Fig. 6: Elasto-inertial focusing mechanisms and recent advances in modeling particle migration in non-Newtonian fluids.

a Schematic of the forces and equilibrium position in inertial only, elasticity dominant, and Elasto-inertial regimes; Reproduced from ref. ⁸, licensed under CC BY 4.0. b A Complex channel design was proposed through DNS simulations and a particle tracer solver using the Oldroyd-B fluid. Numerical results agree with experimental observations for Yeast cells; Reproduced with permission from ref. ²⁷. Copyright © AIP Publishing. c Schematic of the effects of shear-thinning properties near the wall for 7.32 µm particles proposed by DNS simulations using FEM with Giesekus fluid. Reproduced from ref. ²⁶, licensed under CC BY 4.0. d LBM was used to study spheroid particles migration in power-law fluids. (i) Schematic of rotational modes of tumbling (TU) and logrolling (LR) for a prolate and an oblate particle, respectively. (ii) Trajectories of a prolate in the channel cross-section of shear-thinning fluid. (iii) The final rate-of-strain tensor of an oblate spheroid in the channel cross-section of shear-thickening fluid; Reproduced with permission from ref. ¹¹¹, Copyright © 2023, Elsevier. e FEM with a particle tracer model was used to simulate inertial and viscoelastic particle migration in a microchannel with asymmetrical triangular expansions. Particles are collected from the top and the middle outlets, respectively. Reproduced from ref. ¹¹⁸, licensed under CC BY 4.0. f Flow field simulations using FEM showing magnitude and direction of secondary flow in the cross-section of a spiral channel. (i) Asymmetry of the secondary flow is due to the combined effects of the Dean flow and the second normal stress difference (N₂). (ii) Results are used to explain the elasto-inertial focusing mechanics in spiral channels. In this study, DNS simulations failed to converge due to the high Wi number problem. Reproduced from ref. ¹⁵⁷, licensed under CC BY 4.0