Numerical Simulation of the Effect of Rheological Parameters on Shear-Thinning Droplet Formation

Immiscible non-Newtonian-Newtonian fluid systems in microfluidics constitute an essential study as non-Newtonian fluids consistently met in medical and biological systems. Although a large number of experimental investigations have been reported in this area, attempts to develop predictive models appear to be limited. This paper is an attempt to incorporate a non-Newtonian stress model together with front-tracking scheme used in computational fluid dynamics. A conservative two-phase level set method (LSM) was applied for capturing the droplet breakup dynamics and relevant hydrodynamics of shear-thinning carboxymethylcellulose (CMC) droplets. Our droplets comprise of 0.02wt% to 1.2wt% CMC solutions in a Newtonian continuous fluids system (olive oil) employed in a T-shaped microfluidic cell. A Carreau-Yasuda viscosity model for shear-thinning CMC droplets has been implemented. This shear-dependent constitutive model fitted well to our steady state non-linear shear measurements for polymeric CMC solutions, with asymptotic viscosities at zero and infinite shear rates, and with different degrees of shear thinning (η₀/η_∞) in steady state. The particular focus of this study was to systematically undergo parametric studies on the influence of rheological parameters of the specified model such as zero (η₀) and infinite shear viscosity (η_∞), and relaxation time (λ) on the droplet formation processes. The level set simulation predicted that the droplet diameter increases with increasing η₀/η_∞. The effect of η₀/η_∞ has been found to have more prominent impact on droplet diameter for higher CMC concentrations. The variation in droplet diameter becomes less significant at the higher degrees of shear-thinning for all concentrations of CMC dispersed solutions. In the limit of zero shear-thinning effect, the droplet diameter increases when the dispersed phase viscosity decreases. Additionally, the effect of λ on the droplet diameter is also discussed. The reciprocal of the characteristic relaxation time (1/λ) corresponds to a critical shear rate that indicates the onset shear rate for shear-thinning. As λ increases, the numerical studies clearly reveal that the droplet diameter is increasing until it reaches a plateau for larger values of λ. The influence of λ leads to a more significant impact on droplet diameter for higher CMC concentration. These findings will ultimately help in understanding the sensitivity of rheological parameters to the microdroplet formation.