Turbulent incompressible microflow between rotating parallel plates

The paper focuses on modeling of turbulent flow in a rotating flat microchannel. Based on a linearized model of turbulence, an analytical solution of the two-dimensional problem for fully developed flow was obtained. With the help of a complex function, relations for two velocity components were derived in the form of the Kelvin functions. Validation of the analytical solution in comparison with the lattice Boltzmann model (LBM) technique demonstrated their good agreement except for the region close to the channel wall. Both analytical and numerical solutions were obtained for the first time for the given geometry. Effects of the dimensionless rotation parameter and the Knudsen number on flow structure were analyzed. It was shown how the velocity profiles deform with varying dimensionless rotation parameter and the Knudsen number. It was also demonstrated that higher rotation rates lead to an increase in hydraulic resistance, whereas an increase rate of slippage (Knudsen number) leads to a decrease in this resistance. For the first time, an analogy was revealed with radial outflow between parallel co-rotating disks including existence of the source region, Ekman-type layers on the channel wall and reverse flow near the centerline depending on the magnitude of the rotation parameter. For the limiting case of dominating rotation effects, expressions for the flow swirl parameter and tangent of the flow swirl angle on the wall were derived.