Investigation of power-law fluid flow through a two-dimensional microchannel based on a couple stress theory- calculation of characteristic length

The aim of this paper is the investigation of fully developed flow of Newtonian and non-Newtonian fluids in two-dimensional microchannel based on a completely consistent couple stress theory and the calculation of the length scale parameters of these fluids. Therefore, the analytical solutions of the velocity and flow rate are obtained for Newtonian and power law non-Newtonian fluids. Afterward, the characteristic material length of Newtonian water and non-Newtonian blood fluids are calculated using the obtained relations and experimental data. Comparing characteristic material length for water and blood can perceive that the characteristic length scale depends on the fluid type. The blood velocity profile is calculated based on the couple stress theory using the obtained length scale and compared with the results of classical Navier Stokes theory. These results show the difference between the obtained values of the couple stress and classical theories increases by increasing the flow rate. This increase in the difference means decreasing of precision of classical theory for investigating flow through a microchannel. Comparing the calculated and experimental velocity profiles for water shows a good agreement between theoretical and experimental results.