Effect of droplet-phase elasticity on droplet behavior and morphology of immiscible blends

Abstract

The effect of dispersed-phase elasticity on droplet behavior and morphology of immiscible blends in simple shearing flow is investigated for blends of “Boger” fluids and high-molecular-weight polymer melt blends. For blends of “Boger” fluids consisting of polybutadiene (PBd) “Boger” fluids as droplet phase and poly(dimethyl siloxane) (PDMS) as matrix phase, the effect of dispersed-phase elasticity on steady state deformation and breakup of isolated droplets in simple shearing flow is investigated systematically for values of the dispersed-phase Weissenberg number (Wid) ranging up to around 3, where the Weissenberg number is defined as the ratio of the first normal stress difference to twice the shear stress at the imposed shear rate. The dependence on droplet elasticity of steady-state morphology for 10% or 20%- dispersed phase blends is also studied. The polybutadiene droplet phase is an elastic “Boger” fluid prepared by dissolving a high-molecular-weight polybutadiene into low-molecular-weight Newtonian polybutadiene. To isolate the contribution of droplet elasticity, all experiments were carried out on a fixed viscosity ratio of around unity, achieved by adjusting the temperature appropriately for each blend. When the droplet elasticity increases, the steady-state deformation of isolated droplets decreases for a given capillary number. The critical capillary number for breakup (Cacrit) increases linearly with the Weissenberg number of the droplet phase (Wid) up to a value of Wid of around unity. When Wid is greater than unity, Cacrit seems to approach an asymptotic value of 0.95 for high values of Wid. For 10% or 20%-dispersed phase blends, the steady-state capillary number (Cass) calculated from a volume-averaged droplet diameter is less than the Cacrit for isolated droplets for the same blend. Cass increases monotonically with the first normal stress difference of the droplet phase (Nid). For high-molecular-weight polymer melt blends consisting of polystyrene (PS) as a dispersed phases, and high density polyethylene (HDPE) as a matrix phase under the condition of both fluids have the same viscosity, the isolated viscoelastic droplets initially deform in the flow direction after startup of steady shear, but then begin reverting to a spherical shape, and, for the more elastic blend, eventually deform in the vorticity direction. With increasing capillary number, the droplet deforms increasingly along the vorticity direction, and above a critical capillary number Cacrit, breakup occurs when two ends of a drop situated on widely separated streamlines with significantly different velocities are displaced from each other under flow. The transition from alignment in the flow direction for Newtonian or slightly elastic droplets to alignment in the vorticity direction for highly elastic droplets can lead to large increases of the critical capillary number for droplet breakup, up to a factor of thirty greater than for Newtonian liquids. For concentrated high-molecular-weight polymer melt blends containing 20%-dispersed phase, the influence of elasticity of the blend constituent components on the steady-state size and size distribution of dispersed-phase droplets is investigated. The role played by the ratio of drop to matrix elasticity at a fixed viscosity ratio was investigated at which the viscosity ratios are roughly equal to three different values: 0.5, 1, and 2. The correlation between Cass and the elasticity contrast, defined as the ratio, Nlr = Nld/Nlm, of the first normal stress difference of dispersed (Nld) to that of matrix (Nlm) phase, is proposed. For the blend systems with viscosity ratio 0.5, 1 and 2, the values of Cass were found to monotonically increase with Nir and followed a power law with scaling exponents varying between 1.7 and 1.9.