Viscoelastic flow-focusing in microchannels: scaling properties of the particle radial distributions

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.