Settling and transport of spherical particles in power-law fluids at finite Reynolds number

Graham, David I.; Jones, T. E. R.

doi:10.1016/0377-0257(94)80037-5

Cited by 64 publications

(52 citation statements)

References 23 publications

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“…This makes convergence for the momentum equations difficult for n Յ 0.6, as also noted by others. [37][38][39] Therefore, for n values of 0.5 and 0.6, a somewhat coarser grid was used (radial meshing of 0.03D with 60 control volumes around half-sphere for Re Ͼ 20 and meshing of 0.05D with 60 control volumes around the half-sphere for Re Ͻ 20). However, even this coarser mesh was sufficiently fine to resolve the flow inside the boundary layer.…”

Section: Domain and Grid Independencementioning

confidence: 99%

Forced convection heat transfer from a sphere to non‐Newtonian power law fluids

2006

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Section: Domain and Grid Independencementioning

confidence: 99%

Forced convection heat transfer from a sphere to non‐Newtonian power law fluids

2006

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“…The aim of constructing constitutive equations is to find the correlations between dynamic viscosity and shear rate. Power-law model [14], Carreau model [15], Mold flow first-order model [16], and Bingham model [17] have been successfully developed to analyze pressured driven non-Newtonian fluid flows and heat/ mass transfer. As for the electroosmotic flow of non-Newtonian fluids, however, the mathematical models just appear in the literature.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Smoluchowski velocity for electroosmosis of Power‐law fluids over a surface with arbitrary zeta potentials

Zhao

Yang

2010

Electrophoresis

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Electroosmotic flow of Power-law fluids over a surface with arbitrary zeta potentials is analyzed. The governing equations including the nonlinear Poisson-Boltzmann equation, the Cauchy momentum equation and the continuity equation are solved to seek exact solutions for the electroosmotic velocity, shear stress, and dynamic viscosity distributions inside the electric double layer. Specifically, an expression for the general Smoluchowski velocity is obtained for electroosmosis of Power-law fluids in a fashion similar to the classic Smoluchowski velocity for Newtonian fluids. The existing Smoluchowski slip velocities under two special cases, (i) for Newtonian fluids with arbitrary zeta potentials and (ii) for Power-law fluids with small zeta potentials, can be recovered from our derived formula. It is interesting to note that the general Smoluchowski velocity for non-Newtonian Power-law fluids is a nonlinear function of the electric field strength and surface zeta potentials; this is due to the coupling electrostatics and non-Newtonian fluid behavior, which is different from its counterpart for Newtonian fluids. This general Smoluchowski velocity is of practical significance in determining the flow rates in microfluidic devices involving non-Newtonian Power-law fluids.

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“…Thus, the Navier-Stokes equation fails to describe the behaviors of these biofluids, and the more general Cauchy momentum equation with a proper constitutive equation must be used instead. A number of constitutive equations have been established to relate the dynamic viscosity of non-Newtonian fluids to the shear rate, such as the power-law model, 4 Carreau model, 5 Moldflow first-order model, 6 and Bingham model. 7 Electrokinetic phenomena involving non-Newtonian fluids were already shown to behave differently from their Newtonian counterparts.…”

Section: Introductionmentioning

confidence: 99%

Electro-osmotic mobility of non-Newtonian fluids

Zhao

Yang

2011

Biomicrofluidics

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Electrokinetically driven microfluidic devices are usually used to analyze and process biofluids which can be classified as non-Newtonian fluids. Conventional electrokinetic theories resulting from Newtonian hydrodynamics then fail to describe the behaviors of these fluids. In this study, a theoretical analysis of electro-osmotic mobility of non-Newtonian fluids is reported. The general Cauchy momentum equation is simplified by incorporation of the Gouy-Chapman solution to the Poisson-Boltzmann equation and the Carreau fluid constitutive model. Then a nonlinear ordinary differential equation governing the electro-osmotic velocity of Carreau fluids is obtained and solved numerically. The effects of the Weissenberg number ͑Wi͒, the surface zeta potential ͑ s ͒, the power-law exponent ͑n͒, and the transitional parameter ͑␤͒ on electro-osmotic mobility are examined. It is shown that the results presented in this study for the electro-osmotic mobility of Carreau fluids are quite general so that the electro-osmotic mobility for the Newtonian fluids and the power-law fluids can be obtained as two limiting cases.

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Settling and transport of spherical particles in power-law fluids at finite Reynolds number

Cited by 64 publications

References 23 publications

Forced convection heat transfer from a sphere to non‐Newtonian power law fluids

Forced convection heat transfer from a sphere to non‐Newtonian power law fluids

Nonlinear Smoluchowski velocity for electroosmosis of Power‐law fluids over a surface with arbitrary zeta potentials

Electro-osmotic mobility of non-Newtonian fluids

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