Time-resolved rheometry of coarsening foams using three-dimensionally printed fractal vanes

Aqueous foams are useful in several applications, especially to reduce liquid loading in the oil and gas industry. The rheology of these foams evolves rapidly, and suitable constitutive models are required to describe the resulting multiphase flow. We describe a new experimental setup for advanced rheometry involving 4-arm and 12-arm vane-in-textured-cup toolsets. The cup was designed to provide in situ foaming to minimize injection times and flow-history artifacts before measurement, while the 12-arm vane was selected to eliminate slip and generate a homogeneous stress field in a weak foam. Using these tools, we measure the decay of linear viscoelasticity and yield stress and link the rheological evolution to optical measurements of the bubble size distribution. Time-resolved rheological measurements of the full flow curve of an aging foam are performed and used to construct a rheological master curve. Measurements of the transient linear viscoelastic response and observations of the bubble size distribution show that foams, after an initial induction period, experience an increase in the Sauter mean bubble radius that scales as t1/2. Using the well-known Princen and Kiss model as a framework, we define a single unique time-dependent shift factor that varies with the Sauter mean bubble radius and enables us to use the rheological master curve to predict the temporal evolution of the foam’s elastic and steady-state viscoplastic properties.