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 l _def and the filament lifetime t _c are extracted in order to characterize non-uniform filament thinning. Effects of disperse volume fraction ϕ, droplet size d _sv , and continuous phase viscosity η _c on the flow properties have been investigated. At a critical volume fraction ϕ _c , strong shear thinning, and an apparent shear yield stress τ _y,s occur and shear flow curves are well described by a Herschel–Bulkley model. In CaBER filaments exhibit sharp necking and t _c as well as κ _max  = κ (t = t _c ) increase, whereas l _def decreases drastically with increasing ϕ. For ϕ < ϕ _c , 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 ≥ ϕ _c , D(t) data are fitted using a one-dimensional Herschel–Bulkley approach, but k and τ _y,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 η _c at all ϕ. Above ϕ _c, κ _max as well as t _c /η _c scale linearly with τ _y,s. The Laplace pressure at the critical stretch ratio ε _c which is needed to induce capillary thinning can be identified as the elongational yield stress τ _y,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 τ _y  < 1,000 Pa. For the emulsion series investigated here a ratio τ _y,e/τ _y,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 τ _y,e and τ _y,s are independent material parameters.