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

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 increased rapidly with increasing Wi. However, in the second regime (Wi > 3.16), particle focusing was no greater, but scattering increased with increasing Wi due to the shear thinning effect of suspending medium.