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# Newtonian fluid

About: Newtonian fluid is a research topic. Over the lifetime, 14313 publications have been published within this topic receiving 348668 citations.

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01 Jan 1974

TL;DR: In this article, the stability of Laminar Boundary Layer Flow Appendices has been investigated in Cylindrical and Spherical Coordinates of Incompressible Newtonian Fluids.

Abstract: 1 Preliminary Concepts 2 Fundamental Equations of Compressible Viscous Flow 3 Solutions of the Newtonian Viscous-Flow Equations 4 Laminar Boundary Layers 5 The Stability of Laminar Flows 6 Incompressible Turbulent Mean Flow 7 Compressible Boundary Layer Flow Appendices A Transport Properties of Various Newtonian Fluids B Equations of Motion of Incompressible Newtonian Fluids in Cylindrical and Spherical Coordinates C A Runge-Kutta Subroutine for N Simultaneous Differential Equations Bibliography Index

6,569 citations

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TL;DR: In this paper, an equilibrium relation is developed to govern the behavior of the couples, which constrained the couple stress tensor to be symmetric, and the symmetric curvature tensor became the only properly conjugated high order strain measures in the theory to have a real contribution to the total strain energy of the system.

Abstract: The deformation behavior of materials in the micron scale has been experimentally shown to be size dependent. In the absence of stretch and dilatation gradients, the size dependence can be explained using classical couple stress theory in which the full curvature tensor is used as deformation measures in addition to the conventional strain measures. In the couple stress theory formulation, only conventional equilibrium relations of forces and moments of forces are used. The couple's association with position is arbitrary. In this paper, an additional equilibrium relation is developed to govern the behavior of the couples. The relation constrained the couple stress tensor to be symmetric, and the symmetric curvature tensor became the only properly conjugated high order strain measures in the theory to have a real contribution to the total strain energy of the system. On the basis of this modification, a linear elastic model for isotropic materials is developed. The torsion of a cylindrical bar and the pure bending of a flat plate of infinite width are analyzed to illustrate the effect of the modification.

2,725 citations

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15 Jun 1989

TL;DR: In this article, the authors discuss the importance of non-linearity solids and liquids rheology is a difficult subject for rheological research, and present some demonstrations of high extensional viscosity behaviour.

Abstract: 1) What is rheology? historical perspective the importance of non-linearity solids and liquids rheology is a difficult subject components of rheological research. 2) Viscosity practical ranges of variables which affect viscosity the shear-dependent viscosity of non-Newtonian liquids viscometers for measuring shear viscosity. 3) Linear viscoelasticity the meaning and consequences of linearity the Kelvin and Maxwell models the relaxation spectrum oscillatory shear relationships between functions of linear viscoelasticity methods of measurement. 4) Normal stresses the nature and origin of normal stresses typical behaviour of N 1 and N 2 observable consequences of N 1 and N 2 methods of measuring N 1 and N 2 relationships between viscometric functions and linear viscoelastic functions. 5) extensional viscosity importance of extensional flow theoretical considerations experimental methods experimental results some demonstrations of high extensional viscosity behaviour. 6) Rheology of polymeric liquids general behaviour effect of temperature on polymer rheology effect of molecular weight on polymer rheology effect of concentration on the rheology of polymer solutions polymer gels liquid crystal polymers. molecular theories the method of reduced variables empirical relations between rheological functions practical applications. 7) Rheology of suspensions the viscosity of suspensions of solid particles in Newtonian liquids the colloidal contribution to viscosity viscoelastic properties of suspensions suspensions of deformable particles the interaction of suspended particles with polymer molecules also present in the continuous phase computer simulation studies of suspension rheology. 8. Theoretical rheology basic principles of continuum mechanics successful applications of the formulation principles some general constitutive equations constitutive equations for restricted classes of flows simple constitutive equations of the Oldroyd/Maxwell type solution of flow problems.

2,569 citations

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TL;DR: In this article, a large number of spherical grains of diameter D = 0.13 cm were sheared in Newtonian fluids of varying viscosity (water and a glycerine-water-alcohol mixture) in the annular space between two concentric drums.

Abstract: Dispersions of solid spherical grains of diameter D = 0.13cm were sheared in Newtonian fluids of varying viscosity (water and a glycerine-water-alcohol mixture) in the annular space between two concentric drums. The density σ of the grains was balanced against the density ρ of the fluid, giving a condition of no differential forces due to radial acceleration. The volume concentration C of the grains was varied between 62 and 13 %. A substantial radial dispersive pressure was found to be exerted between the grains. This was measured as an increase of static pressure in the inner stationary drum which had a deformable periphery. The torque on the inner drum was also measured. The dispersive pressure P was found to be proportional to a shear stress λ attributable to the presence of the grains. The linear grain concentration λ is defined as the ratio grain diameter/mean free dispersion distance and is related to C by λ = 1 ( C 0 / C ) 1 2 − 1 where C 0 is the maximum possible static volume concentration. Both the stresses T and P , as dimensionless groups T σ D 2 /λη 2 , and P σ D 2 /λη 2 , were found to bear single-valued empirical relations to a dimensionless shear strain group λ ½ σ D 2 (d U /d y )lη for all the values of λ C = 57% approx.) where d U /d y is the rate of shearing of the grains over one another, and η the fluid viscosity. This relation gives T α σ ( λ D ) 2 ( dU / dy ) 2 and T ∝ λ 1 2 η d U / dy according as d U /d y is large or small, i.e. according to whether grain inertia or fluid viscosity dominate. An alternative semi-empirical relation F = (1+λ)(1+½λ)ηd U /d y was found for the viscous case, when T is the whole shear stress. The ratio T/P was constant at 0·3 approx, in the inertia region, and at 0.75 approx, in the viscous region. The results are applied to a few hitherto unexplained natural phenomena.

2,445 citations

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TL;DR: In this article, the response of a Newtonian fluid saturating the pore space of a rigid isotropic porous medium, subjected to an infinitesimal oscillatory pressure gradient across the sample, is considered.

Abstract: We consider the response of a Newtonian fluid, saturating the pore space of a rigid isotropic porous medium, subjected to an infinitesimal oscillatory pressure gradient across the sample. We derive the analytic properties of the linear response function as well as the high- and low-frequency limits. In so doing we present a new and well-defined parameter Λ, which enters the high-frequency limit, characteristic of dynamically connected pore sizes. Using these results we construct a simple model for the response in terms of the exact high- and low-frequency parameters; the model is very successful when compared with direct numerical simulations on large lattices with randomly varying tube radii. We demonstrate the relevance of these results to the acoustic properties of non-rigid porous media, and we show how the dynamic permeability/tortuosity can be measured using superfluid 4He as the pore fluid. We derive the expected response in the case that the internal walls of the pore space are fractal in character.

1,872 citations