Numerical investigation of dilute suspensions of rigid rods in power-law fluids

Polymer melts filled with rod-like particles like glass and carbon fibers have high practical importance. Here we numerically investigate the properties of power-law fluids filled with rigid rods of different aspect ratios. For that we compute the rheological coefficients of the transversely isotropic fluid (TIF) equation and compare our results with analytical models, specifically with the model of Souloumiac and Vincent (1998). Here we found, that the additional orientation dependence predicted by the model for the nonlinear regime is too strong and overpredicts our numerical results. The rheological coefficient A in the TIF equation depends on the thinning exponent of the power-law model and decreases strongly with increasing nonlinearity. In the Newtonian case we found that Batchelor (1970, 1971) considerably underpredicts our numerical results. Comparing our current data with previous results for spheroids we found, that there is no similarity between the rheological coefficients for these particles at large aspect ratios. We further analyze the angular and translational velocities of the particles. We found that there are negligible differences in the angular velocities between the Newtonian and power-law matrix fluids, especially for large aspect ratios. The translational velocities are exactly the same for the Newtonian and power-law fluids.