Rotational Particle Separation in Solutions: Micropolar Fluid Theory Approach

Shelukhin, V. V.

doi:10.3390/polym13071072

Cited by 4 publications

(12 citation statements)

References 29 publications

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“…Here,

is the viscosity given by the Krieger–Douhgerty empirical closure [ 23 ], with

and

being the maximal reference value of

and the consistency, respectively.…”

Section: Mathematical Modelmentioning

confidence: 99%

Recursive Settling of Particles in Shear Thinning Polymer Solutions: Two Velocity Mathematical Model

Neverov¹,

Shelukhin²

2022

Polymers

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Processing of the available experimental data on particles settling in shear-thinning polymer solutions is performed. Conclusions imply that sedimentation should be recursive, since settling also occurs within the sediment. To capture such an effect, a mathematical model of two continua has been developed, which corresponds to experimental data. The model is consistent with basic thermodynamics laws. The rheological component of this model is a correlation formula for gravitational mobility. This closure is justified by comparison with known experimental data available for particles settling in vertical vessels. In addition, the closure is validated by comparison with analytical solutions to the Kynch one-dimensional equation, which governs dynamics of particle concentration. An explanation is given for the Boycott effect and it is proven that sedimentation is enhanced in a 2D inclined vessel. In tilted vessels, the flow is essentially two-dimensional and the one-dimensional Kynch theory is not applicable; vortices play an important role in sedimentation.

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“…Here,

is the viscosity given by the Krieger–Douhgerty empirical closure [ 23 ], with

and

being the maximal reference value of

and the consistency, respectively.…”

Section: Mathematical Modelmentioning

confidence: 99%

Recursive Settling of Particles in Shear Thinning Polymer Solutions: Two Velocity Mathematical Model

Neverov¹,

Shelukhin²

2022

Polymers

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“…The first condition in (24) states that velocity obeys the no-slip condition. The second condition in (24) has the meaning that the micro-rotation ω depends linearly on the macrorotation ∇ × v/2 [25].…”

Section: Poiseuille Flowsmentioning

confidence: 99%

“…In what follows, we consider quasi-steady slow flows. Neglecting terms with small Reynolds numbers in (25), we arrive at the equations…”

Section: Poiseuille Flowsmentioning

confidence: 99%

“…There is one more effect caused by particle rotation and rotational diffusion. This is the separation of particles when flowing between two concentric rotating cylinders [25].…”

Section: Introductionmentioning

confidence: 99%

“…Skew-symmetric and anisotropic viscosities are introduced in addition to the common shear viscosity, which we call here symmetric viscosity. While there are experiments [29] and theories [25] to determine the skew-symmetric viscosity, the question of measuring the anisotropic viscosity remains open. We cannot quantitatively confirm our equations by three-dimensional experiments, since the calculations were carried out on the basis of one-dimensional flows.…”

Section: Introductionmentioning

confidence: 99%

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Flows of Linear Polymer Solutions and Other Suspensions of Rod-like Particles: Anisotropic Micropolar-Fluid Theory Approach

Shelukhin

2021

Polymers

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We formulate equations governing flows of suspensions of rod-like particles. Such suspensions include linear polymer solutions, FD-virus, and worm-like micelles. To take into account the particles that form and their rotation, we treat the suspension as a Cosserat continuum and apply the theory of micropolar fluids. Anisotropy of suspensions is determined through the inclusion of the microinertia tensor in the rheological constitutive equations. We check that the model is consistent with the basic principles of thermodynamics. In addition to anisotropy, the theory also captures gradient banding instability, coexistence of isotropic and nematic phases, sustained temporal oscillations of macroscopic viscosity, shear thinning and hysteresis. For the flow between two planes, we also establish that the total flow rate depends not only on the pressure gradient, but on the history of its variation as well.

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Lateral-Concentration Inhomogeneities in Flows of Suspensions of Rod-like Particles: The Approach of the Theory of Anisotropic Micropolar Fluid

Shelukhin

2023

Mathematics

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To tackle suspensions of particles of any shape, the thermodynamics of a Cosserat continuum are developed by the method suggested by Landau and Khalatnikov for the mathematical description of the super-fluidity of liquid 2He. Such an approach allows us to take into account the rotation of particles and their form. The flows of suspensions of neutrally buoyant rod-like particles are considered in detail. These suspensions include linear polymer solutions, FD-virus and worm-like micelles. The anisotropy of the suspensions is determined through the inclusion of the micro-inertia tensor in the rheological constitutive equations. The theory predicts gradient banding, temporal volatility of apparent viscosity and hysteresis of the flux-pressure curve. The transition from the isotropic phase to the nematic phase is also captured. Our mathematical model predicts the formation of flock-like inhomogeneities of concentration jointly with the hindrance effect.

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Rotational Particle Separation in Solutions: Micropolar Fluid Theory Approach

Cited by 4 publications

References 29 publications

Recursive Settling of Particles in Shear Thinning Polymer Solutions: Two Velocity Mathematical Model

Recursive Settling of Particles in Shear Thinning Polymer Solutions: Two Velocity Mathematical Model

Flows of Linear Polymer Solutions and Other Suspensions of Rod-like Particles: Anisotropic Micropolar-Fluid Theory Approach

Lateral-Concentration Inhomogeneities in Flows of Suspensions of Rod-like Particles: The Approach of the Theory of Anisotropic Micropolar Fluid

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