Capillary break-up rheometry of low-viscosity elastic fluids

We investigate the dynamics of the capillary thinning and break-up process for low viscosity elastic fluids such as dilute polymer solutions. Standard measurements of the evolution of the midpoint diameter of the necking fluid filament are augmented by high speed digital video images of the break up dynamics. We show that the successful operation of a capillary thinning device is governed by three important time scales (which characterize the relative importance of inertial, viscous and elastic processes), and also by two important length scales (which specify the initial sample size and the total stretch imposed on the sample). By optimizing the ranges of these geometric parameters, we are able to measure characteristic time scales for tensile stress growth as small as 1 millisecond for a number of model dilute and semi-dilute solutions of polyethylene oxide (PEO) in water and glycerol. If the final aspect ratio of the sample is too small, or the total axial stretch is too great, measurements are limited, respectively, by inertial oscillations of the liquid bridge or by the development of the well-known beads-on-a-string morphology which disrupt the formation of a uniform necking filament. By considering the magnitudes of the natural time scales associated with viscous flow, elastic stress growth and inertial oscillations it is possible to construct an operability diagram characterizing successful operation of a capillary break-up extensional rheometer. For Newtonian fluids, viscosities greater than approximately 70 mPas are required; however for dilute solutions of high molecular weight polymer, the minimum Viscosity is substantially lower due to the additional elastic stresses arising from molecular extension. For PEO of molecular weight 2.10(6) g/mol, it is possible to measure relaxation times of order 1 ms in dilute polymer solutions with zero-shear-rate viscosities on the order of 2-10 mPas.

Development of a quasi-chemical viscosity model for fully liquid slags in the Al2O3-CaO-'FeO'-MgO-SiO2 system. Part 1. Description of the model and its application to the MgO, MgO-SiO2, Al2O3-MgO and CaO-MgO sub-systems

A structurally-based quasi-chemical viscosity model for fully liquid slags in the Al2O3 CaO-'FeO'-MgO-SiO2 system has been developed. The model links the slag viscosities to the internal structures of the melts through the concentrations of various Si0.5O, Me2/nn+O and Me1/nn+Si0.25O viscous flow structural units. The concentrations of these structural units are derived from a quasi-chemical thermodynamic model of the system. The model described in this series of papers enables the viscosities of liquid slags to be predicted within experimental uncertainties over the whole range of temperatures and compositions in the Al2O3 CaOMgO-SiO2 system.

Development of a quasi-chemical viscosity model for fully liquid slags in the Al2O3-CaO-'FeO'-MgO-SiO2 system. Part 2. A review of the experimental data and the model predictions for the Al2O3-CaO-MgO, CaO-MgO-SiO2 and Al2O3-MgO-SiO2 systems

A structurally-based quasi-chemical viscosity model has been developed for the Al2O3 CaO-'FeO'-MgO-SiO2 system. The model links the slag viscosity to the internal structure of melts through the concentrations of various anion/cation Si0.5O, Me2/nn+O and Me1/nn+Si0.25O viscous flow structural units. The concentrations of structural units are derived from the quasi-chemical thermodynamic model. The focus of the work described in the present paper is the analysis of experimental data and the viscosity models for fully liquid slags in the Al2O3-CaO-MgO, Al2O3 MgO-SiO2 and CaO-MgO-SiO2 systems.

Transport of simple fluids in nanopores: Theory and simulation

A theory is discussed of single-component transport in nanopores, recently developed by Bhatia and coworkers. The theory considers the oscillatory motion of molecules between diffuse wall collisions, arising from the fluid-wall interaction, along with superimposed viscous flow due to fluid-fluid interaction. The theory is tested against molecular dynamics simulations for hydrogen, methane, and carbon tetrafluoride flow in cylindrical nanopores in silica. Although exact at low densities, the theory performs well even at high densities, with the density dependency of the transport coefficient arising from viscous effects. Such viscous effects are reduced at high densities because of the large increase in viscosity, which explains the maximum in the transport coefficient with increase in density. Further, it is seen that in narrow pore sizes of less than two molecular diameters, where a complete monolayer cannot form on the surface, the mutual interference of molecules on opposite sides of the cross section can reduce the transport coefficient, and lead to a maximum in the transport coefficient with increasing density. The theory is also tested for the case of partially diffuse reflection and shows the viscous contribution to be negligible when the reflection is nearly specular. (c) 2005 American Institute of Chemical Engineers AIChE J, 52: 29-38, 2006.

The effect of blending on selected physical properties of crude oils and their products

A study was made of the effect of blending practice upon selected physical properties of crude oils, and of various base oils and petroleum products, using a range of binary mixtures. The crudes comprised light, medium and heavy Kuwait crude oils. The properties included kinematic viscosity, pour point, boiling point and Reid vapour pressure. The literature related to the prediction of these properties, and the changes reported to occur on blending, was critically reviewed as a preliminary to the study. The kinematic viscosity of petroleum oils in general exhibited non-ideal behaviour upon blending. A mechanism was proposed for this behaviour which took into account the effect of asphaltenes content. A correlation was developed, as a modification of Grunberg's equation, to predict the viscosities of binary mixtures of petroleum oils. A correlation was also developed to predict the viscosities of ternary mixtures. This correlation showed better agreement with experimental data (< 6% deviation for crude oils and 2.0% for base oils) than currently-used methods, i.e. ASTM and Refutas methods. An investigation was made of the effect of temperature on the viscosities of crude oils and petroleum products at atmospheric pressure. The effect of pressure on the viscosity of crude oil was also studied. A correlation was developed to predict the viscosity at high pressures (up to 8000 psi), which gave significantly better agreement with the experimental data than the current method due to Kouzel (5.2% and 6.0% deviation for the binary and ternary mixtures respectively). Eyring's theory of viscous flow was critically investigated, and a modification was proposed which extends its application to petroleum oils. The effect of blending on the pour points of selected petroleum oils was studied together with the effect of wax formation and asphaltenes content. Depression of the pour point was always obtained with crude oil binary mixtures. A mechanism was proposed to explain the pour point behaviour of the different binary mixtures. The effects of blending on the boiling point ranges and Reid vapour pressures of binary mixtures of petroleum oils were investigated. The boiling point range exhibited ideal behaviour but the R.V.P. showed negative deviations from it in all cases. Molecular weights of these mixtures were ideal, but the densities and molar volumes were not. The stability of the various crude oil binary mixtures, in terms of viscosity, was studied over a temperature range of 1oC - 30oC for up to 12 weeks. Good stability was found in most cases.

Investigation of capacitive discharge heating of metallic glasses

In recent years, the discovery of bulk metallic glasses with exceptional properties has generated much interest. One of their most intriguing features is their capacity for viscous flow above the glass transition temperature. This characteristic allows metallic glasses to be formed like plastics at modest temperatures. However, crystallization of supercooled metallic liquids in the best bulk metallic glass-formers is much more rapid than in most polymers and silicate glass-forming liquids. The short times to crystallization impairs experimentation on and processing of supercooled glass-forming metallic liquids. A technique to rapidly and uniformly heat metallic glasses at rates of 10⁵ to 10⁶ kelvin per second is presented. A capacitive discharge is used to ohmically heat metallic glasses to temperatures in the super cooled liquid region in millisecond time-scales. By heating samples rapidly, the most time-consuming step in experiments on supercooled metallic liquids is reduced orders of magnitude in length. This allows for experimentation on and processing of metallic liquids in temperature ranges that were previously inaccessible because of crystallization.

A variety of forming techniques, including injection molding and forging, were coupled with capacitive discharge heating to produce near net-shaped metallic glass parts. In addition, a new forming technique, which combines a magnetic field with the heating current to produce a forming force, was developed. Viscosities were measured in previously inaccessible temperature ranges using parallel plate rheometry combined with capacitive discharge heating. Lastly, a rapid pulse calorimeter was developed with this technique to investigate the thermophysical behavior of metallic glasses at these rapid heating rates.

Vortex Shedding Dynamics in Long Aspect-Ratio Aerodynamics Bodies

The focus of the current dissertation is to study qualitatively the underlying physics of vortex-shedding and wake dynamics in long aspect-ratio aerodynamics in incompressible viscous flow through the use of the KLE method. We carried out a long series of numerical experiments in the cases of flow around the cylinder at low Reynolds numbers. The study of flow at low Reynolds numbers provides an insight in the fluid physics and also plays a critical role when applying to stalled turbine rotors. Many of the conclusions about the qualitative nature of the physical mechanisms characterizing vortex formation, shedding and further interaction analyzed here at low Re could be extended to other Re regimes and help to understand the separation of the boundary layers in airfoils and other aerodynamic surfaces. In the long run, it aims to provide a better understanding of the complex multi-physics problems involving fluid-structure-control interaction through improved mathematical computational models of the multi-physics process. Besides the scientific conclusions produced, the research work on streamlined and bluff-body condition will also serve as a valuable guide for the future design of blade aerodynamics and the placement of wind turbines and hydrakinetic turbines, increasing the efficiency in the use of expensive workforce, supplies, and infrastructure. After the introductory section describing the main fields of application of wind power and hydrokinetic turbines, we describe the main features and theoretical background of the numerical method used here. Then, we present the analysis of the numerical experimentation results for the oscillatory regime right before the onset of vortex shedding for circular cylinders. We verified the wake length of the closed near-wake behind the cylinder and analysed the decay of the wake at the wake formation region, and then studied the St-Re relationship at the Reynolds numbers before the wake sheds compared to the experimental data. We found a theoretical model that describes the time evolution of the amplitude of fluctuations in the vorticity field on the twin vortex wake, which accurately matches the numerical results in terms of the frequency of the oscillation and rate of decay. We also proposed a model based on an analog circuit that is able to interpret the concerning flow by reducing the number of degrees of freedom. It follows the idea of the non-linear oscillator and resembles the dynamics mechanism of the closed near-wake with a common configured sine wave oscillator. This low-dimensional circuital model may also help to understand the underlying physical mechanisms, related to vorticity transport, that give origin to those oscillations.

Unsteady-Flow Of A Viscous-Fluid Between 2 Parallel Disks With A Time-Varying Gap Width And A Magnetic-Field

The unsteady incompressible viscous fluid flow between two parallel infinite disks which are located at a distance h(t*) at time t* has been studied. The upper disk moves towards the lower disk with velocity h'(t*). The lower disk is porous and rotates with angular velocity Omega(t*). A magnetic field B(t*) is applied perpendicular to the two disks. It has been found that the governing Navier-Stokes equations reduce to a set of ordinary differential equations if h(t*), a(t*) and B(t*) vary with time t* in a particular manner, i.e. h(t*) = H(1 - alpha t*)(1/2), Omega(t*) = Omega(0)(1 - alpha t*)(-1), B(t*) = B-0(1 - alpha t*)(-1/2). These ordinary differential equations have been solved numerically using a shooting method. For small Reynolds numbers, analytical solutions have been obtained using a regular perturbation technique. The effects of squeeze Reynolds numbers, Hartmann number and rotation of the disk on the flow pattern, normal force or load and torque have been studied in detail

Time dependent rotational flow of a viscous fluid over an infinite porous disk with a magnetic field

Both the semi-similar and self-similar flows due to a viscous fluid rotating with time dependent angular velocity over a porous disk of large radius at rest with or without a magnetic field are investigated. For the self-similar case the resulting equations for the suction and no mass transfer cases are solved numerically by quasilinearization method whereas for the semi-similar case and injection in the self-similar case an implicit finite difference method with Newton's linearization is employed. For rapid deceleration of fluid and for moderate suction in the case of self-similar flow there exists a layer of fluid, close to the disk surface where the sense of rotation is opposite to that of the fluid rotating far away. The velocity profiles in the absence of magnetic field are found to be oscillatory except for suction. For the accelerating freestream, (semi-similar flow) the effect of time is to reduce the amplitude of the oscillations of the velocity components. On the other hand the effect of time for the oscillating case is just the opposite.

Intrinsic equations of steady rotating, incompressible viscous fluid flow

The equations governing the flow of a steady rotating incompressible viscous fluid are expressed in intrinsic form along the vortex lines and their normals. Using these equations the effects of rotation on the geometric properties of viscous fluid flows are studied. A particular flow in which the vortex lines are right circular helices is discussed.

A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

Pulsatile flow of a viscous fluid in elliptical pipe of variable cross-section

The pulsatile flow of an incompressible viscous fluid in an elliptical pipe of slowly varying cross-section is considered. Asymptotic series solutions for the velocity distribution and pressure gradient are obtained in terms of Mathieu functions for a low Reynold number flow in which the volume flux is prescribed. An expression for shear stress on the boundary is derived. The physically significant quantities governing the flow are computed numerically and analysed for different types of constrictions. The effect of eccentricity and Womerslay parameter on the flow is discussed.