Viscoelastic focusing has emerged as a promising method for label-free and passive manipulation of micro and nanoscale bioparticles. However, the design of microfluidic devices for viscoelastic particle focusing requires a thorough comprehensive understanding of the flow condition and operational parameters that lead to the desired behavior of microparticles. While recent advancements have been made, viscoelastic focusing is not fully understood, particularly in straight microchannels with rectangular cross sections. In this work, we delve into inertial, elastic, and viscoelastic focusing of biological cells in rectangular cross-section microchannels. By systematically varying degrees of fluid elasticity and inertia, we investigate the underlying mechanisms behind cell focusing. Our approach involves injecting cells into devices with a fixed, non-unity aspect ratio and capturing their images from two orientations, enabling the extrapolation of cross-sectional equilibrium positions from two dimensional (2D) projections. We characterized the changes in hydrodynamic focusing behaviors of cells based on factors, such as cell size, flow rate, and fluid characteristics. These findings provide insights into the flow characteristics driving changes in equilibrium positions. Furthermore, they indicate that viscoelastic focusing can enhance the detection accuracy in flow cytometry and the sorting resolution for size-based particle sorting applications. By contributing to the advancement of understanding viscoelastic focusing in rectangular microchannels, this work provides valuable insight and design guidelines for the development of devices that harness viscoelastic focusing. The knowledge gained from this study can aid in the advancement of viscoelastic particle manipulation technique and their application in various fields.
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