Drag of contaminated bubbles in power-law fluids

Flow and drag phenomena of spherical bubbles in contaminated power-law fluids are numerically investigated using the spherical stagnant cap model over the range of conditions as the Reynolds number (Re: 0.1–200), the power-law index (n: 0.2–1.6) and the degree of contamination (α: 0–180°). The conservation equations of mass and momentum are solved using the semi-implicit method for pressure-linked equations (SIMPLE) algorithm along with the quadratic upstream interpolation for convective kinematics (QUICK) scheme for momentum terms. The solver has been thoroughly validated with the existing literature results over wide range of pertinent conditions. The new results show that for Re > 20 and α ≥ 60°, a recirculation wake behind the contaminated bubble is observed for all values of power-law index; and the size of the recirculation wake is found to decrease with the increasing power-law index. Furthermore, a crossover Reynolds number (at Re ≈ 5) exists for drag coefficient vs. Reynolds number behavior with respect to the power-law index; and it is found to be independent of the degree of contamination. Below this crossover Reynolds number, compared to Newtonian fluid results, the normalized drag coefficients are large for shear-thinning fluids (n < 1) and are smaller for shear-thickening fluids; and opposite trends are observed beyond the crossover Reynolds number.