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 in the cone-plate viscometer under conditions typically applied in biological studies. The analysis demonstrates that at higher shear rates, besides linear primary flow in the rotational direction, prominent non-linear secondary flow causes additional fluid circulation in the radial direction. Two parameters, the cone angle and Reynolds number, characterize flow in the viscometer over all ranges of shear rate. Our results indicate that secondary flow causes positional variations in: (i) the velocity gradient, (ii) the direction and magnitude of the wall shear stress at the plate surface, (iii) inter-particle collision frequency, (iv) magnitude and periodicity of normal and shear forces applied during particle-particle interactions, and (v) inter-particle attachment times. Thus, secondary flow may significantly influence cellular aggregation, platelet activation and endothelial cell mechanotransduction measurements. Besides cone-plate viscometers, this analysis methodology can also be extended to other experimental systems with complex non-linear flows.