Despite great developments in inertial microfluidics, there is still a lack of knowledge to precisely define the particles' behavior in the microchannels. In the present study, as a prerequisite to experimental studies, numerical simulations have been used to study the capture efficiency of target particles in the contraction-expansion microchannel, aiming to provide an estimation of the conditions at which the channel performs best. Fluid analysis based on Navier-Stokes equations is conducted using the finite element method to determine the streamlines and vortices. The highest capture efficiency for 10, 15, and 19-micron particles occurs when the center of the vortex is approximately in the middle of the wide section (at the flow rate of 0.35 ml/ min). In addition to investigating the effect of particle diameter and input flow rate, the effect of channel geometry parameters (channel height and initial length of the channel) on particle trapping has also been studied. Also, to consider great interest in separating different-sized bioparticles from a sample, a three-stage platform has been designed to separate four types of bone marrow cells and evaluate the possibility of using contraction-expansion channels in this application.