The effect of finite boundaries on the drag experienced by a sphere settling in quiescent power law fluids in cylindrical vessels has been investigated numerically. In particular, the momentum equations have been solved numerically over the following ranges of conditions: sphere Reynolds number, 1-100; power law index, 0.2-1; and sphere-to-tube diameter ratio, 0-0.5. Due to the backflow of the fluid caused by a falling sphere and the corresponding changes in the velocity field close to the sphere, the presence of finite boundaries leads to an increase in the drag force acting on a falling sphere thereby slowing its descent. The effect, however, is more significant at low Reynolds numbers than at high Reynolds numbers. Similarly, the additional drag due to the walls increases with the increasing degree of confinement, i.e., the sphere-to-tube diameter ratio. Overall, all else being equal, the wall effect is less severe in power law fluids than in Newtonian fluids. Furthermore, the confining walls also influence the onset of flow separation and subsequently the size of the recirculation region. The present numerical predictions are consistent with the experimental results available in the literature.
This work endeavors to elucidate the influence of confining walls on the convective heat transfer from a sphere to power-law fluids. The governing equations (mass, momentum, and thermal energy) have been solved numerically over the following ranges of conditions: power-law index, 0.2−1, i.e., only for shear-thinning fluid behavior; sphere Reynolds number, 5−100; sphere-to-tube-diameter ratio, 0−0.5; and Prandtl number, 1−100. Extensive results of the local and surface averaged values of the Nusselt number are presented herein to delineate the influence of each of the aforementioned parameters on the rate of heat transfer from a sphere. Broadly speaking, the Nusselt number shows positive dependence on both the Reynolds and Prandtl numbers. All else being equal, shear-thinning fluid behavior is seen to facilitate heat transfer with reference to that in Newtonian fluids. Indeed, it is possible to augment the rate of heat transfer by up to 60−70% under appropriate conditions. However, the imposition of confining walls is seen to limit the enhancement in heat transfer, especially at low Reynolds and/or Prandtl numbers. Therefore, the severity of confinement together with the values of the Reynolds and Prandtl numbers influences the value of the Nusselt number in an intricate manner.
The effect of finite boundaries on the drag experienced by a sphere exposed to the Poiseuille flow of power-law fluids in cylindrical vessels has been investigated numerically. In particular, the momentum equations have been solved over the following ranges of conditions: sphere Reynolds number based on the area average velocity in the pipe, Re 1-100; power law index, n: 0.2-1, and sphere-to-tube diameter ratio, λ: 0-0.5. Due to the obstruction in the path of the fluid caused by the sphere fixed at the axis of the tube and the corresponding changes in the velocity field close to the sphere, there is extra viscous dissipation at the walls and this, in turn, leads to an increase in the drag force acting on the sphere. Conversely, there is an extra pressure drop caused by the fixed sphere for the flow of the fluid in the tube. The effect, however, is more significant at low Reynolds numbers than that at high Reynolds numbers. Similarly, the additional drag due to the confining walls increases with the increasing degree of obstruction, i.e., sphere-to-tube diameter ratio. Overall, all else being equal, the wall effect is seen to be less severe in power-law fluids than that in Newtonian fluids. Furthermore, the confining walls also influence the onset of flow separation and subsequently the size of the recirculation region. The present numerical predictions are consistent with the scant experimental results available in the literature for Newtonian and power-law fluids.
in Wiley Online Library (wileyonlinelibrary.com).Water-based pressure-sensitive adhesives are formulated by combining a polymer latex with a tackifier emulsion. The latter is an oil-in-water emulsion made by the process of phase inversion. The phase inversion itself is carried out in a stirred tank fitted with a heating jacket by progressively adding water to a water-in-oil emulsion. The point of onset of phase inversion and the characteristics of the emulsion that is formed depend on process conditions; these include temperature, rate of water addition, and agitation speed. The role of these operating conditions is elucidated here. Increasing temperature delayed the onset of phase inversion slightly, but it did not affect emulsion particle size, provided it remained below a critical value. Agitation speed had to be increased upon increasing the water flow rate to prevent increasing the particle size. Finally, the point of onset of phase inversion could be predicted reasonably well using a model available in the literature.
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