Lattice Boltzmann method for studying the dynamics of a single rising bubble in shear-thickening power-law fluids

Abstract

Bubble motion in non-Newtonian fluids is widespread in various industrial processes such as crude oil extraction, enhancement of boiling heat transfer, CO<sub>2</sub> sequestration and wastewater treatments. Systems containing non-Newtonian liquids, as opposed to Newtonian liquids, have shear-dependent viscosity, which can alter the hydrodynamic characteristics of the bubbles, such as their size, deformation, instability, terminal velocity, shear rate, and ultimately affect the bubble rising behaviors. In this work, The dynamic behavior of bubble rising in a shear-thickened fluid was studied using an incompressible lattice Boltzmann non-Newtonian gas-liquid two-phase flow model. The effects of the rheological exponent <i>n</i>, the Eötvös number (<i>Eo</i>), and the Galilei number (<i>Ga</i>) on the bubble deformation, terminal velocity, and the shear rate were investigated. The numerical results show that the degree of bubble deformation increases as <i>Eo</i> grows, and the effect of <i>n</i> on bubble deformation degree is correlated with <i>Ga</i>. On the other hand, the terminal velocity of the bubbles increases monotonically and nonlinearly with <i>Ga</i> for a given <i>Eo</i> and <i>n</i>, and the effect of <i>n</i> on the terminal velocity of the bubbles gets stronger as <i>Ga</i> increases. When <i>Ga</i> is fixed and small, the terminal velocity of the bubble increases and then decreases with the increase of <i>n</i> at small <i>Eo</i>, and increases with the increase of <i>n</i> when <i>Eo</i> is large; but when <i>Ga</i> is fixed and large, the terminal velocity of the bubble increases with the increase of <i>n</i> in a more uniform manner. In addition, regions with high shear rates can be found near the left and right ends of the bubble. The size of these regions increases as both <i>Eo</i> and <i>Ga</i>, and it first increases and then decreases as <i>n</i> increases. Finally, the orthogonal experimental method was used to obtain the impact of the aforementioned three factors on the shear rate and terminal velocity. For the shear rate, the order of influence is <i>n</i>, <i>Ga</i> and <i>Eo</i> in descending order. For the terminal velocity, <i>Ga</i> has the greatest influence, followed by <i>n</i>, and <i>Eo</i> has the least influence.