The competing roles of extensional viscosity and normal stress differences in complex flows of elastic liquids

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2) especially N(1), and the extensional viscosity eta(E). In this paper, we shall be mainly interested in `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1) and eta(E). We shall concentrate on two important flows - axisymmetric contraction flow and ""splashing"" (particularly that which arises when a liquid drop falls onto the free Surface of the same liquid). Modem numerical techniques are employed to provide the theoretical predictions. It is shown that the two obvious manifestations of viscoelastic rheometrical behaviour can sometimes be opposing influences in determining flow characteristics. Specifically, in an axisymmetric contraction flow, high eta(E) , can retard the flow, whereas high N(1) can have the opposite effect. In the splashing experiment, high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming some early suggestions, but, again, other rheometrical influences can also have a role to play and the overall picture may not be as clear as it was once envisaged.

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.

Verhopäällystyspastojen analyysimenetelmät

Diplomityön tarkoitus oli selvittää verhopäällystyspastoille sopivia analyysimenetelmiä. Verhopäällystyksessä onnistunut päällystystapahtuma vaatii venymäviskositeetin ja pintajännityksen hyvää hallintaa. Kirjallisuusosassa käsiteltiin verhopäällystystä, verhopäällystyspastojen koostumusta, reologiaa ja pintajännitystä. Kirjallisuusosassa käsiteltiin lisäksi verhopäällystyspastojen reologian ja pintajännityksen mittaamiseen soveltuvia mittausmenetelmiä. Verhopäällystyksen luonteen vuoksi kirjallisuusosassa syvennyttiin venymäviskositeetin ja dynaamisen pintajännityksen mittaamiseen tarkoitettuihin menetelmiin. Kokeellisessa osassa tutkittiin päällystyspastasarjojen reologiaa ja pintajännitystä verhopäällystystä varten. Osaan päällystyspastoista luotiin venymäviskositeettia ja osasta laskettiin pintajännitystä. Venymäviskositeetin mittaamista varten työssä käytettiin ACAV A2 -reometriin liitettyjä teräsreikälevyjä. Dynaamisen pintajännityksen mittaamista varten työssä käytettiin KSV BPA-800P -pintajännitysmittaria. ACAV A2 -reometriin liitettyjen teräsreikälevyjen (reiän sisähalkaisija 0,5 tai 0,7 mm) avulla mitattiin venymäviskositeettia kuvaavia Eulerin lukuarvoja onnistuneesti suurilla kiintoainepitoisuuksilla (50, 60 tai 65 p %). Erikoispaksuntajan määrää lisäämällä onnistuttiin luomaan huomattavaa venymäviskositeettia. Kiintoainepitoisuuden kasvaessa kasvoi myös venymäviskositeetti. Tavanomaisille paksuntajille mitattiin hieman kohonneita venymäviskositeetteja verrattuna referenssipäällystyspastaan. Pigmenttikoostumuksella (kalsiumkarbonaatti/kaoliini) ei näyttänyt olevan vaikutusta venymäviskositeettiin, tai vaikutus oli suhteellisen pieni. Dynaamisen pintajännityksen mittaamista varten käytössä ollut KSV BPA-800P -pintajännitysmittari ei toiminut luotettavasti, vaikka näytteitä laimennettiin. Kiintoainepitoisuudessa 10 p-% olleilla laimennoksilla saavutettiin analysoinnin kannalta parhaat tulokset. Tuloksista saatiin kuitenkin viitteitä, että kyseinen mittari voisi olla potentiaalinen menetelmä dynaamisen pintajännityksen mittaamiseksi.

A computational study of some rheological influences on the ""splashing experiment""

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2), especially N(1), the extensional viscosity, and the dynamic moduli G` and G ``. In this paper, we shall confine attention to `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1), eta(E), G` and G ``. We shall concentrate on the ""splashing"" problem (particularly that which arises when a liquid drop falls onto the free surface of the same liquid). Modern numerical techniques are employed to provide the theoretical predictions. We show that high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming earlier suggestions, but other rheometrical influences (steady and transient) can also have a role to play and the overall picture may not be as clear as it was once envisaged. We argue that this is due in the main to the fact that splashing is a manifestly unsteady flow. To confirm this proposition, we obtain numerical simulations for the linear Jeffreys model. (C) 2010 Elsevier B.V. All rights reserved.

A Numerical Study of the FENE-CR Model Applied to a Jet Flow Problem

The FENE-CR model is investigated through a numerical algorithm to simulate the time-dependent moving free surface flow produced by a jet impinging on a flat surface. The objective is to demonstrate that by increasing the extensibility parameter L, the numerical solutions converge to the solutions obtained with the Oldroyd-B model. The governing equations are solved by an established free surface flow solver based on the finite difference and marker-and-cell methods. Numerical predictions of the extensional viscosity obtained with several values of the parameter L are presented. The results show that if the extensibility parameter L is sufficiently large then the extensional viscosities obtained with the FENE-CR model approximate the corresponding Oldroyd-B viscosity. Moreover, the flow from a jet impinging on a flat surface is simulated with various values of the extensibility parameter L and the fluid flow visualizations display convergence to the Oldroyd-B jet flow results.

Ocean Ultrasonic Shear and Compression Viscosities

[EN]A comprehensive description of ocean molecular flow and deformation is provided with the help of hydrodynamic and ultrasonic principles. Hydrodynamic computation of true or natural viscosities shows that ocean shear viscosity (?G), compression viscosity (?K), and extensional viscosity (?E) are interrelated. There are no experimental methods available for the in situ measurement of these viscosities. Sound absorption coefficients (? obs) allow to know the ultrasonic shear (?UG), compression (?UK), and longitudinal (?L) viscosities, which decrease with increasing frequency and increase with increasing temperature, the flow activation energies having nearly equivalent values; pressure (depth) increase/decrease them at low/high frequencies. The viscosities ?* UG, ?* UK, ?* L are approached at about 1000 KHz. They decrease with temperature and pressure, and increase with salinity. The ?*UG becomes equal to the true shear viscosity ? G at the viscosity ratio ? = ?UK / ?UG = 0.

Batchelor's theory extended to elongated cylindrical or ellipsoidal particles

Extensions to Batchelor's theory have been derived to take into account different shaped particles while relating extensional viscosity enhancement to three parameters - shape, volume fraction and particle aspect ratio. The extended theory now allows calculation of the extensional viscosity enhancement, at a given volume fraction of particles, for either ellipsoidal or cylindrical particles. The formula improves the predictive capability of Batchelor's theory when compared with measurements found in the literature for different rod-like polymer solutions. (c) 2005 Elsevier B.V. All rights reserved.

The Inertio-Elastic Planar Entry Flow of Low-Viscosity Elastic Fluids in Micro-fabricated Geometries

The non-Newtonian flow of dilute aqueous polyethylene oxide (PEO) solutions through microfabricated planar abrupt contraction-expansions is investigated. The contraction geometries are fabricated from a high-resolution chrome mask and cross-linked PDMS gels using the tools of soft-lithography. The small length scales and high deformation rates in the contraction throat lead to significant extensional flow effects even with dilute polymer solutions having time constants on the order of milliseconds. The dimensionless extra pressure drop across the contraction increases by more than 200% and is accompanied by significant upstream vortex growth. Streak photography and videomicroscopy using epifluorescent particles shows that the flow ultimately becomes unstable and three-dimensional. The moderate Reynolds numbers (0.03 ≤ Re ≤ 44) associated with these high Deborah number (0 ≤ De ≤ 600) microfluidic flows results in the exploration of new regions of the Re-De parameter space in which the effects of both elasticity and inertia can be observed. Understanding such interactions will be increasingly important in microfluidic applications involving complex fluids and can best be interpreted in terms of the elasticity number, El = De/Re, which is independent of the flow kinematics and depends only on the fluid rheology and the characteristic size of the device.

Comparing Near-infrared Conventional Diffuse Reflectance Spectroscopy And Hyperspectral Imaging For Determination Of The Bulk Properties Of Solid Samples By Multivariate Regression: Determination Of Mooney Viscosity And Plasticity Indices Of Natural Rubber.

Conventional reflectance spectroscopy (NIRS) and hyperspectral imaging (HI) in the near-infrared region (1000-2500 nm) are evaluated and compared, using, as the case study, the determination of relevant properties related to the quality of natural rubber. Mooney viscosity (MV) and plasticity indices (PI) (PI0 - original plasticity, PI30 - plasticity after accelerated aging, and PRI - the plasticity retention index after accelerated aging) of rubber were determined using multivariate regression models. Two hundred and eighty six samples of rubber were measured using conventional and hyperspectral near-infrared imaging reflectance instruments in the range of 1000-2500 nm. The sample set was split into regression (n = 191) and external validation (n = 95) sub-sets. Three instruments were employed for data acquisition: a line scanning hyperspectral camera and two conventional FT-NIR spectrometers. Sample heterogeneity was evaluated using hyperspectral images obtained with a resolution of 150 × 150 μm and principal component analysis. The probed sample area (5 cm(2); 24,000 pixels) to achieve representativeness was found to be equivalent to the average of 6 spectra for a 1 cm diameter probing circular window of one FT-NIR instrument. The other spectrophotometer can probe the whole sample in only one measurement. The results show that the rubber properties can be determined with very similar accuracy and precision by Partial Least Square (PLS) regression models regardless of whether HI-NIR or conventional FT-NIR produce the spectral datasets. The best Root Mean Square Errors of Prediction (RMSEPs) of external validation for MV, PI0, PI30, and PRI were 4.3, 1.8, 3.4, and 5.3%, respectively. Though the quantitative results provided by the three instruments can be considered equivalent, the hyperspectral imaging instrument presents a number of advantages, being about 6 times faster than conventional bulk spectrometers, producing robust spectral data by ensuring sample representativeness, and minimizing the effect of the presence of contaminants.

The viscosity parameter's dependence on the profile of the disk scale height

It is shown that, for accretion disks, the height scale is a constant whenever hydrostatic equilibrium and the subsonic turbulence regime hold in the disk. In order to have a variable height scale, processes are needed that contribute an extra term to the continuity equation. This contribution makes the viscosity parameter much greater in the outer region and much smaller in the inner region. Under these circumstances, turbulence is the presumable source of viscosity in the disk.

Ultrasonic Viscosity Measurement Using the Shear-Wave Reflection Coefficient with a Novel Signal Processing Technique

Real-time viscosity measurement remains a necessity for highly automated industry. To resolve this problem, many studies have been carried out using an ultrasonic shear wave reflectance method. This method is based on the determination of the complex reflection coefficient`s magnitude and phase at the solid-liquid interface. Although magnitude is a stable quantity and its measurement is relatively simple and precise, phase measurement is a difficult task because of strong temperature dependence. A simplified method that uses only the magnitude of the reflection coefficient and that is valid under the Newtonian regimen has been proposed by some authors, but the obtained viscosity values do not match conventional viscometry measurements. In this work, a mode conversion measurement cell was used to measure glycerin viscosity as a function of temperature (15 to 25 degrees C) and corn syrup-water mixtures as a function of concentration (70 to 100 wt% of corn syrup). Tests were carried out at 1 MHz. A novel signal processing technique that calculates the reflection coefficient magnitude in a frequency band, instead of a single frequency, was studied. The effects of the bandwidth on magnitude and viscosity were analyzed and the results were compared with the values predicted by the Newtonian liquid model. The frequency band technique improved the magnitude results. The obtained viscosity values came close to those measured by the rotational viscometer with percentage errors up to 14%, whereas errors up to 96% were found for the single frequency method.

Viscosity measurement of Newtonian liquids using the complex reflection coefficient

This work presents the implementation of the ultrasonic shear reflectance method for viscosity measurement of Newtonian liquids using wave mode conversion from longitudinal to shear waves and vice versa. The method is based on the measurement of the complex reflection coefficient (magnitude and phase) at a solid-liquid interface. The implemented measurement cell is composed of an ultrasonic transducer, a water buffer, an aluminum prism, a PMMA buffer rod, and a sample chamber. Viscosity measurements were made in the range from 1 to 3.5 MHz for olive oil and for automotive oils (SAE 40, 90, and 250) at 15 and 22.5 degrees C, respectively. Moreover, olive oil and corn oil measurements were conducted in the range from 15 to 30 degrees C at 3.5 and 2.25 MHz, respectively. The ultrasonic measurements, in the case of the less viscous liquids, agree with the results provided by a rotational viscometer, showing Newtonian behavior. In the case of the more viscous liquids, a significant difference was obtained, showing a clear non-Newtonian behavior that cannot be described by the Kelvin-Voigt model.

Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford, is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case.

Which one of these is not like the others? An inter-hospital study of the viscosity of thickened fluids

Engineering This investigation examined the rheological (viscosity and yield stress) and material property (density) characteristics of the thickened meal-time and videofluorscopy fluids provided by 10 major metropolitan hospitals. Differences in the thickness of thickened fluids were considered as a source of variability and potential hazard for inter-hospital transfers of dysphagic patients. The results indicated considerable differences in the viscosity, density, and yield stress of both meal-time and videofluoroscopy fluids. In theory, the results suggest that dysphagic patients transferred between hospitals could be placed on inappropriate levels of fluid thickness because of inherent differences in the rheology and material property characteristics of the fluids provided by different hospitals. Slowed improvement or medical complications are potential worst-case scenarios for dysphagic patients if the difference between the thick fluids offered by 2 hospitals are extreme. The investigation outlines the most appropriate way to assess the rheological and material property characteristics of thickened fluids. In addition, it suggests a plan of quality improvement to reduce the variability of the thickness of fluids offered at different hospitals.

Theoretical and numerical analyses of convective instability in porous media with temperature-dependent viscosity

Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.