References
- Altunbaş , A. , Kelbaliyev , G. , and Ceylan , K. ( 2002 ). Eddy diffusivity of particles in turbulent flow in rough channels , J. Aerosol Sci. , 33 ( 7 ), 1075 – 1086 .
- Angeli , P. and Hewitt , G. F. ( 2000 ). Drop size distribution in horizontal oil-water dispersed flows , Chem. Eng. Sci. , 55 , 3133 – 3143 .
- Bhaga , D. and Weber , M. E. ( 1981 ). Bubbles in viscous liquids: Shape, wakes and velocities , J. Fluid Mech. , 105 , 61 – 85 .
- Bird , R. R. , Stewart , W. E. , and Lightfoot , E. N. ( 1960 ). Transport Phenomena , John Wiley , New York .
- Bozzano , G. and Dente , M. ( 2001 ). Shape and velocity of single bubble motion: A novel approach , Comput. Chem. Eng. , 25 , 571 – 576 .
- Bringell , A. S. ( 1973 ). The deformation of a liquid drops at small Reynolds number , Q. J. Appl. Math. , 26 , 99 – 107 .
- Brownstein , B. I. and Shegolev , V. V. ( 1988 ). Hydrodynamics, Heat and Mass Transfer in Column , Chimia , Moscow . ( in Russian )
- Ceylan , K. , Altunbaş , A. , and Kelbaliyev , G. ( 2001 ). A new model for estimation of drag force in the flow of Newtonian fluids around rigid or deformable particles , Powder Technol. , 119 ( 2–3 ), 250 – 256 .
- Chester , W. and Breach , D. R. ( 1969 ). On the flow past a sphere at low Reynolds numbers , J. Fluid Mech. , 37 ( 4 ), 751 – 760 .
- Chorin , A. J. ( 1968 ). Numerical solution of Navier-Stokes equations , Math. Comput. , 22 ( 104 ), 745 – 762 .
- Christov , C. I. and Volkow , P. K. ( 1985 ). Numerical investigation of the steady viscous flow past a stationary deformable bubble , J. Fluid Mech. , 158 , 341 – 364 .
- Clift , R. , Grace , J. R. , and Weber , M. E. ( 1978 ). Bubbles, Drops and Particles , Academic Press , New York .
- Cox , B. G. ( 1962 ). On driving a viscous fluid out of a tube , J. Fluid Mech. , 14 , 81 – 91 .
- Dewsbury , K. H. , Karamanev , D. D. , and Maragaritis , A. ( 2002 ). Rising solid sphere hydrodynamics at high Reynolds number in non-Newtonian fluids , Chem. Eng. J. , 87 , 129 – 133 .
- Harmathy , T. Z. ( 1960 ). AIChE J. , 6 ( 2 ), 281 – 288 .
- Harper , J. F. ( 1972 ). The motions of bubbles and drops through liquids , Adv. Appl. Mech. , 12 , 59 – 129 .
- Helenbrook , B. T. and Edwards , C. F. ( 2002 ). Quasi-steady deformation and drag of uncontaminated liquid drops , Int. J. Multiph. Flow , 28 , 1631 – 1657 .
- Kelbaliyev , G. and Ceylan , K. ( 2005 ). Estimation of the minimum stable drop sizes, the break-up frequencies and the size distributions in turbulent dispersions , J. Dispers. Sci. Technol. , 26 ( 4 ), 487 – 494 .
- Kondratev , A. S. and Naumova , E. A. ( 2003 ). Calculation of the velocity of free settling of solid particles in a Newtonian liquid , Theor. Found. Chem Eng. , 37 ( 6 ), 606 – 612 .
- Kutateladze , S. S. (1990). Heat Transfer and Hydrodynamical Drag Handbook , Nauka , Moscow.
- Landau , L. D. and Liftshitz , E. M. ( 1953 ). Mechanics of Continuous Medium , Nauka , Moscow .
- Lasheras , J. C. , Eastwood , C. , Martinez-Bazan C. , and Montanes , J. L. ( 2002 ). A review of statistical models for the drop-breakup of an immiscible fluid immersed into fully developed turbulent flow , Int. J. Multiph. Flow , 28 , 247 – 278 .
- LeClair , B. P. , Hamielek , A. E. , and Pruppacher , H. R. ( 1970 ). A numerical study of the drag on a sphere at low and intermediate Reynolds numbers , J. Atmos. Sci. , 27 , 308 – 315 .
- Levich , V. G. ( 1962 ). Physicochemical Hydrodynamics , Prentice-Hall , Englewood Cliffs , N.J.
- Loth , E. , Taeibi-Rahni , M. , and Tryggvason , G. ( 1997 ). Deformable bubbles in free shear layer , Int. J. Multiph. Flow , 23 , 977 – 1001 .
- Maxworthy , T. , Grann , C. , Kurten , M. , and Durst , F. ( 1996 ). Experiments on the rise of air bubbles in clean viscous liquids , J. Fluid Mech. , 321 , 421 – 441 .
- McLaughlin , J. B. ( 1996 ). Numerical simulation of bubble motion in water , J. Colloid Interface Sci. , 184 , 614 – 625 .
- Moore , D. W. ( 1965 ). The boundary layer on spherical gas bubbles , J. Fluid Mech. , 16 , 161 – 176 .
- Ockedon , J. R. and Evens , G. A. ( 1972 ). The drag on the spheres at low Reynolds numbers flow , J.Aerosol Sci. , 3 ( 4 ), 237 – 242 .
- Perry , J. H. ( 1950 ). Chemical Engineer's Handbook , McGraw-Hill , New York .
- Pruppacher , H. R. and Steinberger , E. H. ( 1968 ). An experimental determination of the drag on a sphere at low Reynolds numbers , J. Appl. Phys. , 18 , 4129 – 4132 .
- Raymond , F. and Rosant , J. M. ( 2000 ). A numerical and experimental study of the terminal velocity and shape of bubbles in viscous liquids , Chem. Eng. Sci. , 55 , 943 – 955 .
- Sajjadi , S. , Zerfa , M. , and Brooks , B. M. ( 2002 ). Dynamic behaviors of drops in oil/water oil dispersions , Chem. Eng. Sci. , 57 , 663 – 675 .
- Schlichting , H. ( 1968 ). Boundary-Layer Theory , McGraw-Hill , New York .
- Soo , S. L. ( 1970 ). Fluid Dynamics of Multiphase Systems , Blaisdell , London .
- Taylor , T. and Acrivos , A. ( 1964 ). On the deformation and drag of a falling drop at low Reynolds numbers , J. Fluid Mech. , 18 , 466 – 476 .
- Tudose , E. T. and Kawaji , M. ( 1999 ). Experimental investigation of Taylor bubble acceleration mechanism in slug flow , Chem. Eng. Sci. , 54 , 5761 – 5775 .
- Voloshuk , V. M. and Sedunow , J. S. ( 1976 ). The Processes of Coagulation in Dispersed Systems , Nauka , Moscow .
- Wellek , R. M. , Angrawal , A. K. , and Skelland , A. H. P. ( 1966 ). Shape of liquid drops mowing in liquid media , AIChE J. , 12 , 854 – 866 .
- Zhang , J. , Li , Y. , and Fan , L.-S. ( 2000 ). Numerical studies of bubble and particle dynamics in three-phase fluidized bed at elevated pressures , Powder Technol. , 112 , 46 – 56 .