Nonlinear flow affects hydrodynamic forces and neutrophil adhesion rates in cone-plate viscometers

We present a theoretical and experimental analysis of the effects of nonlinear flow in a cone-plate viscometer. The analysis predicts that flow in the viscometer is a function of two parameters, the Reynolds number and the cone angle. Nonlinear flow occurs at high shear rates and causes spatial variations in wall shear stress, collision frequency, interparticle forces and attachment times within the viscometer. We examined the effect of these features on cellular adhesion kinetics. Based on recent data (Taylor, A. D., S. Neelamegham, J. D. Hellums, et al. 1996. Biophys. J. 71:3488-3500), we modeled neutrophil homotypic aggregation as a process that is integrin-limited at low shear and selectin-limited at high shear. Our calculations suggest that selectin and integrin on-rates lie in the order of 10^-2-10^-4/s. They also indicate that secondary flow causes positional variations in adhesion efficiency in the viscometer, and that the overall efficiency is dependent not only on the shear rate, but also the sample volume and the cone angle. Experiments performed with isolated neutrophils confirmed these predictions. In these experiments, enhancing secondary flow by increasing the sample volume from 100 to 1000 μl at 1500/s for a 2° cone caused up to an ∼45% drop in adhesion efficiency. Our results suggest that secondary flow may significantly influence cellular aggregation, platelet activation, and endothelial cell mechanotransduction measurements made in the viscometer over the range of conditions applied in typical biological studies.