Numerical investigation of fluid flow in a chandler loop

The Chandler loop is an artificial circulatory platform for in vitro hemodynamic experiments. In most experiments, the working fluid is subjected to a strain rate field via rotation of the Chandler loop, which, in turn, induces biochemical responses of the suspended cells. For low rotation rates, the strain rate field can be approximated using laminar flow in a straight tube. However, as the rotation rate increases, the effect of the tube curvature causes significant deviation from the laminar straight tube approximation. In this manuscript, we investigate the flow and associated strain rate field of an incompressible Newtonian fluid in a Chandler loop as a function of the governing nondimensional parameters. Analytical estimates of the strain rate from a perturbation solution for pressure driven steady flow in a curved tube suggest that the strain rate should increase with Dean number, which is proportional to the tangential velocity of the rotating tube, and the radius to radius of curvature ratio of the loop. Parametrically varying the rotation rate, tube geometry, and fill ratio of the loop show that strain rate can actually decrease with Dean number. We show that this is due to the nonlinear relationship between the tube rotation rate and height difference between the two menisci in the rotating tube, which provides the driving pressure gradient. An alternative Dean number is presented to naturally incorporate the fill ratio and collapse the numerical data. Using this modified Dean number, we propose an empirical formula for predicting the average fluid strain rate magnitude that is valid over a much wider parameter range than the more restrictive straight tube-based prediction.