A Study of the Translational and Rotational Velocities of a Cylinder Slipping Down a Channel at Low Reynolds Number Conditions
An investigation into the behaviour of a dense cylinder rolling down a smooth inclined narrow channel was conducted at highly laminar flow conditions to simulate particle rotation behaviour at a microfluidic scale. The main variables were channel incline [15°<θ<75°] and cylinder diameter to channel height ratio [22%, 80%, 82%]. The experiment was undertaken in a rectangular Perspex channel [100 x 11 x 400 mm] filled with UCON 75-H-90 at a typical viscosity of 47.5 Pa.s (19°C). The cylinders were found to start slipping at 8.5° elevation, suggesting a static friction factor of 0.05. Relatively little rolling was observed compared to slipping at angles above 15°.
Cylinders with a small diameter to channel height ratio maintained frictional rolling throughout the range of channel angles, whereas the large diameter to channel height ratio cylinders stopped rotating at 45-60°, and rolled counter to contact friction at steeper angles. The results suggested that the hydrodynamic torque on the cylinders increased proportionally with channel angle and was amplified by decreasing the gap between the top wall and the cylinder in the channel.