A phase-field model for the Hele-Shaw flow of non-Newtonian fluids isdeveloped. It extends a previous model for Newtonian fluids to a wide range ofshear-dependent fluids. The model is applied to perform simulations of viscousfingering in shear- thinning fluids, and it is found to be capable ofdescribing the complete crossover from the Newtonian regime at low shear rateto the strongly shear-thinning regime at high shear rate. The width selectionof a single steady-state finger is studied in detail for a 2-plateauxshear-thinning law (Carreau law) in both its weakly and strongly shear-thinninglimits, and the results are related to previous analyses. In the stronglyshear-thinning regime a rescaling is found for power-law (Ostwald-de-Waehle)fluids that allows for a direct comparison between simulations and experimentswithout any adjustable parameters, and good agreement is obtained.
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