Rheology of suspensions of small fibres in turbulent channel flow. Part 1: Simple steady flows

A stochastic simulation (Monte-Carlo-) method for the dynamics and rheological behaviour of small Brownian axisymmetric particles or fibres in a Newtonian solvent is tested and verified. The stress field due to the presence of the particles in a sheared or strained flow field is related to the conformation of the particles via the second and fourth moments of the conformation distribution function and material coefficients arising from rheological theory. The moments of the distribution function are computed solving Jeffery’s equation supplemented with a stochastic term which corresponds to the rotational diffusivity due to Brownian motion. Results are presented and verified against analytical or experimental results for the following configuration. The evolution of the moments of an ensemble of non-Brownian particles in simple shear flow in compared with the analytical solution of Okagawa et al. (1973). The influence of Brownian motion on the response of a dilute suspension of spheroids to sudden shearing is compared with experimentally obtained results for the degree of alignment and orientation angle by Frattini and Fuller (1986). The rheological results of Brenner (1974) are used to verify the presented numerical scheme for axisymmetric and plane extensional flow as well as for simple shear flow.