investigation of rheological behavior of suspensions included power-law fluid by combined lattice-Boltezmann method with smoothed profile method

Authors

1 Department of Chemical engineering, Faculty of engineering, shahid Bahonar University of Kerman

2 Department of Energy, Institute of Science and High Technology and Environmental Sciences, Graduate University of Advanced Technology, Kerman, Iran.

Abstract

In the present work, we offer a novel numerical algorithm based on the lattice Boltzmann method (LBM) to consider the motion of many circular particles in a non-Newtonian power law fluid in Couette flow and it is combined with the smoothed profile method which explains the movement of particles. At first, the velocity variation of shear-thickening has been analyzed and the results was compared with the numerical results of the previous works. The present study is a first report, which investigate flow behavior of circular particles with the same and different size in power law medium in Couette flow on the LBM framework. The effective viscosity of a particulate suspension that are placed randomly inside two parallel walls is considered for 0.04

Keywords

Main Subjects


[1] Chevalier T, Rodts S, Chateau X, Chevalier C, Coussot P (2014) Breaking of non-Newtonian character in flows through a porous medium. Physical Review E 89: 023002
[2] Yun BM, Dasi LP, Aidun CK, Yoganathan AP (2014) Computational modelling of flow through prosthetic heart valves using the entropic lattice-Boltzmann method. J Fluid Mech 743: 170-201.
[3] Brady JFA, Bossis G (1988) Stokesian dynamics. Ann Rev Fluid Mech 20: 111-157.
[4] Ladd AJC (1994) Numerical simulations of particulate suspensions via a discretized Boltzmann equation, I. Theoretical foundation. J Fluid Mech 271: 285-310.
[5] Ladd AJC (1994) Numerical simulations of particulate suspensions via a discretized Boltzmann equation, II. Numerical results. J Fluid Mech 271: 311-339.
[6] Jafari S, Yamamoto R, Rahnama M (2011) Lattice-Boltzmann method combined with smoothed-profile method for particulate suspensions. Physical review E 83: 026702.
[7] Aharonov E, Rothman DH (1993) Non-Newtonian flow (through porous-media): A lattice Boltzmann method. Geophys Res Lett 20: 679-682.
[8] Jahanshahi Javaran E, Rahnama M, Jafari S (2013) Combining Lees–Edwards boundary conditions with smoothed Profile-lattice Boltzmann methods to introduce shear into particle suspensions. Adv Powder Technol 24: 1109-1118
[9] Feng Z, Michaelides EE (2004) The immersed boundary-lattice Boltzmann method for solving fluids-particles interaction problems. J Comput Phys 195: 602-628.
[10] Nakayama Y, Yamamoto R (2005) Simulation method to resolve hydrodynamic interactions in colloidal dispersions. Phys Rev E 71: 036707.
[11] Gabbanelli S, Drazer G, Koplik J (2005) Lattice Boltzmann method for non-Newtonian (power-law) fluids. Phys Rev E 72: 046312.
[12] Subrahmanyam Mendu S, Das PK (2012) Flow of power-law fluids in a cavity driven by the motion of two facing lids – A simulation by lattice Boltzmann method. J Non-Newton Fluid 175-176: 10-24.
[13] Kromkamp J, Endec D, Kandhaid D, Smana R, Boom R (2006) Lattice Boltzmann simulation of 2D and 3D non-Brownian suspensions in Couette flow. Chem Eng Sci 61: 858-873.
[14] Kromkamp J, Endec D, Kandhaid D, Smana R, Boom R (2005) Shear-induced self-diffusion and microstructure in non-Brownian suspensions at non-zero Reynolds numbers. J Fluid Mech 529: 253-278.
[15] Einstein A (1906) A new determination of molecular dimensions. Ann Phys-New York 19(4): 289-306.
[16] Krieger I, Dougherty T (1959) A mechanism for non-Newtonian flow in suspension of rigid spheres. J Rheol 3(1): 137-152.
[17] Shakib-Manesh A, Raiskinmäki P, Koponen A, Kataja M, Timonen J (2002) Shear stress in a couette flow of liquid-particle suspensions. J Stat Phys 107, Nos. 1/2.
[18] Jahanshahi javaran E, Rahnama M, Jafari S (2013) Investigating the applicability of combined lattice Boltzmann-Smoothed profile methods in particulate system. Particul Sci Technol 31: 1-10.
[19] Succi S (2001) The lattice Boltzmann equation for fluid dynamics and beyond. Oxford University Press, Oxford.
[20] Wang CH, Ho JR (2011) A lattice Boltzmann approach for the non-Newtonian effect in the blood flow. Comput Math Appl 62: 75-86.
[21] Amiri Delouei A, Nazari M, Kayhani MH (1393) Applying ‘SHARP’ interface scheme in the immersed boundary–lattice Boltzmann method for simulation non-Newtonian fluid flow over a cylinder. Journal of Solid and Fluid Mechanics 4: 157-174.
[22] Bell BC, Surana KS (1994) p-version least squares finite element formulation for two dimensional, incompressible, non-Newtonian isothermal and non-isothermal fluid flow. Int J Numer Meth Fl 18: 127-162
[23] Krüger T, Varnik F, Raabe D (2009)  Shear stress in lattice Boltzmann simulations. Phys Rev E 79: 046704.
[24] Batchelor GK (1970) The stress system in a suspension of force free particles. J Fluid Mech 41(3): 545-570.
[25] Kulkarni PM, Morris JF (2008) Suspension properties at finite Reynolds number from simulated shear flow. Phys Fluids 20: 040602.
[26] Fallah K, Taeibi Rahni M, Mohammadzadeh A, Najafi M (1394) Force convection heat transfer from a stationary circular cylinder in non-newtonian fluids. Journal of Solid and Fluid Mechanics 5: 229-242.
[27] Amiri deluei A, Nazari M, Kayhani Mk, Kang SK, Succi S (2016) Non-Newtonian particulate flow simulation: A direct-forcing immersed boundary-lattice Boltzmann approach. Physica A 447: 1-20.