Effect of secondary flow on biological experiments in the cone-plate viscometer: Methods for estimating collision frequency, wall shear stress and inter-particle interactions in non-linear flow

We present a theoretical analysis of fluid flow and particle interactions i n the cone-plate viscometer under conditions typically applied in biologica l studies. The analysis demonstrates that at higher shear rates, besides li near primary flow in the rotational direction, prominent non-linear seconda ry flow causes additional fluid circulation in the radial direction. Two pa rameters, the cone angle and Reynolds number, characterize flow in the visc ometer over all ranges of shear rate. Our results indicate that secondary f low causes positional variations in: (i) the velocity gradient, (ii) the di rection and magnitude of the wall shear stress at the plate surface, (iii) inter-particle collision frequency, (iv) magnitude and periodicity of norma l and shear forces applied during particle-particle interactions, and (v) i nter-particle attachment times. Thus, secondary flow may significantly infl uence cellular aggregation, platelet activation and endothelial cell mechan otransduction measurements. Besides cone-plate viscometers, this analysis m ethodology can also be extended to other experimental systems with complex non-linear flows.