Confined tube flow of low viscosity emulsions: Effect of matrix elasticity

Abstract

This study is addressed to the effect of the elasticity of the continuous phase on confined flow of low viscosity emulsions, a topic of interest in several applications. A Newtonian silicone oil was used as the dispersed phase, while three different water-based fluids, a Newtonian and two Boger fluids, were used as the continuous phase. All the fluids have the same viscosity (ca. 0.05 Pa s). Emulsions were prepared by feeding the two phases to a T-junction followed by a membrane. When the continuous phase was a Boger fluid, the average drop size of the so obtained emulsions was higher (as compared to the Newtonian continuous phase) and a bimodal distribution was observed. Such lower mixing efficiency for a Boger continuous phase is in line with the result for an isolated droplet that breakup is hindered by matrix elasticity. High-speed microscopy visualization of the emulsions flowing through a microcapillary allowed one to determine the velocity profiles and the droplet spatial distribution as a function of the shear rate. In all the experiments, the formation of a droplet-rich core and of a droplet-devoid wall region Δ was observed, with a significant enhancement when the continuous phase was a Boger fluid (where values of Δ as high as 37% of capillary radius were found). So, confinement here refers to the fact that, although the droplets are much smaller than capillary radius, the droplet-free layer takes up a significant fraction of the capillary radius. The observed nonhomogeneous droplet spatial distribution was not due to a transient entry effect, as shown by imaging the emulsions flow at different sections from the capillary inlet, but can be explained by a balance between collision-induced drop diffusion and wall lift force. The former acts to homogenize droplet spatial distribution, while the latter tends to push droplets away from the wall and is enhanced by matrix elasticity. These effects lead to the accumulation of larger droplets around the center of the channel, while smaller droplets are pushed toward the periphery. The velocity profiles for the Boger continuous phase were flat in the droplet-rich core, thus suggesting that the confined emulsions behave as a Bingham fluid. The corresponding yield stress was determined by data fitting of the velocity profiles and rather large values were so obtained. This result is consistent with the high values, close to the maximum packing for spherical particles in binary dispersions, of the droplet volume fraction in the core, which were estimated by measuring the thickness of the droplet-devoid annular region as a function of the applied flow rate and making a volume balance. Overall, the results of this work bear strong analogies with the confined flow of other concentrated suspensions of deformable particles, such as red blood cells in microcirculation, where the formation of a cell-free layer at the wall, which is referred to as margination, has important pathophysiological implications. These findings suggest that low viscosity emulsions with an elastic matrix under confined flow can be used as a tunable model system of biomedical relevance.