Drag coefficient of a rising bubble in a shear-thinning fluid using the power-law scheme coupled with a Cahn-Hilliard equation with a variable mobility: A lattice Boltzmann study and comparison with experiment

TL;DR

This paper extends a lattice Boltzmann model with a power-law scheme and variable mobility to accurately simulate the rising bubble behavior in shear-thinning fluids, showing good agreement with experimental data and improved stability.

Contribution

It introduces a novel LB model with variable mobility for non-Newtonian fluids, enhancing stability and accuracy in simulating bubble dynamics in shear-thinning fluids.

Findings

Variable mobility improves stability and reduces interface dissipation.

The model achieves 5.66% average error in terminal velocity predictions.

Simulations align well with experimental results across various flow conditions.

Abstract

This study aims to investigate the behavior of multicomponent fluid flows consisting of Newtonian and non-Newtonian components, especially terminal velocity of a rising bubble in a power-law fluid. A recent lattice Boltzmann (LB) model is extended using power-law scheme to be able to simulate both Newtonian and non-Newtonian fluid flows at high density and viscosity ratios. Also, a variable mobility is introduced in this study to minimize the unphysical error around small bubbles in the domain. A three-component fluid flow system is examined using a constant and variable mobility. It is shown that each component has more stability using variable mobility while constant mobility causes interface dissipation, leading to mass loss gradually. In addition, two test cases including power-law fluid flows driven between two parallel plates are conducted to show the accuracy and capability of the model. To find a grid-independent computational domain, a grid independency test is carried out to show that a 200*400 domain size is suitable for our computations. Then, terminal velocity of a rising bubble is compared to an existing correlation in the literature, indicating that the results are in good agreement with existing study so that average relative error in six different cases is 5.66 %. Also, the simulated examples show good conformity to experimental results over a range of the Reynolds and Eotvos numbers.