Solutions For Viscosity Research Articles

Reciprocal identities and integral formulations for diffusive scalar transport and Stokes flow with position-dependent diffusivity or viscosity

Reciprocal relations between any two solutions of the equations of diffusive scalar transport with position-dependent diffusivity are derived, and integral representations involving the Green’s function of Laplace’s equation and accompanying integral equations are developed. When the diffusivity exhibits mild variations over the solution domain, the rate of transport across an isoscalar surface can be predicted from the solution for uniform diffusivity. A corresponding analysis is presented for the equations of Stokes flow with position-dependent fluid viscosity. When the viscosity exhibits mild variations, the force and torque exerted on a surface moving as a rigid body can be predicted from the solution for constant viscosity. Numerical methods for solving the integral equations based on boundary-element and domain discretizations into triangular elements are developed in two dimensions.

FLOW OF A JEFFREY FLUID THROUGH A POROUS MEDIUM IN NARROW TUBES

In this paper, the effects of porous medium on a two-fluid model for the flow of Jeffrey fluid in tubes of small diameters are studied. It is assumed that the core region consists of Jeffrey fluid and Newtonian fluid in the peripheral region. The analytical solutions for velocity, flow flux, effective viscosity, core hematocrit and mean hematocrit have been derived and the effects of various relevant parameters on these flow variables have been studied. It is noticed that the flow exhibits the anomalous Fahraeus-Lindqvist effect.

Numerical Solution for Variable Viscosity and Internal Heat Generation Effects on Boundary Layer Flow Over an Exponentially Stretching Porous Sheet with Constant Heat Flux and Thermal Radiation

AbstractA numerical study has been carried out to analyze the constant heat flux, internal heat generation, variable viscosity and thermal radiation effects on the flow and heat transfer of a Newtonian fluid over an exponentially stretching porous sheet. Using a similarity transformation, the governing partial differential equations are transformed into coupled, non-linear ordinary differential equations with variable coefficients. Numerical solutions to these equations subject to appropriate boundary conditions are obtained by using an efficient Chebyshev spectral method. The effects of various physical parameters such as viscosity parameter, the suction parameter, the radiation parameter, internal heat generation or absorption parameter and the Prandtl number on velocity and temperature are discussed by using graphical approach. Moreover, numerical results indicate that in the presence of constant heat flux, the skin-friction coefficient as well as Nusselt number is strongly affected by the viscosity parameter, suction parameter, radiation parameter and the internal heat generation parameter.

Numerical approach to the Stokes problem with high contrasts in viscosity

An algorithm based on Sherman–Morrison–Woodbury formula to solve numerically the Stokes problem is described. The algorithm allows to obtain the solution for viscosity contrasts up to ten orders of magnitude, moreover solution speed does not depend on viscosity contrast. Tests of accuracy of the algorithm are provided.

Wave-modified Ekman current solutions for the vertical eddy viscosity formulated by K-Profile Parameterization scheme

A Fourier series solution is presented for the time-dependent wave-modified Ekman current resulting from the Stokes drift, wind input and wave dissipation for the vertical eddy viscosity formulated by the K-Profile Parameterization scheme. An exact steady solution can be concluded as a special example. The parameters involved in the solution can be determined by the two-dimensional surface wave spectrum, wind vector, the Coriolis parameter and the densities of air and water. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with those when wave is absent or includes only the effect of the Stokes drift by using the extended Donelan and Pierson (1987) spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. The exact solutions are also compared with well-known published observational data of the Ekman layer. It is shown that the solution presented is a reasonable analytic current model with the right dependence on wind, wave and Coriolis parameter for unstratified Ekman layer.

Treating Heavy Oil Wastewater for Beneficial Use by Integrated Technology of Bio-Oxidation and RO

Heavy oil exploitation wastewater is characterized by its high concentration of emulsified oil, high salinity, high temperature and complex chemical components. This paper discuss a successful pilot-scale demonstration application of a unique technology integrating heat exchanger, gas floatation, biological contact oxygen, filtration, ultra-filtration, reverse osmosis at Chenzhuang oilfield. The scale of the process was about 360 m 3 /d, and the performance of the treatment process, the effectiveness of the technology for removal of oil and for controlling RO membranes fouling, and the economic effect are also discussed. Operation results show that the biological contact oxidation--ultra filtration process can reduce the oil contents to less than 0.5 mg/L and TDS to less than 3. The conductivity of RO effluent is below 456 μS·cm -1 , the treated water can meet the required standard for steam-injected boiler, and it can also be used to prepare polymer solution for viscosity keeping. Key words : Heavy oil wastewater; Biological contact oxygen; RO; Steam boiler; Polymer solution

Remarks on vanishing viscosity limits for the 3D Navier-Stokes equations with a slip boundary condition

The authors study vanishing viscosity limits of solutions to the 3-dimensional incompressible Navier-Stokes system in general smooth domains with curved boundaries for a class of slip boundary conditions. In contrast to the case of flat boundaries, where the uniform convergence in super-norm can be obtained, the asymptotic behavior of viscous solutions for small viscosity depends on the curvature of the boundary in general. It is shown, in particular, that the viscous solution converges to that of the ideal Euler equations in C([0, T];H1(Ω)) provided that the initial vorticity vanishes on the boundary of the domain.

On the evolving flow of grains down a chute

A continuum model leads to a partial differential equation for the evolving flow of grains down a chute. This is addressed for different effective viscosities in the system. Solutions for small viscosity are obtained which describe separating grains and clashing grains. Steady-state solutions are also found for any viscosity value, these being considered as a large time limit. Restrictions on the steady-state solutions are discussed, along with cases which yield re-structuring within a finite time.

Functional Properties of Extrudates Prepared with Blends of Wheat Flour/Pinto Bean Meal with Added Wheat Bran

Blends made of wheat flour and bean meal at various levels of moisture and bran content, were subjected to extrusion cooking by varying temperature and screw speed. Extrudates were analysed for expansion index, bulk density, apparent viscosity, water absorption index and water solubility index using a second-order rotatable central composite design. Excepting water absorption index, functional properties were significantly affected ( p<0.05) by levels of moisture, bran or extrusion conditions. Expansion index decreased with increasing levels of moisture in the blends; for bran the effect was the inverse. Response surface solution for apparent viscosity was maximum at 24% levels of moisture, 209r.p.m., 180°C and 10% bran. For water absorption index the response surface solution was a saddle point, with a minimum at 29% levels of moisture, 232r.p.m., 177°C and 25% bran. The higher apparent viscosity and lower absorption index reflected minor damage to starch and proteins, which was attributed to a protective role of the added fibre.

Effective Viscosity of Suspensions of Spheres

Modeling the effective viscosity of suspensions of spheres beyond the dilute limit is a difficult problem that has challenged researchers for nearly a century since Einstein derived an equation for dilute suspensions. Hydrodynamics modeling requires complex mathematical treatments of integral equations describing interactions between spheres, and its solutions have been limited to semidilute dispersion of monosized hard spheres. Mechanics modeling treats suspensions in a statistical sense and generally provides upper and lower bounds solutions for polydispersed suspensions. A closed‐form solution for the effective viscosity of concentrated suspensions of monosized spheres using both the elastic‐viscous analogy and the analogy between the effective dielectric constant of a polarizable medium and the effective viscosity of two‐phase flow is derived in the present study. Existing measurements and numerical simulations support present analytical results. A closed‐form solution for polydispersed suspensions using a differential model is also derived, and the results are within existing bounds solutions.

Constitutive equations for extensional flow of wormlike micelles: stability analysis of the Bautista–Manero model

We carry out a stability analysis of the Bautista–Manero (B–M) constitutive equations for extensional flow of wormlike micelles. We show that all solutions for the steady-state extensional viscosity η E are unstable when the elongational rates ɛ ˙ exceed some critical value. In some cases the only real solution for the extensional viscosity is negative at intermediate values of the elongational rate. This critical elongational rate is not unfeasibly large, e.g., 250 s −1 for a typical EHAC solution. We note that the extension rates at which enhanced pressure drop is observed experimentally in porous media flow is generally well below the onset of the instability in the B–M model. However, the extension rates presented here are only average values for the porous media in question and at the pore scale a wide range of values will be encountered. For this reason, we require an improved rheological equation of state. We first separate the contributions to the viscosity of the solution and the wormlike micelles. Then, we remove the term containing the retardation time λ J . We now find that the extensional flow behaviour is well defined for both the transient and steady-state cases.

Mass Transport Velocity in Free Barotropic Poincaré Waves

Abstract The mass transport velocity induced by long surface waves in a shallow, rotating viscous ocean is studied theoretically by using a Lagrangian description of motion. The depth is constant, and the water is homogeneous. Such waves are referred to as Poincare waves, or sometimes Sverdrup waves, where the latter name usually is reserved for cases in which the effect of friction is taken into account. In the linear case, the primary wave field is significantly affected by the earth's rotation, requiring wave frequencies that are larger than the inertial frequency. In the nonlinear case, the inviscid version of these waves does not induce any mean mass transport. This situation changes when the effect of viscosity is taken into account, and it is shown that for long waves there exists a mean Lagrangian flow confined to a suitably defined bottom friction layer. A solution for constant eddy viscosity and a no-slip bottom is obtained analytically. This result is compared with those obtained numerically fo...

On global solutions for the Constantin–Lax–Majda equation with a generalized viscosity term

We consider a one-dimensional model for the three-dimensional vorticity equation of incompressible and viscous fluids. This model is obtained by adding a generalized viscous diffusion term to the Constantin–Lax–Majda equation, which was introduced as a model for the three-dimensional Euler equation (Constantin P, Lax P D and Majda A 1985 A simple one-dimensional model for the three-dimensional vorticity equation Commun. Pure. Appl. Math. 38 715–24). It is shown in Sakajo T (2003 Blow-up solutions of the Constantin–Lax–Majda equation with a generalized viscosity term J. Math. Sci. Univ. Tokyo 10 187–207) that the solution of the model equation blows up in finite time for sufficiently small viscosity, however large a diffusion term it may have. In this paper, we discuss the existence of a unique global solution for large viscosity.

Non-persistence of roll-waves under viscous perturbations

In this paper, we study the existence of periodic traveling waves for the equations of the Shallow-water theory with a small viscosity. This small viscosity leads to a singularly perturbed problem. The slow-fast system involves a point where normal hyperbolicity breaks down. We first prove the existence of a slow manifold around this point. Then we show that there are no periodic solutions for small viscosity and describe completely the structure of a travelling wave.

SIMULATION STUDY OF SELECTIVE CEREBRAL PERFUSION SYSTEM WITH SINGLE CENTRIFUGAL PUMP

Background: We successfully developed a simple and safety non-roller extra-corporeal circulation system (NRECC). In aortic arch operation, more than two pumps are generally used for usual perfusion and selective cerebral perfusion (SCP). We newly developed a pressure-dependent perfusion system for SCP. The system was developed based on the NRECC we developed and was operated with a single centrifugal pump (Figure). Method: The cerebral perfusion line was branched from the main perfusion line. The perfusion pressure was regulated with a tube occluder. Glycerin was added to the priming solution for a similar viscosity to blood.FigureIn this study, one 15F and two 12F cannulae were used for SCP. After load was changed from 30 to 80 mmHg, and the pressure of the SCP line was increased from 80 to 200 mmHg and flow volume were measured. Results When after load was set at 50mmHg, according to the change of the perfusion pressure, flow volume of 15F cannula increased from 280 to 950 ml/min.FigureIn the same condition, flow volume of 12F cannula increased from 160 to 560 ml/min. Conclusions: The flow volume of the SCP lines was sufficiently obtained under the SCP line pressure over 80mmHg. These suggested that aortic arch operation is possible using this SCP system.

A mathematical model and numerical solution technique for a novel adjustable hydrodynamic bearing

An analysis model for a novel adjustable hydrodynamic fluid film bearing is described. The principles of hydrodynamic lubrication are outlined together with an expanded version of the governing pressure field equation as related to the novel bearing. Finite difference approximations are given for the pressure field equation and a temperature model, both related to the fluid film thickness. Relationships of viscosity with temperature and pressure are included. A finite element model and an iterative computational process are described, whereby full simultaneously converged field solutions for fluid film thickness, temperature, viscosity and pressure were obtained, together with oil film forces. The model and solution process were developed to apply to a variety of hydrodynamic bearings and an outline is given of its extensive use in the design and simulation of one version of the novel bearing. Observations are given on the operation, success rates and verifications of the computational process. Copyright © 1999 John Wiley & Sons, Ltd.

A mathematical model and numerical solution technique for a novel adjustable hydrodynamic bearing

An analysis model for a novel adjustable hydrodynamic fluid film bearing is described. The principles of hydrodynamic lubrication are outlined together with an expanded version of the governing pressure field equation as related to the novel bearing. Finite difference approximations are given for the pressure field equation and a temperature model, both related to the fluid film thickness. Relationships of viscosity with temperature and pressure are included. A finite element model and an iterative computational process are described, whereby full simultaneously converged field solutions for fluid film thickness, temperature, viscosity and pressure were obtained, together with oil film forces. The model and solution process were developed to apply to a variety of hydrodynamic bearings and an outline is given of its extensive use in the design and simulation of one version of the novel bearing. Observations are given on the operation, success rates and verifications of the computational process. Copyright © 1999 John Wiley & Sons, Ltd.

On Nonlinear Ekman Surface-Layer Pumping

Simple expressions are presented for the corrections to the classic Ekman pumping law We = ẑ·curl(τ0/f) due to nonlinear advection effects in the surface boundary layer. These involve products of the surface Reynolds stress, τ0 and the underlying ocean currants v0(x, y, t) and their derivatives, and products of τ0(x, y, t) and its own derivatives. The former interaction is independent of the turbulence closure, while the latter is obtained using solutions for a constant eddy viscosity. The corrections are usually small, as is assumed when the linear Ekman pumping relation is applied in ocean modeling. However, they can become significant in circumstances involving very high wind stresses (e.g., a hurricane), or in situations where a strong narrow oceanic current flows under a region of moderate but perhaps relatively uniform surface stress.

A very slowly moving viscous shock of burgers' equation in the quarter plane

We study slowly moving viscous shock associated with the Burgers equation defined in the quarter plane ubject to the constant input data. The true splution for the given problem is derived by using the classical Cole-Hopf transformation and the Robin function of the resultant problem, and is written in terms of the complementary error function and its first iterated integral. A viscous shocj structure is botained by analyzing the asymptotic behavior of the true solution for small viscosity and is expressed in terms of the hyperbolic tangent function. The obtained viscous shocj is not of the form that one might expect a Pariori. The location of the viscous shock, which is governed by a nonlin ear algebraic equation, is solved by using the Lambert W function. A full charactrization of shock location and shock speed is shown.

On the one-dimensional nonlinear elastohydrodynamic lubrication

In this paper the authors prove an abstract theorem for solutions of a variational inequality on a cone and use it to study the free boundary problem of elastohydrodynamic lubrication from mechanical engineering. The mathematical model is set in a one-dimensional geometry. The existence of a solution for every non-negative lubricant viscosity is proved, and some properties useful for the numerical analysis are obtained.