Experimental footprints of a water-rich depletion layer in the Herschel–Bulkley pipe flow of solidifying polyelectrolytes

Abstract

A fundamental understanding of the transition from fluid-like to gel-like behavior is critical for a range of applications including personal care, pharmaceuticals, food products, batteries, painting, biomaterials, and concrete. The pipe flow behavior of a Herschel–Bulkley fluid is examined by a combination of rheology, ultrasound imaging velocimetry, and pressure measurements together with modeling. The system is a solution of 0.50 wt. % polyelectrolytes of sulfated polysaccharides in water that solidifies on cooling. Fluids with different ionic strengths were pumped at various rates from a reservoir at 80 °C into a pipe submerged in a bath maintained at 20 °C. The fluid velocity, pressure drop ΔP, and temperature were monitored. The same quantities were extracted by solving continuity, energy, and momentum equations. Moreover, the modeling results demonstrate that the local pressure gradient along the pipe dPdx|x is related to the local yield stress near the pipe wall τywall|x, which explains the variations of dPdx|x along the pipe. Experimental results show much lower values for ΔP compared to those from modeling. This discrepancy is exacerbated at higher ionic strengths and smaller flow rates, where fluid shows a higher degree of solidification. The tabulated experimental ΔP data against the solidification onset length Lonset (where the fluid is cool enough to solidify) along with the ultrasound imaging velocimetry associate these discrepancies between experiments and models to a depletion layer of ∼1 μm, reflecting the lubrication effects caused by the water layer at the wall.