Modeling the shear-induced migration of rigid and deformable particles in a Newtonian suspending fluid

Shear-induced migration is vital to understanding the mechanisms associated with several critical applications. Particles tend to migrate from areas of high stress to low-stress areas. In this work, we develop a constitutive rheological model that considers deformable particles' migration due to gradients in viscosity, shear rate, and concentration in cylindrical Couette and tube Poiseuille flows by extending the diffusive flux model of Phillips et al. “A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration,” Phys. Fluids 4(1), 30–40 (1992) which considers rigid spherical particles in a Newtonian suspending fluid, to handle deformable particles. The new model demonstrates that particle deformability plays a crucial role in migration. In a tube Poiseuille flow, we note a greater migration of deformable particles toward the centerline and a centerline velocity increase relative to rigid ones; similarly, in a cylindrical Couette flow, there is an increase in the velocity, particularly in the center region between the two cylinders, and an increased migration of deformable particles toward the outer (stationary) cylinder. Our modification of the model of Phillips et al. “A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration,” Phys. Fluids 4(1), 30–40 (1992) for deformable particles agrees with experimental data and dissipative particle dynamics simulations for blood suspensions from the literature. The use of the revised constitutive model in numerical simulations of more complicated geometries, such as bifurcations or T-shaped microchannels, will enrich our understanding of the mechanisms associated with the flow of deformable particles in many significant technological applications.