Red blood cells (RBCs) in microchannels has tendency to undergo axial migration due to the parabolic velocity profile, which results in a high shear stress around wall that forces the RBC to move towards the centre induced by the tank treading motion of the RBC membrane. As a result there is a formation of a cell free layer (CFL) with extremely low concentration of cells. Based on this phenomenon, several works have proposed microfluidic designs to separate the suspending physiological fluid from whole in vitro blood. This study aims to characterize the CFL in hyperbolic-shaped microchannels to separate RBCs from plasma. For this purpose, we have investigated the effect of hyperbolic contractions on the CFL by using not only different Hencky strains but also varying the series of contractions. The results show that the hyperbolic contractions with a Hencky strain of 3 and higher, substantially increase the CFL downstream of the contraction region in contrast with the microchannels with a Hencky strain of 2, where the effect is insignificant. Although, the highest CFL thickness occur at microchannels with a Hencky strain of 3.6 and 4.2 the experiments have also shown that cells blockage are more likely to occur at this kind of microchannels. Hence, the most appropriate hyperbolic-shaped microchannels to separate RBCs from plasma is the one with a Hencky strain of 3.