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to dense gas–solid flows in fluidized beds. Chem Eng Sci 62(21):5854–5869
31. Lu L, Xu J, Ge W, Yue Y, Liu X, Li J (2014) EMMS-based discrete particle method (EMMS–
DPM) for simulation of gas–solid flows. Chem Eng Sci 120:67–87
32. Lun C, Savage SB, Jeffrey D, Chepurniy N (1984) Kinetic theories for granular flow: inelastic
particles in Couette flow and slightly inelastic particles in a general flowfield. J Fluid Mech
140:223–256
33. Makkawi YT, Wright PC (2002) Fluidization regimes in a conventional fluidized bed
characterized by means of electrical capacitance tomography. Chem Eng Sci 57(13):2411–2437
34. Makkawi YT, Wright PC (2004) Electrical capacitance tomography for conventional fluidized
bed measurements—remarks on the measuring technique. Powder Technol 148(2–3):142–157
35. Mazzei L, Lettieri P (2007) A drag force closure for uniformly dispersed fluidized suspensions.
Chem Eng Sci 62(22):6129–6142
36. Mikami T, Kamiya H, Horio M (1998) Numerical simulation of cohesive powder behavior in
a fluidized bed. Chem Eng Sci 53(10):1927–1940
37. Müller C, Holland D, Sederman A, Scott S, Dennis J, Gladden L (2008) Granular temperature:
comparison of magnetic resonance measurements with discrete element model simulations.
Powder Technol 184(2):241–253
38. Pannala S, Syamlal M, O’Brien TJ (2011) Computational gas-solids flows and reacting systems:
theory, methods and practice. IGI Global, Hershey
39. Passalacqua A, Marmo L (2009) A critical comparison of frictional stress models applied to
the simulation of bubbling fluidized beds. Chem Eng Sci 64(12):2795–2806
40. Penn A, Boyce CM, Kovar T, Tsuji T, Pruessmann KP, Müller CR (2018) Real-time magnetic
resonance imaging of bubble behavior and particle velocity in fluidized beds. Ind Eng Chem
Res 57(29):9674–9682
41. Regelink MA (2000) Formation of regular bubble patterns in periodically pulsed gas-solid
fluidized beds. MSc thesis, Delft University of Technology, Delft, The Netherlands
42. Saayman J, Nicol W, van Ommen JR, Mudde RF (2013) Fast X-ray tomography for the quantification of the bubbling-, turbulent- and fast fluidization-flow regimes and void structures.
Chem Eng J 234:437–447
43. Sakai M, Koshizuka S (2009) Large-scale discrete element modeling in pneumatic conveying.
Chem Eng Sci 64(3):533–539
44. Schaeffer DG (1987) Instability in the evolution equations describing incompressible granular
flow. J Differ Equ 66(1):19–50
45. Silbert LE, Ertas D, Grest GS, Halsey TC, Levine D, Plimpton SJ (2001) Granular flow down
an inclined plane: Bagnold scaling and rheology. Phys Rev E 64(5):051302
46. Sines JN, Hwang S, Marashdeh QM, Tong A, Wang D, He P, Straiton BJ, Zuccarelli CE, Fan
L-S (2019) Slurry bubble column measurements using advanced electrical capacitance volume
tomography sensors. Powder Technol 355:474–480
47. Snider D (2001) An incompressible three-dimensional multiphase particle-in-cell model for
dense particle flows. J Comput Phys 170(2):523–549
48. Sun J, Sundaresan S (2011) A constitutive model with microstructure evolution for flow of
rate-independent granular materials. J Fluid Mech 682:590–616
49. Sundaresan S (2003) Instabilities in fluidized beds. Annu Rev Fluid Mech 35(1):63–88
50. Syamlal M, Rogers W, O’Brien TJ (1993) MFIX documentation: theory guide. Technical
Note DOE/METC-95/1013 and NTIS/DE95000031. National Energy Technology Laboratory,
Department of Energy
51. Tsuji Y, Tanaka T, Ishida T (1992) Lagrangian numerical simulation of plug flow of cohesionless
particles in a horizontal pipe. Powder Technol 71(3):239–250
52. Tsuo YP, Gidaspow D (1990) Computation of flow patterns in circulating fluidized beds. AlChE
J 36(6):885–896
53. van der Hoef M, van Sint Annaland M, Deen NG, Kuipers JAM (2008) Numerical simulation of
dense gas-solid fluidized beds: a multiscale modeling strategy. Annu Rev Fluid Mech 40:47–70
113
30. Lindborg H, Lysberg M, Jakobsen HA (2007) Practical validation of the two-fluid model applied
to dense gas–solid flows in fluidized beds. Chem Eng Sci 62(21):5854–5869
31. Lu L, Xu J, Ge W, Yue Y, Liu X, Li J (2014) EMMS-based discrete particle method (EMMS–
DPM) for simulation of gas–solid flows. Chem Eng Sci 120:67–87
32. Lun C, Savage SB, Jeffrey D, Chepurniy N (1984) Kinetic theories for granular flow: inelastic
particles in Couette flow and slightly inelastic particles in a general flowfield. J Fluid Mech
140:223–256
33. Makkawi YT, Wright PC (2002) Fluidization regimes in a conventional fluidized bed
characterized by means of electrical capacitance tomography. Chem Eng Sci 57(13):2411–2437
34. Makkawi YT, Wright PC (2004) Electrical capacitance tomography for conventional fluidized
bed measurements—remarks on the measuring technique. Powder Technol 148(2–3):142–157
35. Mazzei L, Lettieri P (2007) A drag force closure for uniformly dispersed fluidized suspensions.
Chem Eng Sci 62(22):6129–6142
36. Mikami T, Kamiya H, Horio M (1998) Numerical simulation of cohesive powder behavior in
a fluidized bed. Chem Eng Sci 53(10):1927–1940
37. Müller C, Holland D, Sederman A, Scott S, Dennis J, Gladden L (2008) Granular temperature:
comparison of magnetic resonance measurements with discrete element model simulations.
Powder Technol 184(2):241–253
38. Pannala S, Syamlal M, O’Brien TJ (2011) Computational gas-solids flows and reacting systems:
theory, methods and practice. IGI Global, Hershey
39. Passalacqua A, Marmo L (2009) A critical comparison of frictional stress models applied to
the simulation of bubbling fluidized beds. Chem Eng Sci 64(12):2795–2806
40. Penn A, Boyce CM, Kovar T, Tsuji T, Pruessmann KP, Müller CR (2018) Real-time magnetic
resonance imaging of bubble behavior and particle velocity in fluidized beds. Ind Eng Chem
Res 57(29):9674–9682
41. Regelink MA (2000) Formation of regular bubble patterns in periodically pulsed gas-solid
fluidized beds. MSc thesis, Delft University of Technology, Delft, The Netherlands
42. Saayman J, Nicol W, van Ommen JR, Mudde RF (2013) Fast X-ray tomography for the quantification of the bubbling-, turbulent- and fast fluidization-flow regimes and void structures.
Chem Eng J 234:437–447
43. Sakai M, Koshizuka S (2009) Large-scale discrete element modeling in pneumatic conveying.
Chem Eng Sci 64(3):533–539
44. Schaeffer DG (1987) Instability in the evolution equations describing incompressible granular
flow. J Differ Equ 66(1):19–50
45. Silbert LE, Ertas D, Grest GS, Halsey TC, Levine D, Plimpton SJ (2001) Granular flow down
an inclined plane: Bagnold scaling and rheology. Phys Rev E 64(5):051302
46. Sines JN, Hwang S, Marashdeh QM, Tong A, Wang D, He P, Straiton BJ, Zuccarelli CE, Fan
L-S (2019) Slurry bubble column measurements using advanced electrical capacitance volume
tomography sensors. Powder Technol 355:474–480
47. Snider D (2001) An incompressible three-dimensional multiphase particle-in-cell model for
dense particle flows. J Comput Phys 170(2):523–549
48. Sun J, Sundaresan S (2011) A constitutive model with microstructure evolution for flow of
rate-independent granular materials. J Fluid Mech 682:590–616
49. Sundaresan S (2003) Instabilities in fluidized beds. Annu Rev Fluid Mech 35(1):63–88
50. Syamlal M, Rogers W, O’Brien TJ (1993) MFIX documentation: theory guide. Technical
Note DOE/METC-95/1013 and NTIS/DE95000031. National Energy Technology Laboratory,
Department of Energy
51. Tsuji Y, Tanaka T, Ishida T (1992) Lagrangian numerical simulation of plug flow of cohesionless
particles in a horizontal pipe. Powder Technol 71(3):239–250
52. Tsuo YP, Gidaspow D (1990) Computation of flow patterns in circulating fluidized beds. AlChE
J 36(6):885–896
53. van der Hoef M, van Sint Annaland M, Deen NG, Kuipers JAM (2008) Numerical simulation of
dense gas-solid fluidized beds: a multiscale modeling strategy. Annu Rev Fluid Mech 40:47–70