Hydrodynamic stability of evaporation fronts in porous media

The stability of phase transition fronts in water flows through porous media is considered. In the short-wave approximation a linear stability analysis is carried out and a sufficient condition of hydrodynamic instability of the phase discontinuity is proposed. The problem of injection of a water-vapor mixture into a two-dimensional mixture-saturated formation is solved and its numerical solution is compared with an exact solution of the corresponding one-dimensional self-similar problem. It is discovered that, instead of the unstable discontinuities in the one-dimensional formulation, in the two-dimensional case a lengthy mixing zone with a characteristic scale that increases self-similarly with time is formed.     

Particle motions in non-newtonian media

Summary The rotation of rigid rods and discs, and the deformation and burst of liquid drops were observed in elasticoviscous solutions of polyacrylamide undergoingCouette flow at shear rates from 0.1 to ~ 10 sec^–1. The study extended previous work (1) to cylindrical particles having axis ratios closer to unity and to liquid drops in systems having zero interfacial tension.The period of rotation of discs was appreciably longer than predicted by theory applicable toNewtonian fluids. Depending on the axis ratio and shear rate, the particles drifted into orbits in which the conventional orbit constantC varied periodically throughout each orbit. Above a given shear rate, rods aligned themselves in the direction of flow without rotating, in a metastable equilibrium position; in the case of discs at higher shear rates the position of alignment was stable.The oscillating deformation and orientation of drops in a system of two solubleNewtonian silicone oils was in fair accord with theory. With pairs of elasticoviscous polyacrylamide solutions, deformation and burst of viscous drops occurred along the vorticity axis, in contrast to the behaviour of elasticoviscous drops of polyisobutylene in Decalin having a finite interfacial tension, which deformed and burst in a manner similar toNewtonian drops.

---

Zusammenfassung Die Rotation starrer Stäbchen und Scheibchen sowie die Verformung und das Aufbrechen flüssiger Tröpfchen wurde in viskoelastischen Polyacrylamid-Lösungen untersucht, die in einerCouette-Apparatur mit Schergeschwindigkeiten zwischen 0,1 und ca. 10 sec^–1 geschert wurden. Diese Untersuchung ergänzt eine frühere Arbeit (1), insofern zylindrische Teilchen mit einem Achsenverhältnis näher bei eins und Tröpfchen in Systemen mit verschwindender Grenzflächenspannung berücksichtigt werden.Die Umdrehungsperiode der Scheibchen kam erheblich langsamer heraus, als sie auf Grund der fürnewtonsche Flüssigkeiten gültigen Theorie vorausgesagt wird. Die Teilchen trieben, abhängig von ihren Achsenverhältnissen und der Schergeschwindigkeit, in Kreisbahnen hinein, für welche die konventionelle KreisbahnkonstanteC sich periodisch änderte. Oberhalb einer bestimmten Schergeschwindigkeit orientierten sich die Stäbchen in Richtung der Strömung in einer metastabilen Gleichgewichtseinstellung; für Scheibchen war bei höheren Schergeschwindigkeiten diese Einstellung stabil.Oszillationsverformung und Orientierung der Tröpfchen in einem System zweier ineinander lösbarernewtonscher Siliconöle stimmte zufriedenstellend mit der Theorie überein. Für Paare viskoelastischer Polyacrylamid-Lösungen wurden die zähen Tröpfchen entlang der Richtung der Rotationsachse verformt und aufgebrochen im Gegensatz zu viskoelastischen, eine endliche Grenzflächenspannung aufweisenden Tröpfchen von Polyisobutylen in Dekalin, die ähnlich wienewtonsche Tröpfchen verformt und aufgebrochen wurden.

---

---

This paper is, in effect, an addendum to Reference (1). To avoid unnecessary repetition, identical symbols have been used (with the addition of andD which are defined in the text), and frequent use is made of figures and equations from references (1) and (2).

---

This work was supported by the Defence Research Board of Canada. (DRB Grant 9530-47).

---

With 3 figures and 2 tables     

Time-asymptotic stability of non-newtonian fluid or plastic solid

We consider adiabatic shearing of solids exhibiting strain rate sensitivity and thermal softening or non-Newtonian liquids with temperature dependent viscosity. The processes are caused by a steady boundary force. We prove that there exists a unique solution and, as the time tends to ∞, the processes converge to the shearing under constant shear stress. The proof is based on a priori estimates, which are obtained with the help of identities for solutions of the system of conservation laws and constitutive relation describing the processes. The result idicates that, as expected, the viscosity or thermal diffusion play a stabilizing role.     

Transient spherical flow of non-newtonian power-law fluids in porous media

The transient spherical flow behavior of a slightly compressible non-Newtonian, power-law fluids in porous media is studied. A nonlinear partial differential equation of parabolic type is derived. The diffusivity equation for spherical flow is a special case of the new equation. We obtain analytical, asymptotic and approximate solutions by using the methods of Laplace transform and weighted mass conservation. The structures of asymptotic and approximate solutions are similar, which enriches the theory of one-dimensional flow of non-Newtonian fluids through porous media.     

Convective stability of a vertical layer of a non-newtonian liquid

We consider the convective stability of a non-Newtonian (nonlinearly viscous) liquid in a two-dimensional vertical channel. We solve a nonlinear boundary value problem concerning plane-parallel stationary convection for the case of piecewise-linear and power-law type rheological characteristics. We discuss the problem concerning the stability of equilibrium and of stationary motions.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 88–95, September–October, 1973.The authors thank D. V. Lyubimov for his help in carrying out the calculations.     

The stability of two stratified non-newtonian liquids in couette flow

Consideration is given to the stability of the interface between two Oldroyd liquids with shear-dependent viscosities, flowing in distinct layers while undergoing plane Couette flow. Results are presented as regions of stability in the plane determined by the logarithms of the viscosity and depth ratios. The work of previous authors for two Newtonian, power-law and constant-viscosity Oldroyd liquids is revealingly presented in a similar fashion. It is found that the dependence of the viscosities on shear-rate can drastically affect the regions of interfacial stability in a way over and above that due to just a change in the effective viscosity ratio. It is also found that for the Oldroyd liquids this viscosity variation affects the stability when it is present in the less-viscous layer.     

The nonlinear stability of plane poiseulle flow for non-newtonian power series fluid

Non-Newtonan fluid is a kind of fluid whose components of stresstensor aren’t theliear funtions of compoents of the strain rate tensor.Non-Newtonianfluid is beingprocessed in many kinds of modern industry,Stability of flows for Non-Newtonianfluid is of important applicatuib,In this article we calculate subcritical thrdshold of flow which oecurs in polymer-processing when the melting substance is driven throughtwo parallel fixed boundaries.     

Hydrodynamic stability of boundary layers with mass transfer

The stability of boundary layers involving mass transfer described by a two-parameter family of Fockner-Scane (F-S) solutions is analyzed. An effective method of solving the boundary problem is proposed for the F-S equation. A determinant method is proposed for solving the stability equation. The critical values of the stability characteristics are found over a wide range of gradient and mass-transfer parameters.     

Hydrodynamic stability of boundary layers with surface mass transfer

The linear stability of the flat plate boundary layer with surface blowing and suction is investigated by the application of numerical techniques. Complete neutral stability curves, critical Reynolds numbers and wave numbers, and other stability characteristics are determined for a wide range of surface mass transfer intensities. The critical Reynolds number, based on the displacement thickness, is found to vary from 59 to 32500 between the extreme limits of blowing and suction that are investigated. Comparisons are made between the present results and available linear stability information for boundary layers with surface mass transfer and with free-stream pressure gradients. The universal stability bound of Joseph is evaluated and compared with the corresponding numerically exact neutral stability curve.     

Hydrodynamic averaging of highly inhomogeneous porous media with linear flow

A method is proposed for constructing homogeneous anisotropic models of new classes of highly inhomogeneous nondeformable porous media consisting of arbitrarily oriented systems of layers representing fractures and impermeable barriers (screens) embedded in each other with an arbitrary depth of embedment. It is assumed that the permeability functions of the elementary cells of the media can be represented in some Cartesian coordinate system (proper to each cell) in the form of a product of three integrable functions that depend on the corresponding coordinates. As distinct from known methods of averaging differential operators, the method in question is based on porous media flow considerations and reduces to replacing the highly inhomogeneous soils with homogeneous anistropic soils, so that on the boundaries of the domain considered the basic flow parameters remain the same.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika, Zhidkosti i Gaza, No. 5, pp. 190–192, September–October, 1993.     

Hydrodynamic stability of Poiseuille flow of a viscoplastic non-Newtonian fluid

The hydrodynamic stability of Poiseuille flow of a viscoplastic fluid is investigated. The flow is shown to be stable for infinitesimal disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 152–154, November–December, 1974.In conclusion the authors thank S. A. Regirer for critical remarks.     

The approximate solution of the self-similar problem for radial flow of non-newtonian fluids through porous media

In this paper, we study the approximate solution of the self-simikar problem for radial flow of non-Newtonian fluids through porous media. Assuming that the fluids obey the exponential function law, we obtain an exact solution for the exponent n=0 and compare it with the approximate solution in ref. [1]. For n>1 and n<1, we obtain respectively approximate solutions. Some exampls are presented.     

The stability of a revolving non-newtonian liquid in the presence of an axial pressure gradient

Summary The effect of cross-viscosity on the stability in fluids has been investigated. It is found that this effect destabilizes the flow of an incompressible non-newtonian liquid between coaxial rotating cylinders when an axial pressure gradient is applied.     

Hydrodynamic stability of dense plasma in a corrugated magnetic field

The hydrodynamic stability of plasma in a corrugated magnetic field is considered. A stability criterion is established for flute oscillations; it is valid for arbitrary values of β = 8πp/B². In a fairly long system unstable flute perturbations with a wavelength much greater that the period of corrugation always exist. The equations of motion are solved for these most dangerous perturbations, and the instability increments are derived for the case of an ideal plasma and also with due allowance for viscosity. The viscosity is considerable for large β and may lead to a reduction by a factor of ～ √β in the increments.     

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.     

Hydrodynamic stability,the Chebyshev tau method and spurious eigenvalues

The Chebyshev tau method is examined; a numerical technique which in recent years has been successfully applied to many hydrodynamic stability problems. The orthogonality of Chebyshev functions is used to rewrite the differential equations as a generalized eigenvalue problem. Although a very efficient technique, the occurrence of spurious eigenvalues, which are not always easy to identify, may lead one to believe that a system is unstable when it is not. Thus, the elimination of spurious eigenvalues is of great importance. Boundary conditions are included as rows in the matrices of the generalized eigenvalue problem and these have been observed to be one cause of spurious eigenvalues. Removing boundary condition rows can be difficult. This problem is addressed here, in application to the Bénard convection problem, and to the Orr-Sommerfeld equation which describes parallel flow. The procedure given here can be applied to a wide range of hydrodynamic stability problems.Received: 4 July 2002, Accepted: 13 September 2002, Published online: 27 June 2003     

Hydrodynamic models as applied to the investigation of magnetic plasma stability

In the present paper magnetohydrodynamic models are employed to investigate the stability of an inhomogeneous magnetic plasma with respect to perturbations in which the electric field may be regarded as a potential field (rot E 0). A hydrodynamic model, actually an extension of the well-known Chew-Goldberg er-Low model [1], is used to investigate motions transverse to a strong magnetic field in a collisionless plasma. The total viscous stress tensor is given; this includes, together with magnetic viscosity, the so-called inertial viscosity.Ordinary two-fluid hydrodynamics is used in the case of strong collisions=. It is shown that the collisional viscosity leads to flute-type instability in the case when, collisions being neglected, the flute mode is stabilized by a finite Larmor radius. A treatment is also given of the case when epithermal high-frequency oscillations (not leading immediately to anomalous diffusion) cause instability in the low-frequency (drift) oscillations in a manner similar to the collisional electron viscosity, leading to anomalous diffusion.Notation f particle distribution function - E electric field component - H₀ magnetic field - density - V particle velocity - e charge - m, M electron and ion mass - _i, _e ion and electron cyclotron frequencies - viscous stress tensor - P pressure - r_i Larmor radius - P pressure tensor - t time - frequency - T temperature - collision frequency - collision time - j current density - _i, _e ion and electron drift frequencies - k_x, k_y, k_z wave-vector components - n₀ particle density - g acceleration due to gravity. The authors are grateful to A. A. Galeev for valuable discussion.     

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.