Dynamics of viscoelastic fluid filaments in microfluidic devices

Abstract

The effects of fluid elasticity and channel dimension on polymeric droplet formation in the presence of a flowing continuous Newtonian phase are investigated systematically by using different molecular weight (MW) poly(ethylene oxide) (PEO) solutions and varying microchannel dimensions with constant orifice width (w) to depth (h) ratio (w∕h=1∕2) and w=25μm, 50μm, 100μm, and 1mm. The flow rate is varied so that the mean shear rate is practically identical for all cases considered. Relevant times scales include inertia-capillary Rayleigh time τR=(Rmax3ρ∕σ)1∕2, viscocapillary Tomotika time τT=η0Rmax∕σ, and the polymer relaxation time λ, where ρ is the fluid density of the dispersed phase, σ is the interfacial tension, η0 is the zero shear viscosity of the dispersed polymer phase, and Rmax is the maximum filament radius. Dimensionless numbers include the elasticity number E=λν∕Rmax2, elastocapillary number Ec=λ∕τT, and Deborah number, De=λ∕τR, where ν=η0∕ρ is the kinematic shear viscosity of the fluids. Experiments show that higher MW Boger fluids possessing longer relaxation times and larger extensional viscosities exhibit longer thread lengths and longer pinch-off times (tp). The polymer filament dynamics are controlled primarily by an elastocapillary mechanism with increasing elasticity effect at smaller length scales (larger E and Ec). However, with weaker elastic effects (i.e., larger w and lower MW), pinch-off is initiated by inertia-capillary mechanisms, followed by an elastocapillary regime. A high degree of correlation exists between the dimensionless pinch-off times and the elasticity numbers. We also observe that higher elasticity number E yields smaller effective λ. Based on the estimates of polymer scission probabilities predicted by Brownian dynamics simulations for uniaxial extensional flows, polymer chain scission is likely to occur for ultrasmall orifices and high MW fluids, yielding smaller λ. Finally, the inhibition of bead-on-a-string formation is observed only for flows with large Deborah number (De⪢1).