Asymptotic solutions of weakly compressible Newtonian Poiseuille flows with pressure-dependent viscosity (original) (raw)
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Incompressible Poiseuille flows of Newtonian liquids with a pressure-dependent viscosity
Journal of Non-Newtonian Fluid Mechanics, 2011
The pressure-dependence of the viscosity becomes important in flows where high pressures are encountered. Applications include many polymer processing applications, microfluidics, fluid film lubrication, as well as simulations of geophysical flows. Under the assumption of unidirectional flow, we derive analytical solutions for plane, round, and annular Poiseuille flow of a Newtonian liquid, the viscosity of which increases linearly with pressure. These flows may serve as prototypes in applications involving tubes with small radius-to-length ratios. It is demonstrated that, the velocity tends from a parabolic to a triangular profile as the viscosity coefficient is increased. The pressure gradient near the exit is the same as that of the classical fully developed flow. This increases exponentially upstream and thus the pressure required to drive the flow increases dramatically.
Perturbation solutions of Poiseuille flows of weakly compressible Newtonian liquids
Journal of Non-Newtonian Fluid Mechanics, 2009
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit:
Laminar axisymmetric flow of a weakly compressible viscoelastic fluid
The combined effects of weak compressibility and viscoelasticity in steady, isothermal, laminar axisymmetric Poiseuille flow are investigated. Viscoelasticity is taken into account by employing the Oldroyd-B constitutive model. The fluid is assumed to be weakly compressible with a density that varies linearly with pressure. The flow problem is solved using a regular perturbation scheme in terms of the dimensionless isothermal compressibility parameter. The sequence of partial differential equations resulting from the perturbation procedure is solved analytically up to second order. The two-dimensional solution reveals the effects of compressibility and the other dimensionless numbers and parameters in the flow. Expressions for the average pressure drop, the volumetric flow rate, the total axial stress, as well as for the skin friction factor are also derived and discussed. The validity of other techniques used to obtain approximate solutions of weakly compressible flows is also discussed in conjunction with the present results.
Perturbation solution of the compressible annular Poiseuille flow of a viscous fluid
Journal of Non-Newtonian Fluid Mechanics, 2010
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit:
Perturbation solution of Poiseuille flow of a weakly compressible Oldroyd-B fluid
Journal of Non-Newtonian Fluid Mechanics, 2011
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit:
Physics of Fluids, 2011
The compressible Poiseuille gas flow driven by a uniform force is analytically investigated using a phenomenological nonlinear coupled constitutive relation model. A new fully analytical solution in compact tangent (or hyperbolic tangent in the case of diatomic gases) functional form explains the origin behind the central temperature minimum and a heat transfer from the cold region to the hot region. The solution is not only proven to satisfy the conservation laws exactly but also well-defined for all physical conditions (the Knudsen number and a force-related dimensionless parameter). It is also shown that the non-Fourier law associated with the coupling of force and viscous shear stress in the constitutive relation is responsible for the existence of the central temperature minimum, while a kinematic constraint on viscous shear and normal stresses identified in the velocity shear flow is the main source of the nonuniform pressure distribution. In addition, the convex pressure prof...
Weakly compressible Poiseuille flows of a Herschel–Bulkley fluid
Journal of Non-Newtonian Fluid Mechanics, 2009
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit:
International Journal of Engineering Science 104:1-4, 2016
Unidirectional steady flow of Newtonian liquids with a pressure-dependent viscosity in a rectangular duct is considered. Governing momentum equation is reduced to a quasilinear second order elliptic partial differential equation. We give an analytical solution to the governing equation, and investigate the effect of aspect ratio and pressure coefficient on the velocity profiles numerically.
Simple flows of fluids with pressure-dependent viscosities
Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 2001
In his seminal paper on fluid motion, Stokes developed a general constitutive relation which admitted the possibility that the viscosity could depend on the pressure. Such an assumption is particularly well suited to modelling flows of many fluids at high pressures and is relevant to several flow situations involving lubricants. Fluid models in which the viscosity depends on the pressure have not received the attention that is due to them, and we consider unidirectional and two-dimensional flows of such fluids here. We note that solutions can have markedly different characteristics than the corresponding solutions for the classical Navier-Stokes fluid. It is shown that unidirectional flows corresponding to Couette or Poiseuille flow are possible only for special forms of the viscosity. Furthermore, we show that interesting non-unique solutions are possible for flow between moving plates, which has no counterpart in the classical Navier-Stokes theory. We also study, numerically, two two-dimensional flows that are technologically significant: that between rotating, coaxial, eccentric cylinders and a flow across a slot. The solutions are found to provide interesting departures from those for the classical Navier-Stokes fluid.