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 kappa(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 phi, droplet size d (sv) , and continuous phase viscosity eta (c) on the flow properties have been investigated. At a critical volume fraction phi(c) , strong shear thinning, and an apparent shear yield stress tau (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 kappa (max) = kappa (t = t (c) ) increase, whereas l (def) decreases drastically with increasing phi. For phi < phi(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 phi >= phi(c) , D(t) data are fitted using a one-dimensional Herschel-Bulkley approach, but k and tau (y,s) progressively deviate from shear results as phi increases. We attribute this to the failure of the cylindrical filament assumption. Filament lifetime is proportional to eta (c) at all phi. Above phi(c,) kappa (max) as well as t (c) /eta (c) scale linearly with tau (y,s) . The Laplace pressure at the critical stretch ratio epsilon (c) which is needed to induce capillary thinning can be identified as the elongational yield stress tau (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 tau (y) < 1,000 Pa. For the emulsion series investigated here a ratio tau (y,e) /tau (y,s) = 2.8 +/- 0.4 is found independent of phi. 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 tau (y,e) and tau (y,s) are independent material parameters.