Relationship between particle focusing and dimensionless numbers in elasto-inertial focusing

Abstract

We performed particle focusing in viscoelastic fluids in a straight square microchannel based on elasto-inertial focusing. Probability distribution functions (PDFs) were obtained at various flow rates (40–320 μl/h) for a broad range of medium viscoelasticity (PEO solutions) from a dilute regime (0.01–0.2 wt%) to a semi-dilute regime (0.3–1.0 wt%). To evaluate focusing efficiency, PDF values at the centerline of the microchannel were plotted as a function of three dimensionless numbers: Reynolds number (Re), Weissenberg number (Wi), and elasticity number (El). Relaxation times were carefully calculated by using two different methods for each regime of medium to calculate Wi accurately. As a result, PDF at the centerline as a function of Re and El did not display any scaling tendency, but a single master curve was obtained in the plot of PDF at the centerline as a function of Wi, indicating that Wi is a more suitable parameter for manipulating elasto-inertial focusing than Re or El. In the plot of PDF versus Wi, particle focusing could be divided into two regimes at Wi = 3.16, where maximum PDF was observed. In the first regime (Wi 3.16), particle focusing was no greater, but scattering increased with increasing Wi due to the shear thinning effect of suspending medium.