Study of semidilute fibre suspension rheology with lattice-Boltzmann method

A hybrid lattice-Boltzmann numerical simulation method is undertaken to study the rheology of non-colloidal, rigid fibres in sheared, semidilute Newtonian suspension. The viscosity and the first normal stress difference are calculated with the combined use of numerical fibre orientation information and a corrected form of the slender body theory of Batchelor (J Fluid Mech Digit Arch 46(4):813–829, 1971). The corrections make the theory applicable in semidilute suspension flow (Shaqfeh and Fredrickson, Phys Fluids A: Fluid Dyn 2(1):7–24, 1990) with fibres of finite aspect ratio. The corrected theory within its framework, based on spacing among fibres in semidilute suspension, only considers hydrodynamic interactions among fibres and inferences that the effect of actual fibre–fibre mechanical contacts on rheological properties of such suspension systems remains inconsequential. To investigate this issue, the rheological properties of semidilute suspension were calculated directly from the numerical simulation. This approach accounted for both hydrodynamic and mechanical interactions among fibres. This direct measurement proved that the mechanical interactions increase both the relative shear viscosity and the first normal stress difference in the semidilute suspension to values which are larger than permissible within the framework of Batchelor’s theory.