Nonlinear hydrodynamic theory for a dilute gas-solid suspension

A second-order hydrodynamic theory is proposed for a dilute gas-solid suspension within the framework of the inelastic Boltzmann equation. A distribution function based on 14-hydrodynamic fields is used to calculate the colisional source terms that are correct up-to the second-order in hydrodynamic fields. This theory is used to analyse the uniform shear flow of a gas-solid suspension, yielding results on the granular temperature, the shear viscosity and the two normal stress differences. The theoretical results are compared with the predictions of the anisotropic Maxwellian theory (Saha & Alam, 2017, J. Fluid Mech., vol. 833, 206-246) and the particle simulation data over a range of Stokes numbers varying from order one to its dry granular limit. The inclusion of the second order nonlinearity in the collisional source term is found to be responsible for the non-zero second normal stress difference.