Dimensionless analysis on inertial microfluidic particle migration across laminar streams from Newtonian to non-Newtonian fluid

Microscale sample separation based on inertial microfluidic particle migration across laminar streams from Newtonian to non-Newtonian fluid has many advantages including separation resolution, throughput, and simplicity. Precise control of operational conditions is highly required for the separation; however, no concrete theoretical investigation has been conducted. Here, we propose a dimensionless analysis on the inertial particle migration to determine the separation conditions. We adopted a co-flow of Newtonian and non-Newtonian fluids to utilize both inertial and elastic lift forces. Along with Reynolds, Weissenberg, and elastic numbers, we introduce a new dimensionless number composed of viscosity, particle diameter, and width of the Newtonian fluid stream to predict whether the particle migrates from Newtonian to non-Newtonian fluid stream. We experimentally validated the proposed analysis method using polystyrene microparticles with diameter of 2 and 3 μm in a co-flow of water and polyethylene oxide solution at varying concentration.