Infinite interval problems arising in non-linear mechanics and non-Newtonian fluid flows

Existence results are presented for second-order boundary value problems on the infinite interval modelling phenomena which arise in non-Newtonian fluid theory and in circular membranes.     

Dynamics of non-Newtonian fluid interfaces in a porous medium: Incompressible fluids

This paper concerns the applications of frontal advance theory to the dynamics of a moving flat interface in a porous medium, when both displacing and displaced fluids are of power law behaviour. The rheological effects of non-Newtonian behaviour of these fluids on the interface position and its velocity are numerically illustrated and discussed with regard to the practical implications in oil displacement mechanisms. The results obtained should be useful in finding an optimal policy of injection in order to control the dynamics of the moving interface in field projects of enhanced oil recovery floods.     

Comparison of two numerical methods for the solution of non-Newtonian flow in ducts

Two numerical methods, the Galerkin finite element method (FEM) and the boundary-fitted co-ordinate transformation method (BFCTM), have been applied to solve inelastic non-Newtonian fluid flow in ducts of irregular cross-section. Three representative fluid models, namely the power-law, the Ellis and the Bingham models, have been analysed. The application of the FEM is straightforward, while for the BFCTM the accurate estimation of viscosity on the duct boundary and the proper mesh adjustment appear to be critical for generating convergent solutions. A detailed comparison of the two numerical methods in terms of volumetric flow rate, axial velocity, shear rate, viscosity and CPU time is given. Both methods can generate accurate solutions of velocity over a wide range of variables, but the FEM requires much less computing time to reach the same level of accuracy. Only the BFCTM can be used to approximate shear rate and viscosity with reasonable accuracy.     

Automatic extraction using the mini-column liquid chromatography method for analysis of drugs of abuse in biological fluids

Summary The preparation of an automatic extractor using ODS-minicolumn (25mm × 9mm i.d.) for analysis of drugs of abuse in biological fluids and its application are described. The auto-extraction method consists of the sequential operations, adsorption-washing (clean up)-elution(collection of the analyte) and regeneration of column, which continue repeatedly. Recoveries of drugs from spiked plasma and urine samples with the auto-extractor were almost quantitative at the optimum pH and much better than that of the conventional extraction with ether. Reproducibility of the auto-extraction was fairly good and the relative standard deviations of 10 measurements for methamphetamine, THC, morphine, cocaine and methaqualone in urine and plasma were from 0.55% to 4.35%. The simultaneous extractions of methamphetamine, THC, tranquilizers and their metabolites in urine with the autoextractor are presented as applications. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

Simulation of non-Newtonian ink transfer between two separating plates for gravure-offset printing

The inks used in gravure-offset printing are non-Newtonian fluids with higher viscosities and lower surface tensions compared to Newtonian fluids. This paper examines the transfer of a non-Newtonian ink between two parallel plates when the top plate is moved upward with a constant velocity while the bottom plate is held fixed. Numerical simulations were carried out using the Carreau model to explore the behavior of a non-Newtonian ink in gravure-offset printing. The volume of fluid (VOF) model was adopted to demonstrate the stretching and break-up behaviors of the ink. The results indicate that the ink transfer ratio is greatly influenced by the contact angle, especially the contact angle at the upper plate (α). For lower values of α, oscillatory or unstable behavior of the position of minimum thickness of the ink between the two parallel plates during the stretching period is observed. This oscillation gradually diminishes as the contact angle at the upper plate is increased. Moreover, the number of satellite droplets increases as the velocity of the upper plate is increased. The surface tension of the conductive ink shows a positive impact on the ink transfer ratio to the upper plate. Indeed, the velocity of the upper plate has a significant influence on the ink transfer in gravure-offset printing when the Capillary number (Ca) is greater than 1 and the surface tension dominates over the ink transfer process when Ca is less than 1.     

Quantification of fluids injection in a glass-bead matrix using X-ray microtomography

Several daily activities involve the accumulation or percolation of fluids through porous media. X-ray microtomography is a non-invasive technique capable of providing images of the internal microstructure of materials showing the different phases of fluid distribution present in the sample directly or at the pore-scale. This methodology was used to qualitatively and quantitatively assess samples consisting with glass beads of standard size, which contained fluid filling a porous region. Three samples were prepared with 0.6 mm or 0.8 mm diameter glass beads inserted into a glass tube with an inner diameter of 6.7 mm and 1.0 mm wall thickness. The fluids injected were dopant salt–water solution, industrial oil and commercial oil. The samples were scanned using a Skyscan-1172 microtomographic system. All phases present in the sample were differentiated. The values of injected fluids were determined through 2D and 3D analyses. Two types of solutions were used, one doped with KI, and the other with BaCl₂·2H₂O. The percentage of KI used allowed the individualization of the solution and, therefore, the direct quantification of this phase through 2D and 3D images.     

Group properties and exact solutions for two-dimensional flow of a non-newtonian fluid

The Group Properties and the associated Lie Algebra are developed for the equations of motion of the unsteady two-dimensional flow of a non-Newtonian fluid in cartesian coordinates. Then by using the full one-parameter infinitesimal transformation group and its subgroups a number of exact solutions are obtained.     

Weak solutions to the generalized Navier–Stokes equations with mixed boundary conditions and implicit obstacle constraints

This paper is concerned with the investigation of a generalized Navier–Stokes equation for non-Newtonian fluids of Bingham-type (GNSE, for short) involving a multivalued and nonmonotone slip boundary condition formulated by the generalized Clarke subdifferential of a locally Lipschitz superpotential, a no leak boundary condition, and an implicit obstacle inequality. We obtain the weak formulation of (GNSE) which is a generalized quasi-variational–hemivariational inequality. By introducing an Oseen model as an auxiliary (intermediated) problem and employing Kakutani-Ky Fan theorem for multivalued operators as well as the theory of nonsmooth analysis, an existence theorem to (GNSE) is established.     

Inertia effects in circular squeeze film bearing using Herschel–Bulkley lubricants

Recent engineering trends in lubrication emphasize that in order to analyze the performance of bearings adequately, it is necessary to take into account the combined effects of fluid inertia forces and non-Newtonian characteristics of lubricants. In the present work, the effects of fluid inertia forces in the circular squeeze film bearing lubricated with Herschel–Bulkley fluids with constant squeeze motion have been investigated. Herschel–Bulkley fluids are characterized by an yield value which leads to the formation of a rigid core in the flow region. The shape and extent of the core formation along the radial direction is determined numerically for various values of Herschel–Bulkley number and power-law index. The bearing performances such as pressure distribution and load capacity for different values of Herschel–Bulkley number, Reynolds number, power-law index have been computed. The effects of fluid inertia and non-Newtonian characteristics on the bearing performances have been discussed.     

Time dependent viscosity of concentrated alumina suspensions

Viscometric investigations of concentrated aqueous alumina suspensions with particles smaller than 5 μm have been performed. Experimental flow curves indicate thixotropy in the shear rate interval between =20 and 640 s⁻¹. In the range smaller than =200 s⁻¹ we found pseudoplastic flow behavior, in the higher range the material shows dilatancy. The non-Newtonian behavior results from a small content of sodium aluminum oxide in the alumina suspension. This gives rise to interparticle forces that can drive the suspension into a gel-like state. The time scale of this process is some days. On the short-time scale of some hours the material ages slowly increasing moderately the apparent viscosity. Studying the relaxation process after a shear rate jump, the shear stress time dependency at constant shear rate follows an exponential law. There is a single particular relaxation time for each shear rate. The relaxation towards a steady state occurs asymptotically over some 10³ s. Flow curves calculated from steady state data after relaxation processes are below the experimental flow curves which were measured during some 100 s. The flow curves follow the Herschel–Bulkley formula. The shape of the viscosity curves indicates changes of suspension structure at ca. =200 and 400 s⁻¹. At constant shear rates in the interval between =400 and 450 s⁻¹ the apparent viscosity of the alumina suspension fluctuates periodically in time in the same manner found for other suspensions. This effect is interpreted as periodic organization of agglomeration and deglomeration processes. Supposing, that the stabilisation energy of agglomerates is of the order of the energy introduced by the mechanical shear field, the observation of oscillations at =400 s⁻¹ is in agreement with the drastic slope change in the viscosity curves.