Question

used tat terminal velocity ........ and....... are equal ​

Answer 1

Answer:

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Explanation:

Abstract

To describe bubbly flows, an accurate prediction of the bubble rise velocity is crucial. For non-Newtonian fluids, closures for the bubble rise velocity provided in the literature are usually empirical and rather restricted in their applicability. In this work, a Front-Tracking Computational Fluid Dynamics model has been used to investigate the behaviour of a single bubble rising in a power-law fluid, for a very wide range of viscosities covering both shear-thinning and shear-thickening behaviour, where the power-law exponent n was varied between 0.5 and 1.5 and for three different bubble diameters (viz. 0.5 mm, 2 mm and 4 mm). The non-Newtonian behaviour of the continuous phase strongly influences the shape of the single rising bubbles caused by the viscosity profiles that develop in the flow field. As a consequence, large non-spherical bubbles become more spherical in shear-thickening fluids (in comparison to the same bubble in a Newtonian liquid), whereas small spherical bubbles lose their sphericity in shear-thinning fluids. To determine the bubble rise velocity for bubbles in non-Newtonian fluids with a power law behaviour, the drag closure derived for bubbles rising in Newtonian liquids proposed by Dijkhuizen et al. (2010), which combines viscous drag and shape-induced drag in a single correlation, is adapted using a modified Reynolds number. In this work it is shown that this adapted correlation is able to predict the terminal rise velocity of single bubbles rising in non-Newtonian power-law fluids within 20% accuracy for the majority of the investigated cases, provided that the drag regime does not change