Viscometric Behavior Research Articles

Re-entrant corner flows of UCM fluids: the initial formation of lip vortices

We discuss here a third type of boundary-layer structure that arises in steady planar flows at re-entrant corners for the upper convected Maxwell fluid. This structure extends the class of similarity solutions that are associated with the inviscid flow equations and hold in an outer core region local to the corner. In previous work ( Renardy 1995 J. Non-Newtonian Fluid Mech. 58 , 83–39 ; Evans 2005 Proc. R. Soc. A 461 , 117–142 ), single and double layer structures were used to the match outer core similarity solutions to wall boundary layers in which viscometric behaviour is obtained. Here a second double layer structure is discussed, which completes the range of validity for the core similarity solutions. This structure is fundamentally different to the single layer structure in that it only admits reverse flow solutions at the upstream wall, a situation of practical relevance to describe the initial formation of lip vortices in contraction flows.

Viscometric Study of Segmented Poly(ester-urethane) Solutions in Dilute and Extremely Dilute Concentration Domains

ABSTRACT Synthesis and viscometric behavior of segmented poly(ester-urethane)s in N,N-dimethyl-formamide solution ranged from semidilute to extremely dilute concentration were investigated. The data reflected the conformation changes in the 17–45°C range, and the results are discussed in relation to the behavior of the poly(ethylene glycol)adipate in the same solvent. The intrinsic viscosities and critical concentration that separate the dilute–extremely dilute regimes are also studied. A scanning law between the reduced viscosity ηsp/c and the concentration for the extremely dilute regime is found and the deviations from Huggins dependence at different temperatures are discussed.

Re-entrant corner flows of Oldroyd-B fluids

The method of matched asymptotic expansions is used to construct solutions for the planar steady flow of Oldroyd-B fluids around re-entrant corners of angles π / α (1/2≤ α <1). Two types of similarity solutions are described for the core flow away from the walls. These correspond to the two main dominant balances of the constitutive equation, where the upper convected derivative of stress either dominates or is balanced by the upper convected derivative of the rate of strain. The former balance gives the incompressible Euler or inviscid flow equations and the latter balance the incompressible Navier–Stokes equations. The inviscid flow similarity solution for the core is that first derived by Hinch (Hinch 1993 J. Non-Newtonian Fluid Mech. 50 , 161–171) with a core stress singularity that depends upon the corner angle and radial distance as O ( r −2(1− α ) ) and a velocity behaviour that vanishes as O ( r α (3− α )−1 ). Extending the analysis of Renardy (Renardy 1995 J. Non-Newtonian Fluid Mech. 58 , 83–39), this outer solution is matched to viscometric wall behaviour for both upstream and downstream boundary layers. This structure is shown to hold for the majority of the retardation parameter range. In contrast, the similarity solution associated with the Navier–Stokes equations has a velocity behaviour O ( r λ ) where λ ∈(0,1) satisfies a nonlinear eigenvalue problem, dependent upon the corner angle and an associated Reynolds number defined in terms of the ratio of the retardation and relaxation times. This similarity solution is shown to hold as an outer solution and is matched into stress boundary layers at the walls which recover viscometric behaviour. However, the matching is restricted to values of the retardation parameter close to the relaxation parameter. In this case the leading order core stress is Newtonian with behaviour O ( r −(1− λ ) ).

Viscometric Study of Poly(dimethylsiloxaneb-N-vinylpyrrolidone) in Water Solutions

The synthesis and viscometric behavior of poly(dimethylsiloxane-b- N-vinylpyrrolidone) in dilute to extremely dilute water solutions was investigated. The viscometric molecular weights, intrinsic viscosities and critical concentrations which separate the dilute-semi-dilute and dilute-extremely dilute regimes were studied. A dependence between reduced viscosity ηsp /c and concentration for extremely dilute regime was found. The deviation from Huggins dependence is discussed.

Viscometric Behavior of Polystyrene in Binary Solutions Used as Eluents in Adsorption Chromatography

Calculated and experimentally measured characteristic viscosities [η] of polystyrene in some binary solvents used as eluents in chromatographic experiments in a wide range of mixture compositions were compared. The values of [η] were measured in solvents of varied thermodynamic quality, including the theta solvent and mixtures of solvents of the following compositions: two good solvents; good solvent and theta solvent; good solvent and precipitant; poor solvent and theta solvent. An equation that relates the anomalies observed in the dependences of [η] on the composition of a solvent mixture to parameters of the Flory-Huggins thermodynamic interaction was suggested.

Viscometric behavior of high-methoxy and low-methoxy pectin solutions

The hydrodynamic behavior of high-methoxy (HM) and low-methoxy (LM) pectin solutions was examined by capillary viscometric analysis. The LM-pectin was produced from the HM-pectin by PME-deesterification. As a result of the viscometric analysis, the PME-deesterified LM-pectin showed quite different solution behavior from the HM-pectin. The LM-pectin had larger intrinsic viscosity ([ η]) than HM-pectin when dissolved in 0.005 and 0.05 M concentrations of monovalent salts whereas HM-pectin had a higher value of [ η] when dissolved in 0.2 M salt than LM-pectin. The concentration dependence of HM-pectin η red values was fairly constant, whereas the concentration dependence of LM-pectin η red values had a tendency to decrease as the pectin concentration approached zero. The effect of salt-type on the hydrodynamic behavior of both HM- and LM-pectin solutions was almost negligible. The precipitous drop in LM-pectin [ η] upon increasing the salt concentration from 0.05 to 0.2 M is interpreted as arising from its disaggregation. This interpretation is based in part on data from HPSEC with online light scattering and viscosity detection.

On the consequences of material frame-indifference in algebraic stress models

The principle of material frame-indifference (MFI) is a fundamental and controversial principle of continuum mechanics that has been invoked recently to derive nonlinear algebraic models for stresses of viscoelastic liquids. The purpose of the present study is to identify regions of a flow field where MFI should be considered. Such regions are identified by computing the angular velocity of the principal directions of the rate-of-deformation tensor in order to obtain an Euclidean objective vorticity tensor. An analysis is carried out for uniform shear and extensional flows, and for a Couette flow. The method is then applied to the planar flow through an abrupt 4:1 contraction and to the two-dimensional stream past a circular cylinder. The main results are: (1) MFI should be taken into account in regions characterized by the transition between two different kinematics and a significant velocity magnitude, and (2) MFI can be safely ignored in regions of pure viscometric behaviour as well as in recirculation regions. The consequences of MFI being taken into account are then examined upon using the Euclidean objective vorticity tensor in a simple algebraic constitutive law for viscoelastic fluids.

Re–entrant corner flows of the upper convected Maxwell fluid

Steady planar flow of the upper convected Maxwell (UCM) fluid is described for re–entrant corners with angles 180°/α, where ½ ⩽α< 1. Local to the corner we consider a class of similarity solutions associated with the inviscid flow equations which arise from the dominance of the upper convective stress derivative in the constitutive equations. These solutions, first noted by Hinch, hold in an outer (core–flow) region and give stress singularities ofO(r−2(1−α)) (withrthe radial distance from the corner) and a stream function behaviour ofO(rnα). Herenis a parameter defining distinct solutions within this similarity class. We match such solutions to wall boundary layers, in which viscometric behaviour is retrieved. We discuss two types of boundary–layer structure. The first is a single–layer structure, previously noted by Renardy. This single layer occurs forn= 3 −αand has the viscoelastic balance of the constitutive equations holding uniformly within it. Here we complete previous analysis by considering the downstream case. The second type of boundary layer considered is a double–layer structure, which we discuss for the range 1 <n< 3 −α. Now the elastic balance of the constitutive equations holds within its main region, with a thinner region closer to the wall in which the relaxation terms are recovered. This structure extends the range of the core similarity solutions and has not been previously noted.

Biodegradable hydraulic fluids: Rheological behaviour at low temperatures of several oleochemically derived synthetic esters

One of the most important aspects of a hydraulic fluid used in mobile systems (e.g., excavators, wheel loaders) is the viscometric behaviour of the fluid at low temperatures. It has been found that the pour point of the base fluid does not predict this behaviour satisfactorily, and, as a result, the Swedish standard for these products (SS155434) requires that the kinematic viscosity of a hydraulic fluid remains stable at low temperatures (−20 or −30°C) during a period of 72 h. However, in rheological studies under dynamic conditions, it has now been found that certain oleochemically derived esters do not show Newtonian flow behaviour at these low temperatures. The authors have found not only a shear-dependent behaviour of these esters but also a time-dependent behaviour, especially after (high) energy input from an external source to simulate pumping of the fluid. Given the non-Newtonian behaviour of these esters, the kinematic viscosity test method with an Ubbelohde tube was found to be inappropriate for the determination of the low-temperature viscosity because this method assumes Newtonian behaviour. Dynamic viscosity measurements at higher shear rates (e.g., cold cranking simulator) resulted in much better reproducibility and may offer the best method of assessment.

Metastable state of amphiphilic polysaccharide solutions

Abstract This communication reports the time-dependent viscometric behaviour of amphiphilic pullulan (with varied amount of grafted octyl groups, C8) solutions as a function of age and temperature. For lower C8 amount, no ageing effects were observed. With high amount of octyl-bearing groups, the solution exhibits a strong increase of viscosity caused by an increase of intermolecular associations and the simultaneous decrease of intramolecular associations. After longer time, a collapse of chains has been observed. This behaviour is favoured with concentration and temperature. These results evidence the metastable character of amphiphilic polymers in aqueous solution.

Effects of Concentration on Steady-State Viscometric Properties of Short Chain Polymer Solutions Over the Entire Concentration Range

Relationships between viscometric behavior and concentration are observed and evaluated through a series of nonequilibrium molecular dynamics simulations of the behavior of 20-site polymers in solution with explicit solvent across the full concentration range. The zero-shear viscosities, first normal stress coefficients and steady-state shear compliance of the solutions are examined alongside conformational properties including the excluded volume effect. The variation of viscosity with concentration in these solutions is described by the Huggins equation up to relatively high concentrations. At these high concentrations, the effects on conformation of excluded volume interactions decline, while no clear semi-dilute region is identifiable. Although the steady-state shear compliance of the system appears concentration-independent, the dilute and melt behaviors of this system are accurately described by the theories of Zimm and Rouse, respectively.

The Mixing Effect of Glycylglycine with KCl, KBr, and Na2SO4from Volumetric and Viscometric Investigations at 298.15 K

The mixing effect of a simple peptide such as glycylglycine, in the presence of aqueous electrolytes, has been studied by examining their volumetric and viscometric behavior. The increase in the apparent molar properties of both glycylglycine and electrolytes is attributed to the interactions present among cation, anion, the head groups of the peptide, and the peptide bond. Simple equations are developed to account for such interactions with a view to correlate apparent molar properties of glycylglycine and electrolyte in their aqueous mixtures. Transfer properties of both glycylglycine and electrolyte are investigated in order to understand the changes in the property of one component by the addition of another. These interactions are also supported by viscosity data, for which a simple model is developed to correlate the variation in viscosities with composition of a component.

Concentration dependence of viscometric properties of model short chain polymer solutions

We study the concentration dependence of the conformational and viscometric behaviour of short-chain polymer solutions in shear flow by conducting a series of non-equilibrium molecular dynamics simulations, covering the entire concentration range. Our model explicitly incorporates all of the important generic features of real polymer solutions—excluded volume, hydrodynamic interactions and finite chain extensibility. Hydrodynamic interactions are included exactly by treating the solvent explicitly as an atomic fluid. The polymer molecules studied consist of 20-site bead-rod model molecules, which correspond approximately to 12 Kuhn steps in the melt. For polyethylene, this represents a molar mass of 1800 g mol21. In some respects, our results are consistent with experimental and theoretical results obtained for long-chain polymer solutions. We calculate the Flory–Fox constant and find a value that agrees reasonably well with results for long chain polymer solutions. Due to the short chain length of the molecules investigated, no semidilute region exists for these solutions. However, the radius of gyration and viscosity still exhibit strong concentration dependence, which is well described by power series, rather than power law expressions, in contrast to the behaviour usually observed in long-chain polymer solutions.

Concentration dependence of viscometric properties of model short chain polymer solutions

We study the concentration dependence of the conformational and viscometric behaviour of short-chain polymer solutions in shear flow by conducting a series of non-equilibrium molecular dynamics simulations, covering the entire concentration range. Our model explicitly incorporates all of the important generic features of real polymer solutions—excluded volume, hydrodynamic interactions and finite chain extensibility. Hydrodynamic interactions are included exactly by treating the solvent explicitly as an atomic fluid. The polymer molecules studied consist of 20-site bead-rod model molecules, which correspond approximately to 12 Kuhn steps in the melt. For polyethylene, this represents a molar mass of 1800 g mol −1. In some respects, our results are consistent with experimental and theoretical results obtained for long-chain polymer solutions. We calculate the Flory–Fox constant and find a value that agrees reasonably well with results for long chain polymer solutions. Due to the short chain length of the molecules investigated, no semidilute region exists for these solutions. However, the radius of gyration and viscosity still exhibit strong concentration dependence, which is well described by power series, rather than power law expressions, in contrast to the behaviour usually observed in long-chain polymer solutions.

Viscometric behavior of quaternized polysulfones

AbstractThe effects of the quaternary ammonium group size and the solvent nature and composition on the viscometric behavior of several quaternized polysulfones (PSFs) were investigated. The solution viscosity of the cationic PSFs was determined over a wide concentration range in N,N‐dimethylformamide (DMF). The experimental data were plotted in the terms of the Fedors equation. It was found that the intrinsic viscosity values were strongly dependent on the size of quaternary ammonium groups. The viscosity of PSF quaternized with N,N‐dimethylbutylamine (PSF‐DMBA) was also measured in the mixed solvents consisting of DMF/methanol and DMF/diethylether. Polyelectrolyte behavior was observed for PSF‐DMBA in the mixtures of DMF/methanol for all compositions employed and in the mixtures of DMF/diethylether with the diethylether content as high as 25 vol %. The viscosity decrease and precipitation in the polymer solution with increasing diethylether content was attributed to the dipole–dipole attraction between ion pairs formed in a less polar medium. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 465–469, 2003

Viscometric study of poly(sodium 2-acrylamido-2-methylpropanesulfonate) and two random copolymers

Effects of the polyanion synthesis conditions and composition on the viscometric behavior of poly(sodium 2-acrylamido-2-methylpropanesulfonate) (PAMPS) and two random copolymers, poly(sodium 2-acrylamido-2-methylpropanesulfonate-co-methylmethacrylate) (PAMPSMM) and poly(sodium 2-acrylamido-2-methylpropanesulfonate-co- tert-butylacrylamide) (PAMPSTBA), in a wide range of concentrations were reported in this paper. The experimental data obtained in salt-free aqueous solution were plotted in terms of the Fuoss and the Rao equations in order to obtain the intrinsic viscosity values. The C ∗ values obtained as the reciprocal of the intrinsic viscosity were compared with the experimentally determined values and with those calculated according to the Odijk theory. An acceptable agreement between C ∗ values obtained by different approaches was found for the PAMPS samples with high molar masses (0.83 × 10 6–1.4 × 10 6 g/mol). For the same charge density and the same concentration the reduced viscosity values were higher for PAMPSMM comparative with PAMPSTBA indicating a higher chain extension of the former copolymer.

Characterization of polyelectrolyte effect in poly(acrylic acid) solutions

AbstractThe viscometric behavior of poly(acrylic acid) solutions, as well as their ion transport properties, were monitored as a function of polymer concentration and the addition of KOH in nonisoionic conditions. Polyelectrolyte effect was studied and characterized by conductivimetry as well as viscometric properties at the infinite dilution limit. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 191–196, 2003

Viscometric study of polyvinyl alcohol in NaCl/water solutions ranged from dilute to extremely dilute concentration

Viscometric behavior of polyvinyl alcohol (PVA) in NaCl/water solution ranged from dilute to extremely dilute concentrations was thoroughly investigated. Due to the influence of the adsorbed polymer on the walls of Ubbelohde viscometer capillary, an upswing of the reduced viscosity ( η sp/ C) vs. concentration ( C) curve was observed in extremely dilute concentration. If using improved viscosity measurement procedure to delete the influence of the adsorbed polymer upon the viscosity of polymer solution, the linear relationship between η sp/ C and C of PVA in NaCl/water solution was observed to exist, even in extremely dilute solution. Furthermore, the experimental results show that the improved viscosity measurement procedure presented in this article is not only a more reasonable but also a more convenient technique to determine the viscosity of polymer solution. The adsorption of polymer on the walls of viscometer capillary has been found to be greatly associated with the solvent in which the polymer was dissolved.

Viscometric behaviour of some hydrophobically modified cationic polyelectrolytes

Effects of the polycation structure and of the solvent nature and composition on the viscometric behaviour of some cationic polyelectrolytes with (N,N-dimethyl-2-hydroxypropyleneammonium chloride) units in the main chain and non-polar side groups (hexyloxypropyl and decyloxypropyl) were investigated. The solution viscosity of polyelectrolytes was determined over a wide concentration range, in saltless aqueous solution. The experimental data were plotted in the terms of Fuoss and Fedors equations. Viscosity of the polycation PCA5D1, was measured also in the mixed solvents: water/methanol and water/acetone. Polyelectrolyte behaviour was observed for PCA5D1 in the mixtures of water/methanol for all composition employed and in mixtures of water/acetone with the acetone content as high as 60vol%. The intrinsic viscosity, [η], decreased and the overlap concentration, C∗, increased with increasing organic solvent content in the mixed solvents.

Molecular dynamic studies of lubricant related systems—variable temperature IR spectroscopic studies

Molecular interactions are the key to understand the structure and properties of liquids, solutions and solids. The relationship between the molecular structure and viscometric behaviour of fluids has been a subject of considerable importance. Quantitative relationships between molecular structures and various bulk properties of lubricant base fluids, i.e. viscosity, viscosity–temperature and viscosity–pressure variations, pour point etc., are not well defined. The understanding of these relationships is much more difficult in lubricating base fluids where only weak van der Waals interactions are predominant. The dynamic properties of molecular interactions such as correlation functions and relaxation times are of great interest to understand the structure–property relationships.In this paper, vibrational/rotational relaxation time (τIR) data along with half-bandwidth data obtained from infrared (IR) spectra have been used to study the several aspects of the molecular dynamics of base oils of varying physical properties. Relaxation time measurements have been carried out on a few model hydrocarbon compounds and a number of mineral base oils at varied temperatures (25–175°C). Activation energies (Ea) for Newtonian viscous flow (macro process) and vibrational/rotational relaxations (micro process) have been obtained from the temperature dependence of kinematic viscosity and the relaxation data, respectively. The activation energies for base oils containing higher isoparaffins (hydrocracking, HC class oils) have shown lower activation energies compared to those having lower amounts of isoparaffins (hydrofinishing, HF class oils). The activation energies for the micro process involving relaxation of the 1360cm−1 band are lower than the 721cm−1 band. IR spectral half-bandwidths are correlated to the reciprocal of the viscosity of base fluids under study. The linear relationships are used to separate the temperature dependent reorientational effects from vibrational effects.