We perform 3D numerical simulations, heuristic modeling and microfluidic experiments to demonstrate, for the first time, the presence of a bistability scenario for transversal migration of particles suspended in a viscoelastic liquid flowing in a pipe. Our results show that particle migration, either at the centerline or at the wall, can be controlled by the rheological properties of the suspending liquid and by the relative dimensions of the particle and tube. Proper selection of these parameters can promote strict aligning of particles on a line, i.e., 3-D focusing. Simple design rules are given to rationally control particle focusing under flow in micropipes.

The fast growth of microfluidic applications based on complex fluids is a result of the unique fluid dynamics of these systems, enabling the creation of devices for health care or biological and chemical analysis. Microchannels designed to focus, concentrate, or separate particles suspended in viscoelastic liquids are becoming common. The key fluid dynamical issue on which such devices work is viscoelasticity-induced lateral migration. This phenomenon was discovered in the 1960s in macroscopic channels and has received great attention within the microfluidic community in the past decade. This review presents the current understanding, both from experiments and theoretical analysis, of viscoelasticity-driven cross-flow migration. Examples of promising microfluidic applications show the unprecedented capabilities offered by such technology based on geometrically simple microchannels and rheologically complex liquids

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