Pipe rheology of wet aqueous application foams

Foam application of chemicals to the wet web is currently being developed for the paper and board industry. An important part of this work is to understand the rheology of the used application foams. Polyvinyl alcohol (PVOH) is widely used as a strength additive in paper and board, and it was the main surfactant in this study. The PVOH foam density varied between 100 kg/m3 and 300 kg/m3 and the dosage of PVOH varied between 0.5% to 6%. The foam viscosity and slip flow were determined with a pipe rheometer using three pipe diameters. The slip velocity was quantified by recording the foam motion in the vicinity of the wall of an acrylic pipe with a high-speed video camera. A measurement setup was also built for measuring the slip flow indirectly in opaque pipes. General formulas for the foam viscosity and slip flow, based on several physical quantities describing both the foam and the base liquid, were obtained using dimensional analysis. Specifically, dimensionless shear stress and dimensionless wall shear stress were found to be proportional to certain powers of the capillary number and slip capillary number, respectively. The contribution of the slip flow to the total flow rate was significant, especially with lower flow rates when most of the volumetric flow was due to the slip. In the literature, many papers have suggested that there is no slip flow in steel pipes. Our results suggest that this is due to the high pipe roughness used in those works. In our measurements, the slip velocity of a smooth-walled steel pipe was equal to the slip in an acrylic pipe. The obtained viscosity and slip models form a solid basis for developing and running various industrial processes including foam application processes. For new foam recipes, quite a small number of rheological measurements are needed to determine the model parameters.