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460781 Computationally Generated Constitutive Models for Rheology of Frictional Non-Cohesive and Cohesive Particles in Gas-Solid Flows

*ad hoc*modifications to the kinetic theory [4-5] have been proposed to improve the accuracy in dense assemblies and to account for inter-particle friction. To account for inter-particle cohesion, several modifications to kinetic theory have been proposed [6-9].

In the present study, we perform CFD-DEM simulations for gas-fluidization of frictional, non-cohesive and cohesive particles in a periodic domain. By analyzing snapshots gathered from the simulation, quantities of interest in formulating a rheological model are determined. These results then guide refinement to the kinetic theory based stress model.

We first show that this approach, when applied to monodisperse non-cohesive particles, leads to results for pressure and shear viscosity that are consistent with the standard kinetic theory [1] coupled with the radial distribution function at contact from Chialvo & Sundaresan [4]. However, bulk viscosity is found to depend on whether the particle phase is in compression or dilation which is not accounted for in the kinetic theory.

For cohesive particles, it is found that inter-particle cohesion does not noticeably affect the particle phase stress except for at high solid volume fractions and low granular temperatures. This observation is consistent with the previous finding [10] based on simple shear simulations of cohesive particles.

This computational approach can be used to formulate simple rheological models for systems with size distribution, as well as particle-particle interactions due to liquid bridge or electrostatic interactions.

[1] C. K. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Chepurniy, “Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flowfield,” *J. Fluid Mech*. **140**, 223–256 (1984).

[2] D. Gidaspow, *Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions*. San Diego, CA, USA: Academic Press (1994).

[3] V. Garzo and J. W. Dufty, “Dense fluid transport for inelastic hard spheres”, *Phys. Rev. E* **59**, 5895–5911 (1999).

[4] S. Chialvo, S. Sundaresan, “A modified kinetic theory for frictional granular flows in dense and dilute regimes”, *Phys. Fluids* **25**, 070603 (2013).

[5] D Berzi, D. Vescovi, “Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows”, *Phys. Fluids* **27**, 013302 (2015).

[6] D. Gidaspow, L Huilin, “Equation of state and radial distribution functions of FCC particles in a CFB”, *AIChE J.* **44, **279-293 (1998).

[7] H. Kim, H. Arastoopour, “Extension of kinetic theory to cohesive particle flow”, *Powder Technol.* **122**, 83-94 (2002).

[8] M. Ye, M.A. Van Der Hoef, J.A.M. Kuipers, “From discrete particle model to a continuous model of Geldart A particles”, *Chem. Eng. Res. Des.* **83, **833–843 (2005).

[9] B. Van Wachem, S. Sasic, “Derivation, simulation and validation of a cohesive particle flow CFD model”, *AIChE J.*, **54, **9–19 (2008).

[10] Y. Gu, S. Chialvo, and S. Sundaresan. “Rheology of cohesive granular materials across multiple dense-flow regimes”, *Phys. Rev. E ***90**, 032206 (2014).

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