Using hydrophobic surfaces is one of the efficient methods to preserve energy in fluid transfer systems. However, the studies have been concentrated on Newtonian fluids despite the wide applications of non-Newtonian fluids in daily life and many industries such as the biological, foodstuff, chemical, petroleum, cosmetic, and lab on a chip fields. In this study, we consider power-law fluids as a typical example of non-Newtonian fluids and investigate the effect of hydrophobic microgrooves on the pressure drop in channels by utilizing the phase field method. We demonstrate that the optimum size of the rectangular microgrooves in which the maximum pressure drop reduction (PDR) happens for both the considered Newtonian and non-Newtonian fluids is identical, but the PDR is different for the Newtonian and non-Newtonian fluids. For shear-thickening fluids, the PDR is more than shear-thinning fluids, which means that using the hydrophobic surfaces in dilatant fluids provides the best performance. It is seen that pressure drop reduces more at lower Reynolds numbers. We also investigate the efficiency of the microgrooved surfaces in convergent and divergent channels for both the Newtonian and non-Newtonian fluids and find the critical slope angles for a specific length of the channels in which the hydrophobic microgrooves have a sufficient performance in the PDR and stability.

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