Drag on a single fluid sphere translating in power-law liquids at moderate Reynolds numbers

Kishore, Nanda; Chhabra, R.P.; Eswaran, V.

doi:10.1016/j.ces.2007.01.057

Cited by 33 publications

(11 citation statements)

References 45 publications

(50 reference statements)

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“…In the recent literature, few attempts have so far been made to analyze numerically the drop or bubble behavior in non-Newtonian fluids. Kishore et al [5] carried out the numerical investigation to obtain the steady state drag coefficients and flow patterns of a single Newtonian fluid sphere sedimenting in power-law liquids using a finite difference method based SMAC implicit solver on a staggered grid and proposed a simple correlation for the total drag coefficient, which can be used to predict the rate of sedimentation of fluid sphere in power-law liquids. Tsamopoulos et al [6] simulated the rise of a bubble in a Newtonian or a viscoplastic fluid for a wide range of material parameters based on the mixed finite element method coupled with a quasi-elliptic mesh generation scheme in order to follow the large deformation of the physical domain.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of a bubble rising in shear-thinning fluids

Zhang

Yang

Mao

2010

Journal of Non-Newtonian Fluid Mechanics

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a b s t r a c tThe motion of a single bubble rising freely in quiescent non-Newtonian viscous fluids was investigated experimentally and computationally. The non-Newtonian effects in the flow of viscous inelastic fluids are modeled by the Carreau rheological model. An improved level set approach for computing the incompressible two-phase flow with deformable free interface is used. The control volume formulation with the SIMPLEC algorithm incorporated is used to solve the governing equations on a staggered Eulerian grid. The simulation results demonstrate that the algorithm is robust for shear-thinning liquids with large density ( 1 / g up to 103 ) and high viscosity (Á 1 /Á g up to 10 4 ). The comparison of the experimental measurements of terminal bubble shape and velocity with the computational results is satisfactory. It is shown that the local change in viscosity around a bubble greatly depends on the bubble shape and the zero-shear viscosity of non-Newtonian shear-thinning liquids. The shear-rate distribution and velocity fields are used to elucidate the formation of a region of large viscosity at the rear of a bubble as a result of the rather stagnant flow behind the bubble. The numerical results provide the basis for further investigations, such as the numerical simulation of viscoelastic fluids.

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Section: Introductionmentioning

confidence: 99%

Numerical simulation of a bubble rising in shear-thinning fluids

Zhang

Yang

Mao

2010

Journal of Non-Newtonian Fluid Mechanics

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“…The present Sherwood number results were seen to be in a good agreement with the Sherwood number in a Newtonian fluid. [ 22,32,33 ] Evidently, Equation () has a complex dependency on the Reynolds number, Bingham number, Schmidt number, viscosity ratio, and power‐law index. The functional form of Equation () can be consolidated by utilizing the modified definition of the dimensionless numbers based on the effective viscosity defined by Equations () and ().…”

Section: Resultsmentioning

confidence: 99%

Stability criteria and convective mass transfer from the falling spherical drops, part II: Herschel–Bulkley fluids

2022

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The combined effects of yield stress, shear‐thinning, and shear‐thickening fluid behaviour are investigated when a drop is falling in a Herschel–Bulkley fluid. The constitutive relation for Herschel–Bulkley fluids is regularized using the Papanastasiou regularization method. The governing partial differential equations for mass, momentum, and species transport are solved spanning a wide range of dimensionless numbers as Reynolds number, 1≤italicRe≤150; Schmidt number (10); Bingham number, 0≤italicBn≤50; viscosity ratio (0.1 and 10); and power‐law index, 0.4≤n≤1.6. The velocity field and mass transfer characteristics are expressed using streamlines, velocity contours, concentration contours, and sheared and un‐sheared regions, while the surface averaged gross engineering quantities are described as a drag coefficient, yield‐stress parameter, and Sherwood number. All else being equal, sheared regions in shear‐thinning fluids are observed to be larger with respect to the shear‐thickening fluids at finite Reynolds numbers. In the fully plastic flow limit, the yield stress effects dominate in the flow field, and therefore, the critical yield‐stress parameter is observed to be independent of shear‐thinning and shear‐thickening fluid behaviours. However, in the viscoplastic limit (finite Bingham number), shear‐thinning fluid always requires a larger value of yield stress to be static in the fluid with reference to shear‐thickening fluids. The new set of dimensionless parameters are defined based on the effective viscosity scales, and the predictive correlations are put forward for both drag coefficient and Sherwood number.

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“…Later, Basset derived a drag correlation by solving the Stokes equation coupled with the first‐order Navier's slip boundary condition. The correlation of Basset was reproduced later by Feng , Murthy et al , and Kishore et al , . Beresnev et al obtained another drag formula from the kinetic theory.…”

Section: Introductionmentioning

confidence: 83%

Gas‐Solid Drag Coefficient for Ordered Arrays of Monodisperse Microspheres in Slip Flow Regime

Tao

Guo

2017

Chem Eng & Technol

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Numerous analytical and numerical correlations for the drag force of particles in packed arrays are not applicable to microspheres because of the invalidity of the no‐slip assumption at a solid wall. The slip flow through assemblages of spheres is investigated by the lattice Boltzmann method (LBM). Three periodic arrays of static and monodisperse particles, i.e., a simple cubic, a body‐centered cubic, and a face‐centered cubic array, each with a relatively wide range of solid volume fraction, are considered. The LBM is validated for the slip flow over a single unbounded sphere and the continuum flow through spheres in a simple cubic array. The LBM results agree well with the experimental and numerical data in the literature. Simulations of slip flow through the three ordered arrays of spheres are performed. The effects of solid volume fraction and slip are both quantified within the developed drag laws.

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Drag on a single fluid sphere translating in power-law liquids at moderate Reynolds numbers

Cited by 33 publications

References 45 publications

Numerical simulation of a bubble rising in shear-thinning fluids

Numerical simulation of a bubble rising in shear-thinning fluids

Stability criteria and convective mass transfer from the falling spherical drops, part II: Herschel–Bulkley fluids

Gas‐Solid Drag Coefficient for Ordered Arrays of Monodisperse Microspheres in Slip Flow Regime

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