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A local power-law approximation to a smooth viscosity curve with application to flow in conduits and coating dies



Coating dies distribute liquid into a uniform layer for coating onto a moving substrate. A die comprises one or two cavities spanning the coating width and adjoining narrow slots of much higher resistance to flow. In modeling coating dies, the flows in the slots and cavities are often approximated as one-dimensional to achieve a fully geometrically parameterized model of low computational load suitable for optimizing design for multiple liquids and flow rates. The power-law model is mathematically efficient for one-dimensional flows of shear-thinning liquids but does not include limiting viscosities at low and high shear rates that are frequently present. In previous work, the truncated power-law model, which is terminated at the limiting Newtonian viscosities, was used to alleviate this shortcoming without sacrificing the mathematical advantages. In this work, the Carreau–Yasuda model replaces the truncated power-law model as an improvement. For flows in slots and cavities, the Carreau–Yasuda model can be approximated accurately by a local power-law model with little increase in computational load over the truncated power-law model. In the transition regions of the Carreau–Yasuda model between Newtonian and power-law behavior, the local power-law model gives more accurate results than the truncated power-law model. POLYM. ENG. SCI., 54:2301–2309, 2014. © 2013 Society of Plastics Engineers