Entrance flow of unfoamed and foamed Herschel–Bulkley fluids

Abstract

The present study investigates extrusion processing of unfoamed and foamed cocoa butter (CB) crystal-melt suspensions (CMSs) with varying crystal volume fraction Φ SFC. Capillary rheometry derived flow curves were fitted with the Herschel-Bulkley-Papanastasiou (HBP) model, and the derived yield stress to wall shear stress ratio τ 0 =τ w of CB CMSs was compared for the various Φ SFC. Foamed CB CMSs behaved fluidlike for Φ SFC 11:9% and according to a brittle porous solid for Φ SFC. 11:9%. The dimensionless entrance pressure loss n en =α as a function of dimensionless shear stress τ * was higher for foamed compared to unfoamed CB CMSs at Φ SFC 11:9% and lower for foamed compared to unfoamed CB CMSs at Φ SFC. 11:9%. The Φ SFC dependent difference in n en =α was attributed to the crystal confinement in the die entrance flow, which is increased in the case of elastic gas bubble deformation and decreased in the case of plastic gas pore collapse. The computational fluid dynamics simulated flow of unfoamed and foamed CB CMSs through an abrupt circular 20:1 contraction with the HBP model was compared with the experimental results from quantitative entrance flow visualization (QEFV). Furthermore, the QEFV derived half center incidence angle θ as well as the entrance flow shear and elongational rates _ γ ef and _ ϵ ef were derived and used to establish a model predicting the Bagley entrance pressure loss ΔP Bag and calculate an entrance flow characteristic shear and elongational viscosities η s ef and η e ef .