Extensional rheology of concentrated emulsions as probed by capillary breakup elongational rheometry (CaBER)

Elongational flow behavior of w/o emulsions has been investigated using a capillary breakup elongational rheometer (CaBER) equipped with an advanced image processing system allowing for precise assessment of the full filament shape. The transient neck diameter D(t), time evolution of the neck curvature κ(t), the region of deformation ldef and the filament lifetime tc are extracted in order to characterize non-uniform filament thinning. Effects of disperse volume fraction ϕ, droplet size dsv, and continuous phase viscosity ηc on the flow properties have been investigated. At a critical volume fraction ϕc, strong shear thinning, and an apparent shear yield stress τy,s occur and shear flow curves are well described by a Herschel–Bulkley model. In CaBER filaments exhibit sharp necking and tc as well as κmax = κ (t = tc) increase, whereas ldef decreases drastically with increasing ϕ. For ϕ < ϕc, D(t) data can be described by a power-law model based on a cylindrical filament approximation using the exponent n and consistency index k from shear experiments. For ϕ ≥ ϕc, D(t) data are fitted using a one-dimensional Herschel–Bulkley approach, but k and τy,s progressively deviate from shear results as ϕ increases. We attribute this to the failure of the cylindrical filament assumption. Filament lifetime is proportional to ηc at all ϕ. Above ϕc,κmax as well as tc/ηc scale linearly with τy,s. The Laplace pressure at the critical stretch ratio εc which is needed to induce capillary thinning can be identified as the elongational yield stress τy,e, if the experimental parameters are chosen such that the axial curvature of the filament profile can be neglected. This is a unique and robust method to determine this quantity for soft matter with τy < 1,000 Pa. For the emulsion series investigated here a ratio τy,e/τy,s = 2.8 ± 0.4 is found independent of ϕ. This result is captured by a generalized Herschel–Bulkley model including the third invariant of the strain-rate tensor proposed here for the first time, which implies that τy,e and τy,s are independent material parameters.