Figure 4.

Dean vortex shape approximation and calculated average Dean velocities in a curved microchannel with R = 2 cm and cross section area of 150 µm × 150 µm. Dean vortices were assumed to follow (a) an elliptical path for δ < 0.008 ($\delta =D/2R$) and (b) a half-elliptical half-circular path for δ > 0.008¹⁰. (c) The switching lengths obtained experimentally and the approximated average lateral travel distances were used to calculate the average Dean velocities (V_De) at different axial velocities in the abovementioned device. The solid line in (c) shows a power function (V_De = aDe^b) fitted over the experimental data points with constants a = 0.072 and b = 2 (R² = 0.98). The dashed line in (c) shows the Ookawara’s³⁰ equation for Dean velocity (mm s⁻¹) with a = 0.18 and b = 1.63 (R² = 0.71).