Wall Retardation Effects on Flow and Drag Phenomena of Confined Spherical Particles in Shear-Thickening Fluids C. Rajasekhar Reddy and Nanda Kishore* Department of Chemical Engineering, Indian Institute of Technology Guwahati, Assam - 781039, India ABSTRACT: In this work, effects of the wall retardation, Reynolds number, and shear-thickening viscosity behavior of fluids on flow and drag phenomena of confined spherical particles are presented. The governing mass and momentum conservation equations are solved using computational fluid dynamics-based commercial software. The numerical solver is thoroughly validated by comparing present results with existing literature for the case of unconfined spheres in Newtonian and shear- thickening fluids. Extensive new results were presented in the following range of conditions: Reynolds number, Re,1-100; wall factor, λ,2-5; and power-law index, n,1-1.8. The wall factor (λ) is defined as the ratio between the tube diameter and the particle diameter. The severity of wall retardation effects increases with increasing power-law index. For fixed values of the Reynolds number, the recirculation wake length decreases with decreasing wall factor and/or increasing power-law index. For n = 1.8, the wall retardation effects are very strong so that for λ = 2, there is no recirculation wake behind confined sphere even at Re = 100. Furthermore, regardless of values of the Reynolds number, the total drag coefficient increases with increasing power-law index and/or decreasing wall factor. The effect of the Reynolds number on the ratio between pressure and friction drag coefficients decreases with increasing power-law index and/or increasing wall factor. Finally, on the basis of present numerical results, a correlation is developed for the total drag coefficient of confined spherical particles settling in shear-thickening fluids. 1. INTRODUCTION The settling velocity (or the drag coefficient) of solid particles in viscous fluids is a prerequisite to the design of solid-liquid contacting equipments in many process industries. If the design details of such contacting equipments are already known, then the information of drag coefficients of solid particles is useful in rationalizing solid-liquid equipments, or for the mechanical separation of different phases contacting in those equipments. In such processes, often one encounters a variety of irregular particles interacting with neighboring particles, wall, and surrounding fluids; however, the drag coefficients of isolated regular particles can provide adequate information concerned to the physics of such equipments. Hence, voluminous literature has been accrued on the flow and drag phenomena of regular particles such as spheres, cylinders, cubes, etc., settling in Newtonian 1-3 and in a variety of non-Newtonian liquids. 4 Furthermore, the information related to the settling velocity of bluff bodies can be conveniently presented in terms of nondimensional numbers such as the drag coefficients as functions of the Reynolds number, wall retardation factor, and the characteristic constants of the rheology of surrounding fluids. On the other hand, many fluids in chemical, pharmaceutical, food, polymer, and other processing industries display a wide range of non-Newtonian characteristics including shear- thinning, shear-thickening, yield stress, and viscoelastic behavior. However, the majority of aforementioned industrial fluids display Ostwald-de Waele or power-law rheological characteristics including shear-thinning and shear-thickening nature. In the last couple of decades, enormous literature has been published related to shear-thinning fluids, while the shear- thickening fluids are investigated to a lesser extent. However, with the growing importance of highly loaded process systems, there has been renewed interest in studying the shear- thickening behavior of fluids. 4,5 These shear-thickening fluids under normal conditions behave as slightly viscous fluids; however, under the influence of external force, the viscosity of these fluids increases tremendously. Further, the moment the external force was released, they return to their normal slightly viscous fluid behavior. The shear-thickening fluids are generally prepared by suspending nonagglomerating nanoparticles in liquids, and some examples include corn starch in water, titanium oxide-water suspension, china clay-water suspension, etc. Shear-thickening fluids are used as drilling fluids in the oil industry to protect a well from blowouts, used to strengthen body armor, etc. Furthermore, there are several analytical and seminumerical results on the settling velocity of unconfined spheres in power- law fluids in the creeping flow regime, which are thoroughly reviewed in a recent book. 4 Perhaps, Tripathi and Chhabra 6 are the first to report numerical results on the settling behavior of unconfined spheres and spheroids in shear-thickening fluids. Recently, Dhole et al. 7,8 reported results on drag and heat transfer behavior of unconfined sphere in shear-thinning and shear-thickening fluids in the intermediate range of pertinent variables, while Song et al. 9-11 studied the effects of moving wall on the momentum and heat transfer characteristics of confined spheres in shear-thinning fluids only. However, to the best of the authors’ knowledge, no results for wall retardation effects on confined spheres settling in shear-thickening fluids are available even in the creeping flow regime, let alone the Received: October 4, 2012 Revised: November 30, 2012 Accepted: December 3, 2012 Published: December 3, 2012 Article pubs.acs.org/IECR © 2012 American Chemical Society 16755 dx.doi.org/10.1021/ie302707s | Ind. Eng. Chem. Res. 2012, 51, 16755-16762