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.

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.

We demonstrate the possibility to achieve 3D particle focusing in a straight microchannel with a square cross-section by exploiting purely viscoelastic effects. Experiments are carried out by considering an elastic, constant-viscosity aqueous solution of PVP (polyvinylpyrrolidone) as the suspending liquid. Several flow rates and two channel dimensions (with a fixed particle size to channel dimension ratio) are investigated. A novel technique combining particle tracking measurements and numerical simulations is used to reconstruct the position of the flowing particles over the channel cross-section. The results show that, for all the investigated experimental conditions, particles migrate towards the channel centerline. Flow-focusing is enhanced by higher flow rates. The measured particle fractions can be rescaled according to a single dimensionless parameter, as already reported in the literature for the case of cylindrical channels. The so-obtained master curve can be used as a guide to predict the required focusing length. The effect of the entrance on the focusing channel length is also addressed. Finally, analogies and discrepancies with similar previous works are discussed.

Particles suspended in non-Newtonian liquids flowing in channels may migrate transversally to the main flow direction as a result of normal stress gradients. Viscoelasticity-induced migration has proven to be an efficient mechanism to promote 3D flow-focusing in cylindrical microchannels, avoiding the need for complex and expensive apparati. In this work, we demonstrate the existence of a single dimensionless number (Θ) that governs the migration dynamics of particles in viscoelastic liquids flowing in micropipes at low Deborah numbers (Deborah number is the ratio of fluid and flow characteristic times). The definition of Θ in terms of the relevant fluid, flow and geometrical quantities is obtained by generalizing the particle migration velocity expression given in previous asymptotic analytical theories through numerical simulations. An extensive experimental investigation quantitatively confirms the novel predictions: the experimental particle distributions along the channel axial direction collapse on a single curve when rescaled in terms of the proposed dimensionless number. The results reported in this work give a simple and general way to define the flow-focusing conditions promoted by viscoelastic effects.

A novel method to estimate the relaxation time of viscoelastic fluids, down to milliseconds, is here proposed.