Effects of Contamination and Shear-Thinning Fluid Viscosity on Drag Behavior of Spherical Bubbles

Abstract

In this work, the combined effects of contamination and shear-thinning (power-law) viscosity on the free rise of a single bubble have been studied numerically. The influence of insoluble contaminants on the surface of the bubble has been incorporated in the analysis by employing the spherical stagnant cap model which has been employed successfully in Newtonian fluids. The governing differential equations have been solved numerically over a range of conditions: Reynolds number, Re = 10–200; power-law index, n = 0.6–1; and stagnant cap angle, α = 0°–180°. Finally, the effect of each of the parametersnamely, Re, n, and αon streamline patterns, surface pressure and vorticity distributions, and individual and total drag coefficients is discussed in detail. Briefly, for α > 30° and Re ≥ 50, the recirculation length increases and the separation angle moves forward with the increasing Re; however, mixed trends are observed with respect to the power-law index and the stagnant cap angle. The total drag coefficient increases as the cap angle and/or the power-law index increases and/or the Reynolds number decreases; while mixed trends are observed on the dependence of the ratio of the individual drag coefficients on these parameters.

Heat Transfer Phenomena of Assemblages of Smooth Slip Spheres in Newtonian Fluids

“…Table 3 presents a comparison of the present values of average Nusselt numbers of the assemblages of no-slip spheres ( → Ý) of volume fractions Φ = 0.1 and Φ = 0.5 at Re = 1 and Re = 100 with the analytical results of Pfeffer and Happel [14]; and here too the agreement between two values is excellent. Therefore, on the basis of our previous experience [43][44][45][46][47][48][49] and present comparisons, it can be concluded that the present solver is reliable and accurate within ±4%-5% of deviations. number, isotherm contours may be carried in the flow direction due to convection effects.…”

“…The present numerical solver to obtain the velocity, pressure, and temperature profiles associated with single and multiple bubbles/drops/particles in Newtonian and non-Newtonian fluids was extensively validated over wide ranges of conditions with the available experimental and numerical results and presented elsewhere [43][44][45][46][47][48][49]. However, some additional validations are shown in this section.…”

Motion of partially contaminated bubbles in power-law liquids: Effect of wall retardation

“…According to them, the rise velocity and surface mobility of bubble are strongly affected by concentration of contaminants; however bubble shape is found to be independent of concentration of contaminants. Recently Kishore et al (2013), and Kishore (2014a, 2014b) numerically investigated effects of contaminants and powerlaw type non-Newtonian fluid rheology on momentum transfer characteristics of unconfined partially contaminated bubbles over wide range of pertinent conditions. Finally, to the best of authors' knowledge, no studies are available dealing with the numerical investigation of flow and drag phenomena of partially contaminated bubbles confined in tubes filled with power-law liquids even in the low Reynolds number region, let alone moderate to large values of Reynolds number.…”

Heat Transfer from Confined Contaminated Bubbles to Power‐Law Liquids at Low to Moderate Reynolds and Prandtl Numbers

“…The stagnant cap model has been extensively adopted to interpret experimental results and found that this model is consistent with experimental results not only at low to moderate Reynolds numbers but also at large values of the Reynolds numbers. Furthermore, this model is also tested theoretically by many researchers and proved to be reliable under a wide range of Reynolds numbers . As per this model, contaminants can adsorb at the first front half of the bubble surface and move towards the backside of the bubble because of the surface advection caused by the main flow .…”

“…Therefore, both from theoretical and industrial applications viewpoints, development of results on the motion and heat transfer from the contaminated confined bubbles to surrounding contaminated non‐Newtonian liquids is a prerequisite for the rational design and operation of liquid–gas contacting equipment. In this connection, recently Kishore and coworkers reported numerical results on a series of analogous problems. For instance, Kishore and colleagues delineated the flow and drag behavior of contaminated bubbles in Newtonian and shear‐thinning power‐law fluids in the range of conditions: Re = 10 to 200, n = 0.6 to 1 and α = 0 to 180˚ using their in‐house CFD solver namely semi‐implicit marker and cell algorithm implemented on a staggered grid arrangement in spherical coordinates.…”