Experimental and theoretical studies of cross-stream migration of non-spherical particles in a quadratic flow of a viscoelastic fluid

Abstract

We experimentally investigate the cross-stream migration of spherical, prolate, and oblate particles in a circular tube flow of a weakly viscoelastic fluid (De = O(10⁻²)) with negligible inertia (Re ≈ 0). From our previous theoretical studies, we developed mathematical models based on a second order fluid (i.e., retarded expansion for De ≪ 1) to characterize the migration trajectory of the particles in the absence of wall effects. The theory shows that the particle migration speed is proportional to the length the particle spans in the shear gradient direction (L_sg), and furthermore quantifies how particle shape alters the migration timescale. For particles with identical volume, spherical particles show the fastest migration speed among all the particles. The distinctive orientation behavior of prolate and oblate spheroids leads to a faster migration speed for an oblate particle compared to a prolate particle of the same aspect ratio. In this work, we verify our theory with microfluidic flow experiments using a model suspension of polystyrene (PS) micro-particles in a density-matched polyvinylpyrrolidone (PVP) solution (a Boger fluid). The experimental results show good qualitative and quantitative agreement with the theoretically predicted particle migration speed, indicating that the theory is able to provide reasonable predictions for real microfluidic systems.