# Self-organized domain microstructures in a plate-like particle suspension subjected to rapid simple shear

## Abstract

The evolution of the microstructure and rheological properties of plate-like particle suspensions subjected to rapid simple shear is studied numerically. In response to the shear-induced strain, particles in the suspensions rearrange to form a steady-state microstructure, and the suspension viscosity reaches a steady value. Under this condition, the microstructure is composed of two domains having different particle fractions and particle orientations. In the matrix (particle-poor) and cluster (particle-rich) domains, the particles’ long axes are oriented subparallel to the shear plane and normal to the maximum compressive principal direction, respectively. A higher particle concentration and friction coefficient enhance the development of cluster domains relative to matrix domains leading the intensity of the preferred particle orientation to decrease and the number of contacting particles, the aspect ratio of clusters, the inter-particle force, and the suspension viscosity to increase. The domain microstructure is governed by two factors: (1) geometric relations between the particle orientation and the maximum compressive axes and (2) the magnitude of particle–fluid and particle–particle interactions. The first factor results in the coupling of the particle orientation and the local fraction of particles, which is an important character of the domain microstructure. The second factor controls the relative development of the cluster and matrix domains through the change in the particles’ rotational behavior. Our results suggest that the microstructure of plate-like suspensions subjected to rapid shear is predictable in terms of the cluster stability, which has important implications for the kinematics of flow-related microstructures in nature and manufacturing.

## Keywords

Contact force Hydrocluster Microstructure Force chain Simple shear Columnar phase## Notes

### Acknowledgments

We are grateful to Hiroaki Ohfuji for useful suggestions on this study. This work was supported by JSPS KAKENHI Grant Numbers 20740310 (Grant-in-Aid for Young Scientists (B) to H. K.). Constructive reviews by anonymous reviewers and editor Henning Winter improved the quality of this paper and were much appreciated.

## Supplementary material

## References

- Anderson TB, Jackson R (1967) A fluid mechanical description of fluidized beds. Ind Eng Chem Fundam 6:527CrossRefGoogle Scholar
- Arbaret L, Diot H, Bouchez J-L (1996) Shape fabrics of particles in low concentration suspensions: 2D analogue experiments and application to tiling in magma. J Struct Geol 18:941CrossRefGoogle Scholar
- Arbaret L, Diot H, Bouchez JL, Lespinasse P, Saint-Blanquat MD (1997) Analogue 3D simple-shear experiments of magmatic biotite subfabrics. Granites: from segregation of melt to emplacement fabric. Kluwer Academic, Dordrecht, p 129Google Scholar
- Arbaret L, Fernandez A, Ježek J, Ildefonse B, Launeau P, Diot H (2000) Analogue and numerical modelling of shape fabrics: application to strain and flow determination in magmas. Geol S Am 350:97. doi: 10.1130/0-8137-2350-7.97 Google Scholar
- Bell JB, Colella P, Glaz HM (1989) A second order projection method for the incompressible Navier-Stokes equations. J Comput Phys 85:257CrossRefGoogle Scholar
- Bossis G, Brady JF (1989) The rheology of Brownian suspensions. J Chem Phys 91:1866CrossRefGoogle Scholar
- Brown ABD, Clarke SM, Convert P, Rennie AR (2000) Orientational order in concentrated dispersions of plate-like kaolinite particles under shear. J Rheol 44:221CrossRefGoogle Scholar
- Brown ABD, Rennie AR (2000) Monodisperse colloidal plates under shear. Phys Rev E 62:851CrossRefGoogle Scholar
- Chu KW, Wang B, Yu AB, Vince A (2009) CFD-DEM modeling of multiphase flow in dense medium cyclones. Powder Technol 193:235CrossRefGoogle Scholar
- Corwin EI, Jaeger HM, Nagel SR (2005) Structural signature of jamming in granular media. Nature 435:1075CrossRefGoogle Scholar
- Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29:47CrossRefGoogle Scholar
- Dong KJ, Guo BY, Chu KW, Yu AB, Brake I (2008) Simulations of liquid-solid flow in a coal distributor. Miner Eng 21:789CrossRefGoogle Scholar
- Ergun S (1952) Fluid flow through packed columns. Chem Engng Prog 48:89Google Scholar
- Estrada N, Taboada A, Radjaï F (2008) Shear strength and force transmission in granular media with rolling resistance. Phys Rev E 78:021301CrossRefGoogle Scholar
- Fernandez A, Fernandez-Catuxo J (1997) 3D biotite shape fabric experiments under simple shear strain. Granite: From segregation of melt to emplacement fabrics. Kluwer Academic, Dordrecht, p 145Google Scholar
- Fernandez A, Feybesse JL, Mezure JF (1983) Theoretical and experimental study of fabric developed by different shaped markers in two-dimensional simple shear. Bull Soc Géol Fr 25:319Google Scholar
- Ghosh SK, Ramberg H (1976) Reorientation of inclusions by combination of pure shear and simple shear. Tectonophysics 34:1CrossRefGoogle Scholar
- Ildefonse B, Arbaret L, Diot H (1997) Rigid particles in simple shear flow: is there preferred orientation periodic or steady-state? Granite: from segregation of melt to emplacement fabrics. Kluwer Academic, Dordrecht, p 177Google Scholar
- Ildefonse B, Mancktelow NS (1993) Deformation around rigid particles: the influence of slip at the particle/matrix interface. Tectonophysics 221:345CrossRefGoogle Scholar
- Ildefonse B, Launeau P, Bouchez J-L, Fernandez A (1992a) Effect of mechanical interactions on the development of shape preferred orientations: a two-dimensional experimental approach. J Struct Geol 14:73CrossRefGoogle Scholar
- Ildefonse B, Sokoutis D, Mancktelow NS (1992b) Mechanical interactions between rigid particles in a deforming ductile matrix. Analogue experiments in simple shear flow. J Struct Geol 14:1253CrossRefGoogle Scholar
- Jeffery GB (1922) The motion of ellipsoidal particles immersed in a viscous fluid. P Roy Soc London Series A 102:161. doi: 10.1098/rspa.1922.0078 CrossRefGoogle Scholar
- Jogun SM, Zukoski CF (1999) Rheology and microstructure of dense suspensions of plate-shaped colloidal particles. J Rheol 43:847. doi: 10.1122/1.551013 CrossRefGoogle Scholar
- Johnson SE, Lenferink HJ, Price NA, Marsh JH, Koons PO, West Jr DP, Beane R (2009) Clast-based kinematic vorticity gauges: the effects of slip at matrix/clast interfaces. J Struct Geol 31:1322CrossRefGoogle Scholar
- Kawaguchi T, Tanaka T, Tsuji Y (1998) Numerical simulation of two-dimensional fluidized beds using the discrete element method (comparison between the two- and three-dimensional models). Powder Technol 96:129CrossRefGoogle Scholar
- Kulkarni PM, Morris JF (2008) Pair-sphere trajectories in finite-Reynolds-number shear flow. J Fluid Mech 596:413–435CrossRefGoogle Scholar
- Majmudar TS, Behringer RP (2005) Contact force measurements and stress-induced anisotropy in granular materials. Nature 435:1079CrossRefGoogle Scholar
- Mandal N, Kumar Samanta S, Bhattacharyya G, Chakraborty C (2005) Rotation behaviour of rigid inclusions in multiple association: insights from experimental and theoretical models. J Struct Geol 27:679CrossRefGoogle Scholar
- Marechal M, Cuetos A, Martínez-Haya B, Dijkstra M (2011) Phase behavior of hard colloidal platelets using free energy calculations. J Chem Phys 134:094501. doi: 10.1063/1.3552951 CrossRefGoogle Scholar
- Marques FO, Coelho S (2001) Rotation of rigid elliptical cylinders in viscous simple shear flow: analogue experiments. J Struct Geol 23:609CrossRefGoogle Scholar
- Marques FO, Taborda R, Bose S, Antunes J (2005) Effects of confinement on matrix flow around a rigid inclusion in viscous simple shear: insights from analogue and numerical modelling. J Struct Geol 27:379CrossRefGoogle Scholar
- Marthys NS (2005) Study of a dissipative particle dynamics based approach for modeling suspensions. J Rheol 49:401CrossRefGoogle Scholar
- Melrose JR, Ball RC (2004) Continuous shear thickening transitions in model concentrated colloids—The role of interparticle forces. J Rheol 48:937CrossRefGoogle Scholar
- Meng Q, Higdon JL (2008a) Large scale dynamic simulation of plate-like particle suspensions. Part I: non-Brownian simulation. J Rheol 52:1CrossRefGoogle Scholar
- Meng Q, Higdon JL (2008b) Large scale dynamic simulation of plate-like particle suspensions. Part II: Brownian simulation. J Rheol 52:37CrossRefGoogle Scholar
- Moan M, Aubry T, Bossard F (2003) Nonlinear behavior of very concentrated suspensions of plate-like kaolin particles in shear flow. J Rheol 47:1493CrossRefGoogle Scholar
- Morris J (2009) A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheol Acta 48:909CrossRefGoogle Scholar
- Mulchrone KF, Grogan S, De P (2005) The relationship between magmatic tiling, fluid flow and crystal fraction. J Struct Geol 27:179CrossRefGoogle Scholar
- Parsi F, Gadala-Maria F (1987) Fore-and aft symmetry in a concentrated suspension of solid spheres. J Rheol 31:725CrossRefGoogle Scholar
- Qi D, Luo L (2002) Transitions in rotations of a nonspherical particle in a three dimensional moderate Reynolds number Couette flow. Phys Fluids 14:4440CrossRefGoogle Scholar
- Rampall I, Smart JR, Leighton DT (1997) The influence of roughness on the particle-pair distribution function of dilute suspensions of non-colloidal spheres in simple shear flow. J Fluid Mech 399:1CrossRefGoogle Scholar
- Ramsay JDF, Lindner P (1993) Small-angle neutron scattering investigations of the structure of thixotropic dispersions of smectite clay colloids. J Chem Soc. Faraday Trans 89:4207CrossRefGoogle Scholar
- Saar MO, Manga M, Cashman KV, Fremouw S (2001) Numerical models of the onset of yield strength in crystal-melt suspensions. Earth Planet Sci Lett 187:367CrossRefGoogle Scholar
- Smith JV (1998) Interpretation of domainal groundmass textures in basalt lavas of the southern Lamington Volcanics, eastern Australia. J Geophys Res 103:27383. doi: 10.1029/97jb03109 CrossRefGoogle Scholar
- Tabatabaian M, Cox RG (1991) Effect of contact forces on sedimenting spheres in Stokes flows. Int J Multiph Flow 17:395CrossRefGoogle Scholar
- Tordesillas A, Zhang J, Behringer R (2009) Buckling force chains in dense granular assemblies: physical and numerical experiments. Geomech Geoeng 4:3. doi: 10.1080/17486020902767347 CrossRefGoogle Scholar
- Tsuji Y, Kawagushi T, Tanaka T (1993) Discrete particle simulation of two-dimensional fluidized bed. Power Technol 77:79CrossRefGoogle Scholar
- van Der Kooij FM, Kassapidou K, Lekkerkerker HNW (2000) Liquid crystal phase transitions in suspensions of polydisperse plate-like particles. Nature 406:868CrossRefGoogle Scholar
- van Der Kooij FM, Lekkerkerker HNW (2001) Liquid-crystal phase transitions in suspensions of plate-like particles. Philos Trans - Royal Soc, Math Phys Eng Sci 359:985. doi: 10.1098/rsta.2001.0813 CrossRefGoogle Scholar
- Veerman JA, Frenkel D (1992) Phase behavior of disklike hard-core mesogens. Phys Rev A 45:5632CrossRefGoogle Scholar
- Ventura G, De Rosa R, Colletta E, Mazzuoli R (1996) Deformation patterns in a high-viscosity lava flow inferred from the crystal preferred orientation and imbrication structures: an example from Salina (Aeolian Islands, southern Tyrrhenian Sea, Italy). B Volcanol 57:555Google Scholar
- Vermant J, Solomon MJ (2005) Flow-induced structure in colloidal suspensions. J Phys, Condens Matter, p 17. doi: 10.1088/0953-8984/17/4/R02
- Wada K, Senshu H, Matsui T (2006) Numerical simulation of impact cratering on granular material. Icarus 180:528CrossRefGoogle Scholar
- Wang S, Guo S, Gao J, Lan X, Dong Q, Li X (2012) Simulation of flow behavior of liquid and particles in a liquid–solid fluidized bed. Powder Technol 224:365CrossRefGoogle Scholar
- Wen CY, Yu YH (1966) Mechanics of Fluidization. Chem Engng Prog Symp Ser 62:100Google Scholar
- Willis DG (1977) A kinematic model of preferred orientation. Geol Soc Am Bull 88:883CrossRefGoogle Scholar
- Yamamoto S, Matsuoka T (1997) Dynamic simulation of a platelike particle dispersed system. J Chem Phys 107:3300CrossRefGoogle Scholar
- Zhang W, Noda R, Horio M (2005) Evaluation of lubrication force on colliding particles for DEM simulation of fluidized beds. Powder Technol 158:92CrossRefGoogle Scholar
- Zeng S, Kerns ET, Davis RH (1996) The nature of particle contacts in sedimentation. Phys Fluid 8:1389CrossRefGoogle Scholar