Applied Chemistry for Engineering (공업화학)

The Korean Society of Industrial and Engineering Chemistry (한국공업화학회)
권호 표지
DOI QR코드

DOI QR Code

Rheological Modeling of Nanoparticles in a Suspension with Shear Flow

전단 흐름을 갖는 서스펜션 내부 나노 입자의 유변학적 특성 연구

  • Kim, Gu (Department of Chemical Engineering, Faculty of Engineering, Kyushu University) ;
  • Fukai, Jun (Department of Chemical Engineering, Faculty of Engineering, Kyushu University) ;
  • Hironaka, Shuji (Department of Chemical Engineering, Faculty of Engineering, Kyushu University)
  • Received : 2019.05.24
  • Accepted : 2019.06.27
  • Published : 2019.08.10
Download PDF
⟨ Previous Next ⟩

Abstract

Shear thickening is an intriguing phenomenon in the fields of chemical engineering and rheology because it originates from complex situations with experimental and numerical measurements. This paper presents results from the numerical modeling of the particle-fluid dynamics of a two-dimensional mixture of colloidal particles immersed in a fluid. Our results reveal the characteristic particle behavior with an application of a shear force to the upper part of the fluid domain. By combining the lattice Boltzmann and discrete element methods with the calculation of the lubrication forces when particles approach or recede from each other, this study aims to reveal the behavior of the suspension, specifically shear thickening. The results show that the calculated suspension viscosity is in good agreement with the experimental results. Results describing the particle deviation, diffusivity, concentration, and contact numbers are also demonstrated.

Keywords

GOOOB2_2019_v30n4_445_f0001.png 이미지

Figure 1. Discretization of the position and velocity space for a D2Q9 lattice.

GOOOB2_2019_v30n4_445_f0002.png 이미지

Figure 2. Viscosity calculation results.

GOOOB2_2019_v30n4_445_f0003.png 이미지

Figure 3. Modified mean squared displacement.

GOOOB2_2019_v30n4_445_f0004.png 이미지

Figure 4. Diffusivity according to Eq. (27).

GOOOB2_2019_v30n4_445_f0005.png 이미지

Figure 5. Concentration coefficient results.

GOOOB2_2019_v30n4_445_f0006.png 이미지

Figure 6. Physical particle contact numbers at $\acute{\gamma}$ = 40,000 s-1.

Table 1. Parameters Used in the Simulation

GOOOB2_2019_v30n4_445_t0001.png 이미지

References

  1. M. Schmitt, M. Baunach, L. Wengeler, K. Peters, P. Junges, P. Scharfer, and W. Schabel, Slot-die processing of lithium-ion battery electrodes-coating window characterization, Chem. Eng. Process., 68, 32-37 (2013). https://doi.org/10.1016/j.cep.2012.10.011
  2. H. A. Barnes, Shear-thickening ("Dilatancy") in suspensions of non aggregating solid particles dispersed in newtonian liquids, J. Rheol., 33, 329-366 (1989). https://doi.org/10.1122/1.550017
  3. S. Khandavalli and J. Rothstein, Extensional rheology of shear-thickening nanoparticle dispersions in an aqueous polyethylene oxide solutions, J. Rheol., 58(2), 411-431 (2014). https://doi.org/10.1122/1.4864620
  4. H. Liu, Q. Kang, C. R. Leonardi, S. Schmieschek, A. Narvaez, B. D. Jones, J. R. Williams, A. J. Valocchi, and J. Harting, Multiphase lattice Boltzmann simulations for porous media applications, Comput. Geosci., 20(4), 777-805 (2016). https://doi.org/10.1007/s10596-015-9542-3
  5. S. Khandavalli, J. A. Lee, M. Pasquali, and J. P. Rothstein, The effect of shear-thickening on liquid transfer from an idealized gravure cell, J. Nonnewton. Fluid Mech., 221, 55-65 (2015). https://doi.org/10.1016/j.jnnfm.2015.03.007
  6. K. T. Kim and R. E. Khayat, Transient coating flow of a thin non-Newtonian fluid film, Phys. Fluids, 14, 2202-2215 (2002). https://doi.org/10.1063/1.1483306
  7. T. Tsuda, Coating flows of power-law non-newtonian fluid in slot coating, J. Soc. Rheol. Jpn., 38(4-5), 223-230 (2010). https://doi.org/10.1678/rheology.38.223
  8. K. M. Beazley, Industrial aqueous suspensions, in: K. Walters (ed.), Rheometry: Industrial Applications, 339-413, Research Studies Press, Chichester UK (1980).
  9. R. L. Hoffman, Explanations for the cause of shear thickening in concentrated colloidal suspensions, J. Rheol., 42, 111-123 (1998). https://doi.org/10.1122/1.550884
  10. R. L. Hoffman, Discontinuous and dilatant viscosity behavior in concentrated suspensions: III. Necessary conditions for their occurrence in viscometric flows, Adv. Colloid Interface Sci., 17(1), 161-184 (1982). https://doi.org/10.1016/0001-8686(82)80017-1
  11. M. Yang and E. S. G. Shaqfeh, Mechanism of shear thickening in suspensions of rigid spheres in Boger fluids. Part II: Suspensions at finite concentration, J. Nonnewton. Fluid Mech., 234, 51-68 (2016). https://doi.org/10.1016/j.jnnfm.2016.04.003
  12. X. Bian, S. Litvinov, M. Ellero, and N. J. Wagner, Hydrodynamic shear thickening of particulate suspension under confinement, J. Nonnewton. Fluid Mech., 213, 39-49 (2014). https://doi.org/10.1016/j.jnnfm.2014.09.003
  13. Y. Chen, Q. Cai, Z. Xia, M. Wang, and S. Chen, Momentum-exchange method in lattice Boltzmann simulations of particle-fluid interactions, Phys. Rev. E, 88(1), 013303-1-15 (2013). https://doi.org/10.1103/PhysRevE.88.013303
  14. M. C. Sukop and D. T. Thorne, Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers, 31-35, Springer (2007).
  15. G. V. Krivovichev, Linear Bhatnagar-Gross-Krook equations for simulation of linear diffusion equation by lattice Boltzmann method, Appl. Math. Comput., 325, 102-119 (2018). https://doi.org/10.1016/j.amc.2017.12.027
  16. L. S. Lin, H. W. Chang, and C. A. Lin, Multi relaxation time lattice Boltzmann simulations of transition in deep 2D lid driven cavity using GPU, Comput. Fluids, 80(10), 381-387 (2013). https://doi.org/10.1016/j.compfluid.2012.01.018
  17. K. Chen, Y. Wang, S. Xuan, and X. Gong, A hybrid molecular dynamics study on the non-Newtonian rheological behaviors of shear thickening fluid, J. Colloid Interface Sci., 497(1), 378-384 (2017). https://doi.org/10.1016/j.jcis.2017.03.038
  18. P. A. Cundall and O. D. L. Strack, A discrete numerical model for granular assemblies, Geotechnique, 29(1), 47-65 (1979). https://doi.org/10.1680/geot.1979.29.1.47
  19. M. Kuanmin, Y. W. Michael, X. Zhiwei, and C. Tianning, DEM simulation of particle damping, Powder Technol., 142(2), 154-165 (2004). https://doi.org/10.1016/j.powtec.2004.04.031
  20. W. Smith, D. Melanz, C. Senatore, K. Iagnemma, and H. Peng, Comparison of discrete element method and traditional modeling methods for steady-state wheel-terrain interaction of small vehicles, J. Terramechanic, 56, 61-75 (2014). https://doi.org/10.1016/j.jterra.2014.08.004
  21. S. Laryea, M. S. Baghsorkhi, J. F. Ferellec, G. R. McDowell, and C. Chen, Comparison of performance of concrete and steel sleepers using experimental and discrete element methods, Transp. Geotech., 1(4), 225-240 (2014). https://doi.org/10.1016/j.trgeo.2014.05.001
  22. P. P. Prochazka, Application of discrete element methods to fracture mechanics of rock bursts, Eng. Fract. Mech., 71(4), 601-618 (2004). https://doi.org/10.1016/S0013-7944(03)00029-8
  23. H. P. Zhu and A. B. Yu, A theoretical analysis of the force models in discrete element method, Powder Technol., 161(2), 122-129 (2006). https://doi.org/10.1016/j.powtec.2005.09.006
  24. I. Klaus, T. Nils, and R. Ulrich, Simulation of moving particles in 3D with the Lattice Boltzmann method, Comput. Math. Appl., 55, 1461-1468 (2008). https://doi.org/10.1016/j.camwa.2007.08.022
  25. O. Filippova and D. Hanel, Grid refinement for lattice-BGK models, J. Comput. Phys., 147, 219-228 (1998). https://doi.org/10.1006/jcph.1998.6089
  26. R. Mei, L. S. Luo, and W. Shyy, An accurate curved boundary treatment in the lattice Boltzmann method, J. Comput. Phys., 155, 307-330 (1999). https://doi.org/10.1006/jcph.1999.6334
  27. C. Chang, C. H. Liu, and C. A. Li, Boundary conditions for lattice Boltzmann simulations with complex geometry flows, Comput. Math. Appl., 58(5), 940-949 (2002).
  28. M. Bouzidi, M. Firdaouss, and P. Lallemand, Momentum transfer of a boltzmann-lattice fluid with boundaries, Phys. Fluids, 13, 3452-3459 (2001). https://doi.org/10.1063/1.1399290
  29. D. R. J. Owen, C. R. Leonardi, and Y. T. Feng, An efficient framework for fluid-structure interaction using the lattice Boltzmann method and immersed moving boundaries, Int. J. Numer. Methods Eng., 87(1), 66-95 (2011). https://doi.org/10.1002/nme.2985
  30. L. Verlet, Computer "Experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Phys. Rev., 159(1), 98-103 (1967). https://doi.org/10.1103/PhysRev.159.98
  31. H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten, Generalized verlet algorithm for efficient molecular dynamics simulations with long-range interactions, Mol. Simul., 6, 121-142 (1991). https://doi.org/10.1080/08927029108022142
  32. E. P. Honig, G. J. Roeberse, and P. H. Wiersema, Effect of hydrodynamic interaction on coagulation rate of hydrophobic colloids, J. Colloid Interface Sci., 36, 36-97 (1971).
  33. S. L. Dance and M. R. Maxey, Incorporation of lubrication effects into the force-coupling method for particulate two-phase flow, J. Comput. Phys., 189, 212-238 (2003). https://doi.org/10.1016/S0021-9991(03)00209-2
  34. O. I. Vinogradova, Drainage of a thin liquid-film confined between hydrophobic surfaces, Langmuir, 11, 2213-2220 (1995). https://doi.org/10.1021/la00006a059
  35. C. G. de Kruif, E. M. F. van Iersel, A. Vrij, and W. B. Russel, Hardsphere colloidal dispersions - Viscosity as a function of shear rate and volume fraction, J. Chem. Phys., 83, 4717-4725 (1985). https://doi.org/10.1063/1.448997
  36. T. Zhang, B. Shi, Z. Guo, Z. Chai, and J. Lu, General bounce-back scheme for concentration boundary condition in the lattice-Boltzmann method, Phys. Rev., 85, 016701-1-14 (2012).
  37. Y. Zong, C. Peng, Z. Guoc, and L. P. Wang, Designing correct fluid hydrodynamics on a rectangular grid using MRT lattice Boltzmann approach, Comput. Math. Appl., 72, 288-310 (2016). https://doi.org/10.1016/j.camwa.2015.05.021
  38. B. J. Maranzano and N. J. Wagner, The effects of interparticle interactions and particle size on reversible shear thickening: Hard-sphere colloidal dispersions, J. Rheol., 45, 1205-1222 (2001). https://doi.org/10.1122/1.1392295
  39. I. R. Peters, S. Majumdar, and H. M. Jaeger, Direct observation of dynamic shear jamming in dense suspensions, Nature, 532, 214-217 (2016). https://doi.org/10.1038/nature17167
  40. E. Brown and H. M. Jaeger, The role of dilation and confining stresses in shear thickening of dense suspensions, J. Rheol., 56(4), 875-923 (2012). https://doi.org/10.1122/1.4709423
  41. A. Sierou and J. F. Brady, Shear-induced self-diffusion in non-colloidal suspensions, J. Fluid Mech., 506, 285-314 (2004). https://doi.org/10.1017/S0022112004008651
  42. N. Tarantino, J. Y. Tinevez, E. F. Crowell, B. Boisson, R. Henriques, M. Mhlanga, F. Agou, A. Israël, and E. Laplantine, TNF and IL-1 exhibit distinct ubiquitin requirements for inducing NEMO-IKK supramolecular structures, J. Cell Biol., 204(2), 231-245 (2014). https://doi.org/10.1083/jcb.201307172
  43. A. Einstein, Eine neue bestimmung der molekldimensionen, Ann. Phys. (Berl.), 324(2), 289-306 (1906). https://doi.org/10.1002/andp.19063240204
  44. E. Nazockdast and J. F. Morris, Microstructural theory and the rheology of concentrated colloidal suspensions, J. Fluid Mech., 713, 420-452 (2012). https://doi.org/10.1017/jfm.2012.467
  45. N. J. Wagner and J. F. Brady, Shear thickening in colloidal dispersions, Phys. Today, 62, 27-32 (2009).
  46. J. Bergenholtz, J. F. Brady, and M. Vicic, The non-Newtonian rheology of dilute colloidal suspensions, J. Fluid Mech., 456, 239-275 (2002). https://doi.org/10.1017/S0022112001007583
  47. N. J. Wagner and J. F. Brady, Shear thickening in colloidal dispersions, Phys. Today, 62(10), 27-32 (2009). https://doi.org/10.1063/1.3248476
  48. R. G. Egres, F. Nettesheim, and N. J. Wagner, Rheo-SANS investigation of acicular-precipitated calcium carbonate colloidal suspensions through the shear thickening transition, J. Rheol., 50(5), 685-709 (2006). https://doi.org/10.1122/1.2213245
  49. H. M. Jaeger, S. R. Nagel, and R. P. Behringer, Granular solids, liquids, and gases, Rev. Mod. Phys., 68(4), 1259-1273 (1996). https://doi.org/10.1103/RevModPhys.68.1259
  50. W. Huang, Y. Wu, L. Qiu, C. Dong, J. Ding, and D. Li, Tuning rheological performance of silica concentrated shear thickening fluid by using graphene oxide, Adv. Condens. Matter Phys., 2015, 734250 (2015).
  51. N. J. Wagner, E. D. Wetzel, G. Ronald, and J. R. Egres, Shear thickening fluid containment in polymer composites, US Patent 0234572 (2006).