Persistence of straining and flow classification

Thompson, Roney L.; Mendes, Paulo R. Souza

doi:10.1016/j.ijengsci.2004.07.011

Cited by 51 publications

(36 citation statements)

References 30 publications

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“…A few experimental studies on flow of nonNewtonian fluids past a cylinder have also been reported (Coelho and Pinho, 2003), which elucidate the roles of visco-elastic and shear-thinning behavior on the vortex shedding characteristics. Since the fluids used in most of the studies display both elastic and shear-thinning characteristics, it is difficult to delineate their individual contributions unless the special flow classification criteria are used (Astarita, 1979;Thompson and Mendes, 2005). Therefore, possibilities of detailed comparison between the prediction and experimental observation are excluded.…”

Section: Previous Workmentioning

confidence: 99%

Two-dimensional Flow of Power-law Fluids over a Pair of Cylinders in a Side-by-Side Arrangement in the Laminar Regime

Panda

2017

Braz. J. Chem. Eng.

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-This manuscript presents the effect of Reynolds number (Re) and proximity of the bodies on the hydrodynamics of flow of shear-thinning, Newtonian and shear-thickening fluids over a pair of cylinders kept in side-by-side arrangement. Results obtained from the numerical simulations carried out with a combination of different parameters in the range of 0.2 ≤ power law index (n) ≤ 1.8, 0.1 ≤ Re ≤ 100 and 1.2 ≤ G (gap between the cylinders/diameter) ≤ 4 have been discussed in details. Analysis of the results gives a clear insight into the complex influence of Re on streamline patterns, surface pressure profiles, drag and lift coefficients for various fluids when the gap between two cylinder is changed.

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Section: Previous Workmentioning

confidence: 99%

Two-dimensional Flow of Power-law Fluids over a Pair of Cylinders in a Side-by-Side Arrangement in the Laminar Regime

Panda

2017

Braz. J. Chem. Eng.

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“…As was mentioned above the invariants of the rate-of-strain tensor are "objective", i.e., their value is independent of the coordinate system in which they are evaluated [20,22]. This does not hold for the invariants of the vorticity tensor when comparing coordinate systems that rotate with respect to each other.…”

Section: Droplet Break-up In 3d Laminar Flowsmentioning

confidence: 99%

Computational Fluid Dynamics (CFD)-Based Droplet Size Estimates in Emulsification Equipment

Janssen

Mayer²

2016

Processes

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While academic literature shows steady progress in combining multi-phase computational fluid dynamics (CFD) and population balance modelling (PBM) of emulsification processes, the computational burden of this approach is still too large for routine use in industry. The challenge, thus, is to link a sufficiently detailed flow analysis to the droplet behavior in a way that is both physically relevant and computationally manageable. In this research article we propose the use of single-phase CFD to map out the local maximum stable droplet diameter within a given device, based on well-known academic droplet break-up studies in quasi-steady 2D linear flows. The results of the latter are represented by analytical correlations for the critical capillary number, which are valid across a wide viscosity ratio range. Additionally, we suggest a parameter to assess how good the assumption of quasi-steady 2D flow is locally. The approach is demonstrated for a common lab-scale rotor-stator device (Ultra-Turrax, IKA-Werke GmbH, Staufen, Germany). It is found to provide useful insights with minimal additional user coding and little increase in computational effort compared to the single-phase CFD simulations of the flow field, as such. Some suggestions for further development are briefly discussed.

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“…Eqs. (15) and (16) are general enough to include most known rate-type constitutive equations [80]. Leonov [65] rejects equations of change of M where the deformationdependent part differs from the standard lower (ξ = −1) or upper (ξ = 1) convected derivatives (see also [86]); mixed derivatives are rejected because these give rise to Hadamard unstable equations of motion, i.e., equations of motion whose solution does not depend continuously on the initial and boundary conditions [ [87], p. 227].…”

Section: The Approach Of Leonovmentioning

confidence: 99%

“…Similarly, Newton's law of viscosity says that the viscous stress must be linearly proportional to the rate of strain, but the viscosity coefficient can depend non-linearly on the temperature and specific volume or pressure ( [42], pp. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Quasilinear Phenomenological Lawsmentioning

confidence: 99%

“…The length, stiffness, and degree of branching of polymer molecules strongly affect the shear and elongational response of polymer solutions and melts [5]. Polymeric liquids and other microstructured materials behave differently in shear and extensional flows because in extensional flows the liquid rotates locally with the rate of strain; therefore, the straining is persistent, i.e., it is always directed along the same direction from the material's perspective, whereas in shear flows, the material and the principal directions of the rate of strain rotate at different angular velocities [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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Theoretical modeling of microstructured liquids: a simple thermodynamic approach

Pasquali

Scriven

2004

Journal of Non-Newtonian Fluid Mechanics

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A new method is presented for accounting for microstructural features of flowing complex fluids at the level of mesoscopic, or coarse-grained, models by ensuring compatibility with macroscopic and continuum thermodynamics and classical transport phenomena. In this method, the microscopic state of the liquid is described by variables that are local expectation values of microscopic features. The hypothesis of local thermodynamic equilibrium is extended to include information on the microscopic state, i.e., the energy of the liquid is assumed to depend on the entropy, specific volume, and microscopic variables. For compatibility with classical transport phenomena, the microscopic variables are taken to be extensive variables (per unit mass or volume), which obey convection-diffusion-generation equations. Restrictions on the constitutive laws of the diffusive fluxes and generation terms are derived by separating dissipation by transport (caused by gradients in the derivatives of the energy with respect to the state variables) and by relaxation (caused by non-equilibrated microscopic processes like polymer chain stretching and orientation), and by applying isotropy. When applied to unentangled, isothermal, non-diffusing polymer solutions, the equations developed according to the new method recover those developed by the Generalized Bracket [J. Non-Newtonian Fluid Mech. 23 (1987) Rheol. 38 (1994) 769]. Minor differences with published results obtained by the Generalized Bracket are found in the equations describing flow coupled to heat and mass transfer in polymer solutions. The new method is applied to entangled polymer solutions and melts in the general case where the rate of generation of entanglements depends nonlinearly on the rate of strain. A link is drawn between the mesoscopic transport equations of entanglements and conformation and the microscopic equation describing the configurational distribution of polymer segment stretch and orientation. Constraints are derived on the generation terms in the transport equations of entanglements and conformation, and the formula for the elastic stress is generalized to account for reversible formation and destruction of entanglements. A simplified version of the transport equation of conformation is presented which includes many previously published constitutive models, separates flow-induced polymer stretching and orientation, yet is simple enough to be useful for developing large-scale computer codes for modeling coupled fluid flow and transport phenomena in two-and three-dimensional domains with complex shapes and free surfaces.

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Persistence of straining and flow classification

Cited by 51 publications

References 30 publications

Two-dimensional Flow of Power-law Fluids over a Pair of Cylinders in a Side-by-Side Arrangement in the Laminar Regime

Two-dimensional Flow of Power-law Fluids over a Pair of Cylinders in a Side-by-Side Arrangement in the Laminar Regime

Computational Fluid Dynamics (CFD)-Based Droplet Size Estimates in Emulsification Equipment

Theoretical modeling of microstructured liquids: a simple thermodynamic approach

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