Lateral-Concentration Inhomogeneities in Flows of Suspensions of Rod-like Particles: The Approach of the Theory of Anisotropic Micropolar Fluid
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...
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| Format: | Article |
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MDPI AG
2023-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/23/4740 |
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| author | Vladimir Shelukhin |
| author_facet | Vladimir Shelukhin |
| author_sort | Vladimir Shelukhin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T01:47:15Z |
| format | Article |
| id | doaj.art-b5f91f1f63b94c28ae4d8449df585278 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T01:47:15Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b5f91f1f63b94c28ae4d8449df5852782023-12-08T15:21:37ZengMDPI AGMathematics2227-73902023-11-011123474010.3390/math11234740Lateral-Concentration Inhomogeneities in Flows of Suspensions of Rod-like Particles: The Approach of the Theory of Anisotropic Micropolar FluidVladimir Shelukhin0Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, RussiaTo 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.https://www.mdpi.com/2227-7390/11/23/4740suspensionsrod-like particlesmicropolar fluidthermodynamicshysteresisconcentration inhomogeneity |
| spellingShingle | Vladimir Shelukhin Lateral-Concentration Inhomogeneities in Flows of Suspensions of Rod-like Particles: The Approach of the Theory of Anisotropic Micropolar Fluid Mathematics suspensions rod-like particles micropolar fluid thermodynamics hysteresis concentration inhomogeneity |
| title | Lateral-Concentration Inhomogeneities in Flows of Suspensions of Rod-like Particles: The Approach of the Theory of Anisotropic Micropolar Fluid |
| title_full | Lateral-Concentration Inhomogeneities in Flows of Suspensions of Rod-like Particles: The Approach of the Theory of Anisotropic Micropolar Fluid |
| title_fullStr | Lateral-Concentration Inhomogeneities in Flows of Suspensions of Rod-like Particles: The Approach of the Theory of Anisotropic Micropolar Fluid |
| title_full_unstemmed | Lateral-Concentration Inhomogeneities in Flows of Suspensions of Rod-like Particles: The Approach of the Theory of Anisotropic Micropolar Fluid |
| title_short | Lateral-Concentration Inhomogeneities in Flows of Suspensions of Rod-like Particles: The Approach of the Theory of Anisotropic Micropolar Fluid |
| title_sort | lateral concentration inhomogeneities in flows of suspensions of rod like particles the approach of the theory of anisotropic micropolar fluid |
| topic | suspensions rod-like particles micropolar fluid thermodynamics hysteresis concentration inhomogeneity |
| url | https://www.mdpi.com/2227-7390/11/23/4740 |
| work_keys_str_mv | AT vladimirshelukhin lateralconcentrationinhomogeneitiesinflowsofsuspensionsofrodlikeparticlestheapproachofthetheoryofanisotropicmicropolarfluid |