Understanding the Theory--Experiment Discrepancy in Pressure Drop of Dilute Polymer Solutions in Channel Flows

Abstract

For decades researchers have experimentally observed that the flow of dilute viscoelastic polymer solutions through contraction or contraction--expansion channels yields results at odds with theory and simulations. In particular, the experimentally reported pressure drops are larger than those of generalized Newtonian reference fluids with the same shear viscosity, while constitutive models, such as Oldroyd-B and FENE-P, predict smaller pressure drops under conditions of low Reynolds numbers and stable flow at small Weissenberg ($Wi$) or Deborah ($De$) numbers. This apparent contradiction between experiments and theory has been a long-standing puzzle in the field. Here, we characterize the properties of dilute viscoelastic polymer solutions and employ two distinct types of pressure-sensing systems, conventional recessed pressure taps and flush-mounted diaphragm sensors, to systematically measure pressure drops across channels of different geometrical configurations. These measurements yield qualitative agreement with theoretical predictions across all geometries if the largest relaxation time is adopted for the analysis of the flow. Our results indicate that the apparent discrepancies mentioned above can be attributed to improper interpretation of the measurements and to mismatches between experimental conditions and assumptions made in the theoretical and numerical studies, which include hole pressure effects, the choice of relaxation time of the fluid, and the presence of experimental flow instabilities. For quantitative improvements, our results suggest the use of continuum-level constitutive models containing more realistic microscopic features of polymer solutions.