiphase Flow, vol.50, pp.41-57, 2013. ,
Circulation in bubble columns, American Institute of Chemical Engineering Journal, vol.43, issue.6, pp.1390-1402, 1997. ,
A Mathematical Description of the Critical Heat Flux as Nonlinear Dynamic Instability, Gouesbet and A. Berlemont. Instabilities in Multiphase Flow, 1993. ,
Modeling of fluid dynamics and mass transfer in extraction columns, German Chemical Engineering, vol.8, pp.96-103, 1985. ,
The modeling of coalescence processes in fluid-liquid dispersions: A review of current understanding, Chemical Engineering Research and Design: transactions of the Institution of Chemical Engineers: Part A, vol.69, pp.259-270, 1991. ,
A study on coalescence and breakage mechanisms in three different bubble columns, Chemical Engineering Science, vol.54, issue.21, pp.4767-4777, 1999. ,
Turbulence and shear-induced coalescence in gas-liquid pipe flows, ICMF 2004-5th International Conference on Multiphase Flow, 2004. ,
, Dispersed phase interactions in an agitated flow vessel, 1975.
Description of interaction processes in agitated liquid-liquid dispersions, Chemical Engineering Science, vol.32, pp.1289-1297, 1977. ,
Limitations of simple mass transfer models in polydisperse liquid-liquid dispersions, Chemical Engineering Journal, vol.296, pp.112-121, 2016. ,
, The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis, 1997.
The drainage and rupture of a non-foaming liquid film formed upon bubble impact with a free surface, International Journal of Multiphase Flow, vol.17, pp.783-803, 1991. ,
Simulation of turbulent coalescence and breakage of bubbles and droplets in the presence of surfactants, salts, and contaminants, Advances in Chemical Engineering, vol.52, pp.125-188, 2018. ,
Hydrodynamics scale-up of slurry bubble columns, 2003. ,
Validation of cfd models for mono-and polydisperse airâ??water two-phase flows in pipes, Nuclear Engineering and Design, vol.238, issue.3, pp.647-659, 2008. ,
, Smoke, Dust and Haze, 1977.
Two-group interfacial area transport in vertical airwater flow: I. mechanistic model, Nuclear Engineering and Design, vol.219, issue.2, pp.14-168, 2003. ,
Simulation of droplet breakage in turbulent liquid-liquid dispersions with CFD-PBM: Comparison of breakage kernels, Chemical Engineering Science, vol.142, pp.277-288, 2016. ,
CFDbased scale-up of hydrodynamics and mixing in bubble columns, Chemical Engineering Research and Design, vol.136, pp.846-858, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01952005
Hydrodynamics and bubble size in bubble columns: Effects of contaminants and spargers, Chemical Engineering Science, vol.184, pp.93-102, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01899599
Numerical methods for a population-balance model of a periodic fermentation process.', American Institute of, Chemical Engineering Journal, vol.45, pp.1359-1364, 1999. ,
Error bounds in equilibrium statistical mechanics, Journal of Mathematical Physics, vol.9, pp.655-663, 1981. ,
High resolution algorithms for multidimensional population balance equations, American Institute of Chemical Engineering Journal, vol.50, pp.2738-2749, 2004. ,
Bubble size in horizontal pipelines, American Institute of Chemical Engineering Journal, vol.33, pp.663-667, 1987. ,
One-group interfacial area transport of bubbly flows in vertical round tubes, International Journal of Heat and Mass Transfer, vol.43, pp.2711-2726, 2000. ,
Interfacial area transport of bubbly flow in a small diameter pipe, Journal of Nuclear Science and Technology, vol.38, pp.614-620, 2001. ,
Coalescence of drops in a turbulent flow field, Chemical Engineering Science, vol.19, pp.33-38, 1964. ,
, Coalescence of Liquid Droplets and Liquid Dispersion: Recent Advances in Liquid-Liquid Extraction, 1 st edn, 1971.
Analysis of the bubbly/slug flow regime transition, Nuclear Engineering and Design, vol.151, issue.1, pp.15-39, 1994. ,
The modeling of turbulent flow around stationary and vibrating square cylinders, '9th Symposium on Turbulent Shear Flows, 1993. ,
Turbulence intensity in bubble columns, The Chemical Engineering Journal, vol.40, issue.1, pp.55-58, 1989. ,
, Kinetic Theory of Gases, 1938.
Estimation of coalescence and breakage rate constants within a kühni column, Industrial & Engineering Chemistry Research, vol.37, issue.3, pp.1099-1106, 1998. ,
Coalescence of dispersed drops in an agitated tank, Journal of Chemical Engineering of Japan, vol.21, pp.335-338, 1988. ,
Collision and coalescence of dispersed drops in turbulent liquid flow, Journal of Chemical Engineering of Japan, vol.5, pp.423-424, 1972. ,
The cell average technique for solving multi-dimensional aggregation population balance equations, Computers & Chemical Engineering, vol.32, pp.1810-1830, 2008. ,
Validation of bubble breakage, coalescence and mass transfer models for gas-liquid dispersion in agitated vessel, Chemical Engineering Science, vol.61, pp.218-228, 2006. ,
Modelling local bubble size distributions in agitated vessels, Chemical Engineering Science, vol.62, pp.721-740, 2007. ,
A review of statistical models for the break-up of an immiscible fluid immersed into a fully developed turbulent flow, International Journal of Multiphase Flow, vol.28, pp.247-278, 2002. ,
Bubble break-up and coalescence in turbulent gas-liquid dispersions, Chemical Engineering Communications, vol.59, pp.65-84, 1987. ,
A transport equation for the interfacial area density applied to bubble columns, Chemical Engineering Science, vol.56, pp.1159-1166, 1999. ,
Bubble-size distributions and flow fields in bubble columns, American Institute of Chemical Engineering Journal, vol.48, issue.11, pp.2426-2443, 2002. ,
, Physicochemical Hydrodynamics, 1962.
Droplet breakage and coalescence in liquid-liquid dispersions: Comparison of different kernels with EQMOM and QMOM, American Institute of Chemical Engineering Journal, vol.63, issue.6, pp.2293-2311, 2017. ,
A literature review of theoretical models for drop and bubble breakup in turbulent dispersions, Chemical Engineering Science, vol.64, pp.3389-3406, 2009. ,
A literature review on mechanisms and models for the coalescence process of fluid particles, Chemical Engineering Science, vol.65, pp.2851-2864, 2010. ,
Coalescence, breakup and liquid circulation in bubble column reactors, 1993. ,
Modeling and simulation of binary approach by energy conservation analysis, Chemical Engineering Communications, vol.145, pp.145-153, 1996. ,
Computational Models for Polydisperse Particulate and Multiphase Systems, Cambridge Series in Chemical Engineering, 2013. ,
Implementation of the quadrature method of moments in CFD codes for aggregation-breakage problems, Chemical Engineering Science, vol.58, pp.3337-3351, 2003. ,
Quadrature method of moments for aggregation-breakage processes, Journal of Colloid and Interface Science, vol.258, pp.322-334, 2003. ,
New quadrature-based moment method for the mixing of inert polydisperse fluidized powders in commercial cfd codes, American Institute of Chemical Engineering Journal, vol.58, issue.10, pp.3054-3069, 2012. ,
Impact of surfactant chemistry on bubble column systems, Chemical Engineering & Technology, vol.37, issue.4, pp.652-658, 2014. ,
Development of a CFD model of bubble column bioreactors: Part one-a detailed experimental study, Chemical Engineering & Technology, vol.36, issue.12, pp.2065-2070, 2013. ,
Towards a CFD model of bubble columns containing significant surfactant levels, Chemical Engineering Science, vol.127, pp.189-201, 2015. ,
Description of aerosol dynamics by the quadrature method of moments, Aerosol Science and Technology, vol.27, pp.255-265, 1997. ,
Reynolds stress model for bubble column reactor, Industrial & Engineering Chemistry Research, vol.29, issue.6, pp.988-994, 1990. ,
Flow of fluid in gas bubble columns, Kagaku Kogaku, vol.34, issue.9, pp.958-964, 1970. ,
A model for transitional breakage probability of droplets in agitated lean liquid-liquid dispersions, Chemical Engineering Science, vol.34, pp.257-265, 1979. ,
Bubble coalescence in viscous fluids, American Institute of Chemical Engineering Journal, vol.17, pp.182-186, 1971. ,
The effect of coalescence on drop size distribution in an agitated liquid-liquid dispersion, Chemical Engineering Science, vol.30, pp.1057-1064, 1975. ,
Bubble size distribution modeling in stirred gas-liquid reactors with QMOM augmented by a new correction algorithm, American Institute of Chemical Engineering Journal, vol.56, pp.36-53, 2010. ,
Modeling of turbulent drop coalescence in the presence of electrostatic forces, Chemical Engineering Research and Design, vol.108, pp.30-41, 2016. ,
Bubble coalescence and break-up in airsparged bubble columns, American Institute of Chemical Engineering Journal, vol.36, pp.1485-1499, 1990. ,
Analysis and modelization of local hydrodynamics in bubble columns, 2015. ,
URL : https://hal.archives-ouvertes.fr/tel-01267349
Drop fragment distributions under shear with inertia, International Journal of Multiphase Flow, vol.28, pp.1125-1147, 2002. ,
, Coalescence and breakup of fluid particles in multi-phase flow, in 'ICMF 2001-4th International Conference on Multiphase Flow, 2001.
Power dissipation and heat production in bubble columns: Approach based on nonequilibrium thermodynamics, Biotechnology and Bioengineering, vol.22, issue.11, pp.2399-2404, 1980. ,
Liquid velocity distribution in two-phase bubble flow, International Journal of Multiphase Flow, vol.2, issue.1, pp.79-95, 1975. ,
Predicting particle size in agitated dispersions, Industrial and Engineering Chemistry, vol.52, pp.253-256, 1960. ,
Koaleszenz von Tropfen und Tropfenschwärmen, 2004. ,
Modeling of turbulent two-phase jets loaded with discrete particles, pp.259-269, 1990. ,
Breakage and coalescence of drops in a batch stirred vessel-ii comparison of model and experiments, Chemical Engineering Science, vol.36, pp.1567-1573, 1981. ,
Struggle with computational bubble dynamics, Multiphase Science and Technology, vol.10, issue.4, p.369, 1998. ,
A two-equation turbulence model of turbulent bubbly flows, International Journal of Multiphase Flow, vol.27, issue.11, pp.1965-2000, 2001. ,
Approximate population balance equation for aggregationbreakage processes, International Journal of Multiphase Flow, vol.221, pp.143-160, 2000. ,
DOI : 10.1006/jcis.1999.6571
A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow, Chemical Engineering Science, vol.58, issue.20, pp.4629-4637, 2003. ,
DOI : 10.1016/j.ces.2003.07.009
An efficient numerical algorithm for "a novel theoretical breakup kernel function of bubble/droplet in a turbulent flow, Chemical Engineering Science, vol.59, pp.2593-2595, 2004. ,
Population balance model for gasliquid flows: Influence of bubble coalescence and breakup models, Industrial & Engineering Chemistry Research, vol.44, issue.11, pp.7540-7549, 2005. ,
Theoretical prediction of flow regime transition in bubble columns by the population balance model, Chemical Engineering Science, vol.60, pp.6199-6209, 2005. ,
A CFD-PBM coupled model for gas-liquid flows, American Institute of Chemical Engineering Journal, vol.52, pp.125-140, 2006. ,
DOI : 10.1002/aic.10611
Modified moments and gaussian quadratures, Rocky Mountain Journal of Mathematics, vol.4, pp.287-296, 1974. ,
DOI : 10.1216/rmj-1974-4-2-287
URL : https://doi.org/10.1216/rmj-1974-4-2-287
Mathematics for the Physical Sciences, 1962. ,
Numerical advection of moments of the particle size distribution in eulerian models, Journal of Aerosol Science, vol.38, pp.352-369, 2007. ,
Factors affecting coalescence frequency of droplets in a stirred liquid-liquid dispersion, American Institute of Chemical Engineering Journal, vol.40, pp.767-776, 1994. ,
One-group interfacial area transport in vertical bubbly flow, International Journal of Heat and Mass Transfer, vol.41, pp.1103-1112, 1998. ,
DOI : 10.1016/s0017-9310(97)00167-1
Volumetric interfacial area prediction in upward bubbly two-phase flow, International Journal of Heat and Mass Transfer, vol.47, pp.307-328, 2004. ,
DOI : 10.1016/j.ijheatmasstransfer.2003.06.004
Conditional quadrature method of moments for kinetic equations, Journal of Computational Physics, vol.230, pp.8216-8246, 2011. ,
DOI : 10.1016/j.jcp.2011.07.020
Analysis of four MonteCarlo methods for the solution of population balances in dispersed systems, Powder Technology, vol.173, pp.38-50, 2007. ,
Mixing by bubble-induced turbulence, Journal of Fluid Mechanics, vol.776, pp.458-474, 2015. ,
Validation of bubble breakage, coalescence and mass transfer models for gas-liquid dispersion in agitated vessel, Chemical Engineering Science, vol.61, pp.218-228, 2006. ,
Bubble-size distributions and flow fields in bubble columns, American Institute of Chemical Engineering Journal, vol.48, issue.11, pp.2426-2443, 2002. ,
DOI : 10.1002/aic.690481103
A literature review of theoretical models for drop and bubble breakup in turbulent dispersions, Chemical Engineering Science, vol.64, pp.3389-3406, 2009. ,
A literature review on mechanisms and models for the coalescence process of fluid particles, Chemical Engineering Science, vol.65, pp.2851-2864, 2010. ,
CFD simulation of the flow field in a bubble column reactor: Importance of the drag force formulation to describe regime transitions, Chemical Engineering and Processing: Process Intensification, vol.47, issue.9, pp.1726-1737, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00301071
Struggle with computational bubble dynamics, Multiphase Science and Technology, vol.10, issue.4, p.369, 1998. ,
Theoretical prediction of flow regime transition in bubble columns by the population balance model, Chemical Engineering Science, vol.60, pp.6199-6209, 2005. ,
14: Sauter mean diameter at the column centre at different axial positions with a superficial gas velocity equal to 3 cm/s (homogeneous regime) with demineralised water (DMW) and ,
Sauter mean diameter at the column centre at different axial positions with a superficial gas velocity equal to 16 cm/s (heterogeneous regime) with demineralised water (DMW) and, vol.15 ,
Local gas volume fraction at the column centre at different axial positions with a superficial gas velocity equal to 16 cm/s (heterogeneous regime) with demineralised water (DMW) and ethanol 0.05%: 92-holes sparger versus 7-holes sparger, vol.17 ,
Sauter mean diameter at the column centre at different axial positions with a superficial gas velocity equal to 3 cm/s (homogeneous regime) with demineralised water (DMW) and ethanol 0.05%: 92-holes sparger versus 7-holes sparger, vol.21 ,
Sauter mean diameter at the column centre at different axial positions with a superficial gas velocity equal to 16 cm/s (heterogeneous regime) with demineralised water and ethanol 0.05%: 92-holes sparger versus 7-holes sparger, vol.22 ,
Sauter mean diameter at the column centre at different axial positions with a superficial gas velocity equal to 25 cm/s (heterogeneous regime) with demineralised water and ethanol 0.05%: 92-holes sparger versus 7-holes sparger, vol.23 ,
The mechanics of large bubbles rising through extended liquids and through liquids in tubes, Proceedings A-The Royal Society 200, p.1062, 1950. ,
DNS of gas bubbles behaviour using an improved 3D front tracking model-drag force on isolated bubbles and comparison with experiments, Chemical Engineering Science, vol.65, issue.4, pp.1415-1426, 2010. ,
Some aspects of high-pressure phenomena of bubbles in liquids and liquid-solid suspensions, Chemical Engineering Science, vol.54, pp.4681-4709, 1999. ,
The effect of surfactant on the rise of spherical bubble at high reynolds and peclet number, Physics of Fluid, vol.8, issue.2, pp.310-321, 1996. ,
Multi-fluid simulation of turbulent bubbly in pipe flows, International Journal of Multiphase flow, vol.28, pp.1497-1519, 2009. ,
Drag coefficient and relative velocity in bubbly, droplet or particulate flows, American Institute of Chemical Engineering Journal, vol.25, issue.5, pp.843-855, 1979. ,
, Physicochemical Hydrodynamics, 1962.
Experiments on the rise of air bubbles in clean viscous liquids, Journal of Fluid Mechanics, vol.321, pp.421-441, 1996. ,
A drag coefficient correlation, Vdi Zeitung, vol.77, p.318, 1935. ,
On the effect of the internal friction of fluids on the motion of pendulums, Cambridge Philos. Trans, vol.9, pp.8-106, 1851. ,
Struggle with computational bubble dynamics, Multiphase Science and Technology, vol.10, issue.4, p.369, 1998. ,
Terminal velocity of single bubbles in surface tension force dominant regime, International Journal of Multiphase flow, vol.28, pp.1497-1519, 2002. ,
Numerical simulation of dynamic flow behavior in a bubble column: A study of closures for turbulence and interface forces, Chemical Engineering Science, vol.61, pp.7593-7608, 2006. ,
The effects of mesoscale structures on the disperse two-phase flows and their closures for dilute suspensions, International Journal of Multiphase Flow, vol.28, pp.805-822, 2002. ,
The Favre averaged drag model for turbulent dispersion in eulerian multi-phase flows, '5th International Conference on Multiphase Flow, 2004. ,
Equations des gaz turbulents compressibles. i. Formes générales, Journal de Mécanique, vol.4, pp.361-390, 1965. ,
A Favre-averaged turbulence model for gas-particle flows, '2012 AIChE Annual Meeting, 2012. ,
A multiphase turbulence theory for gas-solids flows using Favreaveraging, '2014 NETL Workshop on Multiphase Flow Science, 2014. ,