A note on the flow of a non-newtonian fluid film

Film flow of liquids simulated by the third-grade model down a vertical longitudinallyoscillating wall is investigated. The non-linear partial differential equation resulting from themomentum equation is solved by the method of Galerkin and flow enhancement is predicted fordifferent material constants. It is also found that an increase in either the amplitude or frequency ofthe vibration always leads to an increase in the magnitude of the flow enhancement.     

Stability of non-newtonian fluid flows

The stability of non-Newtonian fluid films moving on inclined planes is studied within the framework of the two-parameter Ostwald-de Waele model taking into account surface tension and van der Waals forces. The problem is solved analytically in the linear formulation, and the evolution of finite-amplitude perturbations is determined numerically. Novosibirsk Military Institute, Novosibirsk 630117. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 75–80, May–June, 2000.     

A note on unsteady unidirectional flows of a non-Newtonian fluid

Exact solutions are established for a class of unsteady unidirectional flows of an in compressible second grade fluid wherein inertial effects are not ignored. Amongst the several interesting flows which belong to this class are the flow due to a rigid plate oscillating in its own direction, the flow between two rigid boundaries one of which is suddenly started and the time-periodic Poiseuille flow due to an oscillating pressure gradient.     

A note on the stability of Beltrami fields for compressible fluid flows

In this paper we study the stability of the magnetostatic equilibrium through a relaxation of a magnetic field B in perfectly conducting compressible and viscous fluid.We establish stability criterion of a large class of Beltrami flows to any admissible displacement about the equilibrium configuration. We show that the field is stable to any displacement with the same 2π-periodicity as the basic flow, except the case where perturbations with wavelength much greater than the scale of the basic flow are included.     

Semi-inverse solutions of a non-newtonian fluid

Solutions for the equations of motion of an incompressible second grade fluid are obtained by employing semi-inverse methods in which we assume certain geometrical or kinematical properties of the fields. Specifically the problems studied in viscous fluids by Jeffery, Hamel and Görtler and Wieghardt, etc. are considered in a second grade fluid and the results for stream lines, velocities and pressure distribution are compared in the two cases.     

A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. A generalized Maxwell model with the fractional calculus was considered. Exact solutions of some unsteady flows of a viscoelastic fluid between two parallel plates are obtained by using the theory of Laplace transform and Fourier transform for fractional calculus. The flows generated by impulsively started motions of one of the plates are examined. The flows generated by periodic oscillations of one of the plates are also studied.     

Two-phase displacement of non-newtonian fluid

This paper considers the problem of non-Newtonian oil displa-cement by water in porous media.adopting the linear permea-tion law with initial pressure gradient.For one-dimensionalflow,the basic equation of non-Newtonian oil displacement bywater in sandstone reservoirs and fractured reservoirs is de-rived and numerical solutions are obtained.The results arecompared with the corresponding ones for Newtonian oil dis-placement to show the essential characteristics of non-Newto-nian oil displacement by water.     

Flow of a simple non-newtonian fluid past a sphere

Summary Creeping flow past a sphere is solved for a limiting case of fluid behaviour: an abrupt change in viscosity.List of Symbols d _ij Component of rate-of-deformation tensor - F _d Drag force exerted on sphere by fluid - G ^(d) Coefficients in expression for _ij in terms of d _ij - G _YOJK ^(d) Coefficients in power series representing G ^(d) - R Radius of sphere - r Spherical coordinate - V Velocity of fluid very far from sphere - v _i Component of the velocity vector - x Dimensionless radial distance, r/R - x _i Rectangular Cartesian coordinate - Dimensionless quantity defined by (26) - ^(d) Potential defined by (7) - Value of x denoting border between Regions 1 and 2 as a function of - ₁, ₂ Lower and upper limiting viscosities defined by (10) - Spherical coordinate - * Value of for which =1 - Value of denoting border between regions 1 and 2 as a function of x - Newtonian viscosity - _ij Component of the stress tensor - Spherical coordinate - ₁, ₂ Stream functions defined by (12) and (14) - Second and third invariants of the stress tensor and of the rate-of-deformation tensor, defined by (3)     

Dynamics of a cavitational cavity in a non-newtonian fluid

The dynamics of a spherical cavity in a non-Newtonian fluid, described by the Reiner-Rivlin rheological equation [1], is investigated. The equation of radial cavity motion is obtained, where the gas in the cavity is subject to a polytropic law and surface tension is taken into account. The equation of cavity motion is solved numerically for a number of values of the transverse viscosity coefficient. The influence of the transverse viscosity on the collapse process of vapor and gas-filled cavities is shown. Numerical computations are also carried out for the rate of energy dissipation and the pressure distribution in the fluid.Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 170–173, July–August, 1973.The authors are grateful to A. T. Listrove for attention to the research.     

Asymptotic analysis of the finite cone-and-plate flow of a non-newtonian fluid

Consider the shearing flow of a viscoelastic fluid trapped by surface tension between a cone and a plate. An asymptotic analysis of this problem in the limit of small gap angle has been done. This limit is realized in many practical situations. It is assumed that the Deborah number De, the Reynolds number Re, and the retardation parameter β are all order unity and that the shape of the free surface is very nearly spherical. Closed form analytic expressions are obtained for the leading terms of the primary and weak secondary motion of the fluid as well as the meniscus shape. It is found that the velocity field is bounded and continuous if and only if . There is a family of curves in the De-β plane on which the velocity field has a removable singularity at the origin. The secondary flow is made up of either one or two toroidal vortices. The meniscus has a bulge near the rotating cone and a trough near the stationary plate.     

Calculating the dissipation in fluid dampers with non-newtonian fluid models

The present paper gives a comparison of the Maxwell, Upperconvected Maxwell and the Oldroyd-B model for the calculation of dissipation in high shear-rate cases. Usage of viscodampers in the automotive industry is the most common. There is a good scope of the computing this power in the case of Newtonian fluids. When a polymeric liquid is considered that part of energy that is irreversible cannot be calculated as P_diss. = τ : d. For fluids where the separation into a solvent and a polymer part is not available but the deformation gradient tensor must be separated into two parts. One part consists of only the elastic deformation while the other is the non-elastic. This paper shows this separation using the Maxwell and the UCM models. A simple problem is shown, solving both analytically and numerically. The steady state temperature distribution of a damper then is validated with measurement.     

A note on similarity-type flows of elastico-viscous fluids

A study is undertaken to ascertain non-Newtonian effects in steady flows of elastic fluids due to an infinite rotating disk when there is suction across its surface. The fluids considered are of a class for which the similarity-type solution of von Kármán is an exact solution. It is shown that the presence of elasticity (of the type considered) does not result in flow reversal, the disk acting as a centrifugal fan as in Newtonian flow.