<div> <div> <div> <p>The motion of synthetic capsules and living cells in microchannels has been the subject of numerous studies in the last decade due to its significance in engineer- ing and biomedical applications. Cell sorting and separation are common processes that are used for various purposes such as separation of leukocytes from blood used in DNA sequencing. Isolation of rare cells in blood is needed for early diagnosis of lethal diseases such as cancer. Cell isolation and enrichment will also provide a better platform to biologists to study and analyze various properties of living cells. Thus, there is a high demand for developing techniques to precisely control trajectories of the cells and manipulate them in a desired manner. Microfluidic devices provide a platform to achieve aforementioned needs while overcoming challenges such as sample contamination, cost and complexity of the procedures. In many of these applications, the background fluid is non-Newtonian due to the presence of DNA and proteins, or polymers are added to control the trajectory of the cells. In this work, we first provide a fundamental study on the dynamics of a single deformable capsule in a viscoelastic matrix under a simple shear flow. Furthermore, we investigate the motion of a single cell and suspension of cells in microchannels. The effects of cell size, inertia, cell volume fraction, cell deformability and fluid elasticity are explored. Our findings on capsule motion in the viscoelastic medium suggest that the use of constant-viscosity viscoelastic fluid pushes the cells toward the channel centerline which can be used in microfluidic devices used for cell focusing such as cytometers. However, viscoelastic fluid with shear-thinning characteristics and drives the flowing cells toward the channel wall. Particle motion in viscoelastic matrix equilibrium positions of the particle in the microchannel for a wide range of inertial and elastic effects. These fundamental studies can provide insight on the role of rheological properties of the fluid that can be tuned to control the motion of the cells and particles for efficient design of microfluidic devices. </p> </div> </div> </div>