Extensional flow resistance of dilute polyacrylamide and surfactant solutions

The extensional flow behaviour of dilute aqueous solutions of a partiallyhy-drolyzed polyacrylamide and a surfactant were investigated in an extensional flow cell. The cell was designed such that fluids were subjected to steady shear before undergoing extensional motion in a converging channel. Extensional resistance was monitored by measuring the pressure drop through the channel. Such measurements were made over a range of extensional rates at fixed values of the upstream shear rate. Solutions of different concentrations were tested — up to 40 ppm of polyacrylamide and 450 ppm of surfactant — at various temperatures in the case of surfactant and for different types and amounts of salt in the case of polyacrylamide. Of the results, the more notable are that the extensional resistance of polyacrylamide solutions is affected much more by CaCl₂ than by NaCl and that surfactant solutions do not exhibit extensional resistance unless they are pre-sheared.     

Flow mechanisms in dense silica-metal oxide-water suspensions

The rheological properties of dense silica in water suspensions (approx. 50% solids by volume) containing additions of metal oxides were examined. Metal oxides used were ferric, zinc and stannic. To prevent settling, testing was performed in a rheometer which was modified to provide for continual stirring of the materials. Relatively small oxide additions had the effect of thickening the mixtures and making them non-Newtonian. Different rate-limiting steps for flow were identified depending on the particular mixture, testing temperature and shear strain rate. Flow could be described using empirical equations which are identical to those often used to describe plastic flow in solid crystalline materials.     

Rheological properties of dilute polymer solutions: An extended thermodynamic approach

It is shown that extended irreversible thermodynamics can be used to account for the shear rate and frequency dependences of several material functions like shear viscosity, first and second normal stress coefficients, dynamic viscosity and storage modulus. Comparison with experimental data on steady shearing and small oscillatory shearing flows is performed. A good agreement between the model and experiment is reached in a wide scale of variation of the shear rate and the frequency of oscillations. The relation between the present model which includes quadratic terms in the pressure tensor and the Giesekus model is also examined.     

Flow birefringence and rheological measurements on shear induced micellar structures

Aqueous solutions of cationic surfactant systems with strongly binding counterions show the striking phenomenon of shear induced phase transitions. At low shear rates or angular frequencies, the solutions exhibit Newtonian flow. At high rates of shear, however, the rheological properties change dramatically. Above a well defined threshold value of the velocity gradient, a supermolecular structure can be formed from micellar aggregates. This shear induced structure (SIS) behaves like a gel and exhibits strong flow birefringence. The formation of the shear induced structure is very complicated and depends on the specific conditions of the surfactant system. In this paper we discuss new results which have been obtained from rheological measurements and from flow birefringence data. We examine the stability of the shear induced state as a function of temperature, surfactant concentration and salt concentration and we analyse the effect of solubilisation of alcohols and hydrocarbons. The results are interpreted in terms of a kinetic model which accounts for the observed behavior.Dedicated to the 60. birthday of Prof. H. Harnisch, Hoechst AGPartly presented at the 2nd Conference of European Rheologists, Prague, June 17–20, 1986     

Pressure driven flow of dilute polymer solutions in a channel: Analytic results for very small and for very large channels

Kinetic theory of dilute macromolecular solutions is applied to pressure driven flow in a small channel where wall- (and interfacial) layers have to be reckoned with. The complete rheology is studied. It turns out that for very small channels both the shear stress and the normal stress are an order of magnitude larger than corresponding quantities in simple shear. On the other hand, when the channel is so wide that the wall layers are very thin in comparison, agreement with results appropriate for simple shear is found. The volume flow rate-pressure difference relation is derived and compared to the prediction which utilizes the slip velocity concept. For very small channels, this concept is five orders of magnitude off, but reproduces asymptotically correct results for very large channels.     

The squeezing flow of a model suspension fluid

The paper is concerned with the squeezing flow of a model suspension fluid. The numerical solution obtained by a time-dependent Boundary Element Method is compared to an asymptotic solution at large radius. It is found that the kinematics are Newtonian in character, and the fibres quickly align themselves radially. Consequently, the squeezing force is only weakly dependent on the initial orientations of the fibres and the device can be used for measuring the effective viscosity of the suspension. The effective viscosity found from the squeezing flow agrees surprisingly well with experimental data and numerical data derived from the falling sphere geometry at low volume fractions ( < 0.1).     

Effect of solids concentration in dense suspensions of silica-iron(III) oxide and water

The rheological properties of dense suspensions, of silica, iron (III) oxide and water, were studied over a range of solids concentrations using a viscometer, which was modified so as to prevent settling of the solid components. Over the conditions studied, the material behaved according to power—law flow relationships. As the concentrations of silica and iron(III) oxide were increased, an entropy term in the flow equation was identified which had a silica dependent and an iron (III) oxide dependent component. This was attributed to a tendency to order into some form of structural regularity. A, A, B, C pre-exponential functions (K Pa^–n s^–1) - C _ox volume fraction iron (III) oxide - Q activation energy (kJ mol^–1) - R gas constant (kJ mol^–1 K^–1) - R _v silica/water volume ratio - T temperature (K) - n power-law index - H enthalpy (kJ mol^–1) - S entropy change (kJ mol^–1 K^–1) - shear strain rate (s^–1) - shear stress (Pa)     

Fragile networks and rheology of concentrated suspensions

Suspensions consisting of particles of colloidal dimensions have been reported to form connected structures. When attractive forces act between particles in suspension they may flocculate and, depending on particle concentration, shear history and other parameters, flocs may build-up in a three-dimensional network which spans the suspension sample. In this paper a floc network model is introduced to interpret the elastic behavior of flocculated suspensions at small deformations. Elastic percolation concepts are used to explain the variation of the elastic modulus with concentration. Data taken from the suspension rheology literature, and new results with suspensions of magnetic -Fe₂O₃ and non-magnetic -Fe₂O₃ particles in mineral oil are interpreted with the model proposed.Non-zero elastic modulus appeared at threshold particle concentrations of about 0.7 vol.% and 0.4 vol.% of the magnetic and non-magnetic suspensions, respectively. The difference is attributed to the denser flocs formed by magnetic suspensions. The volume fraction of particles in the flocs was estimated from the threshold particle concentration by transforming this concentration into a critical volume concentration of flocs, and identifying this critical concentration with the theoretical percolation threshold of three-dimensional networks of different coordination numbers. The results obtained indicate that the flocs are low-density structures, in agreement with cryo-scanning electron micrographs. Above the critical concentration the dynamic elastic modulus G was found to follow a scaling law of the type G ( _f - _f ^c ) ^f , where _f is the volume fraction of flocs in suspension, and _f ^c is its threshold value. For magnetic suspensions the exponent f was found to rise from a low value of about 1.0 to a value of 2.26 as particle concentration was increased. For the non-magnetic a similar change in f was observed; f changed from 0.95 to 3.6. Two other flocculated suspension systems taken from the literature showed a similar change in exponent. This suggests the possibility of a change in the mechanism of stress transport in the suspension as concentration increases, i.e., from a floc-floc bond-bending force mechanism to a rigidity percolation mechanism.     

Different behaviors of concentrated polysaccharide systems in large-amplitude oscillating shear fields

Two series of oscillatory flow tests were carried out on two concentrated polysaccharide systems (hydroxyethyl guar gum and scleroglucan) in order to evaluate the possibilities offered by large-deformation techniques for the discrimination between different classes of macromolecular systems (i.e., entanglement networks and weak gels). Frequently and strain sweeps, as well as combined steady and oscillatory shear tests were performed to analyze the influence of strain amplitude and of the superposed parallel shear rate on the dynamic properties of these materials.     

Apparent thickening behavior of dilute polystyrene solutions in extensional flows

An experimental investigation was undertaken to study the apparent thickening behavior of dilute polystyrene solutions in extensional flow. Among the parameters investigated were molecular weight, molecular weight distribution, concentration, thermodynamic solvent quality, and solvent viscosity. Apparent relative viscosity was measured as a function of wall shear rate for solutions flowing from a reservoir through a 0.1 mm I.D. tube. As increased, slight shear thinning behavior was observed up until a critical wall shear rate was exceeded, whereupon either a large increase in or small-scale thickening was observed depending on the particular solution under study. As molecular weight or concentration increased, decreased and, the jump in above , increased. increased as thermodynamic solvent quality improved. These results have been interpreted in terms of the polymer chains undergoing a coil-stretch transition at . The observation of a drop-off in at high (above ) was shown to be associated with inertial effects and not with chain fracture due to high extensional rates.     

A model for the thermorheological behavior of viscoelastic fluids

Using a power-law ansatz for the temperature dependence of the shear modulus on the level of internal variables, the thermorheological behavior is modeled for viscoelastic fluids of a special group of rheological constitutive equations (rate-type models). The model parameter introduced characterizes thermoelastic contributions. The relation between the model parameter and the physical quantities appearing in deformation processes is discussed. Based on the chosen temperature dependence of the shear modulus, thermodynamically consistent equations like the nonlinear rheological constitutive equation and the temperature equation are derived. The special cases of entirely entropy and energy elastic fluids are also considered. The thermorheological behavior (exo-, - or endothermal processes) of a viscoelastic fluid in a stress-growth experiment followed by relaxation is analyzed with respect to the model parameter.     

Optical and hydrodynamical regimes in dilute solutions of polyelectrolytes

A careful analysis of the equations governing dynamical disturbances in dilute solutions of polyelectrolytes (described on the basis of a conformational model with electromechanical interactions) allows one to place in evidence two extreme regimes, one called the optical regime, which justifies the use of optical methods for measuring the main instantaneous characteristics of the solutions, and the other that corresponds to electrohydrodynamical flows where a hierarchy can be exhibited for the various effects contributing to the flow equations.     

A numerical comparison of two decoupled methods for the simulation of viscoelastic fluid flows

Two decoupled methods for the finite element solution of the planar stick-slip transition problem with Oldroyd-B fluids, namely the method of characteristics and the Lesaint-Raviart technique, are presented and compared. These procedures are used for the local treatment of the stress transport equation imbedded in the constitutive law and allow the approximation of stresses with discontinuous shape functions. Computations are carried out up to a Deborah number of 4 and the methods are shown to yield fairly similar results.     

Analysis of Taylor vortex flow by means of laser light scattering

Rheological measurements and light-scattering experiments were performed on dilute solutions of high molecular polystyrene. We are able to describe the orientation behavior of chain molecules under shear flow by means of light-scattering. Beyond that these investigations of light-scattering of flowing polymer solutions are an useful and suitable tool for detection and characterization of Taylor vortex formation. We can estimate the appearance of these hydrodynamic instabilities, which overlay the laminar main flow and we can observe a typical influence of the solvent power on it.Presented in part at the meeting of the Deutsche Rheologische Gesellschaft, Berlin, 13–15 May, 1991.     

On the derivation of the constitutive equation of the simple fluid from that of a simple material

It is shown, by the use of the symmetry group of a fluid, that the stress in an elastic fluid depends on the current value of the deformation gradient through the absolute value of the determinant of the deformation gradient, whereas in a simple fluid it depends on this value of the determinant and the history of the relative deformation gradient and nothing else. This derivation is then used to show some of the errors in the criticisms made about the work of Noll. Additionally, a lacuna in Noll's derivation is removed to overcome the only valid criticism made about this theory of simple fluids.     

Influence of the formation of associations of macromolecules on the rheo-optical properties of their dilute solutions. I. Theory

Assuming the formation of doublets in the flow according to a mass action law, the shear rate and the concentration dependence of the extinction angle, of the birefringence, and of the average coil expansion are calculated for dilute solutions of flexible macromolecules. It is shown that this reversible association process has a strong influence on the measurable parameters in a flow birefringence experiment. c concentration (g/cm³) - h ² mean square end-to-end distance at shear rate - h ₀ ² mean-square end-to-end distance at zero-shear rate - n refractive index of the solution (not very different from the solvent for a very dilute solution) - E mean coil expansion - K ₀,K constant of the mass action law - M molecular weight - R _G gas constant - T absolute temperature - ₁ – ₂ optical anisotropy of the segment - ₀ Deborah number: - Deborah number: - shear rate - ₀, reduced concentration - _s viscosity of the solvent - [] ₀ intrinsic viscosity at zero-shear rate - [] intrinsic viscosity at shear rate - extinction angle - N _a Avodagro's number - _n magnitude of the birefringence     

On the relationship between swelling of myofibrils and their suspension rheology

The swelling of myofibrils extracted from white bovine muscle was followed by measuring their suspension rheology. Swelling of the myofibril with increasing pH and ionic strength was accompanied by an increase in both the steady shear viscosity of the suspension and the dynamic viscoelastic properties. Swelling was continuously monitored by measuringG while the ionic strength of the suspension was being changed by dialysis. The relationship between the degree of swelling and the rheological parameters is complicated because myofibrils are rodshaped and swell radially and therefore swelling results in a change in shape. To allow for this an attempt was made to generalize the data by plotting viscosity andG againstcS/ø _m , wherec is the protein concentration in the suspension,S is the swollen volume of the myofibrils per weight of protein, and ø _m is the maximum packing fraction.The best fit to the data was represented by the equations _sp = 1.05 (cS/ _m – 0.84)^1.23 Pa · sG = 8.78 (cS/ _m – 0.67)^2.22 N m^–2. The scatter was greatest forG, possibly because at low degrees of shear the myofibrils were associated and this was confirmed by optical microscopy. Pronounced non-Newtonian behavior was observed and it was suggested that this was due to the disruption of aggregate structures, although at low concentration, orientation of the rods in the shear field may also be important.     

Experimental investigations of the stability limit of the helical flow of pseudoplastic liquids

The stability of the laminar helical flow of pseudoplastic liquids has been investigated with an indirect method consisting in the measurement of the rate of mass transfer at the surface of the inner rotating cylinder. The experiments have been carried out for different values of the geometric parameter = R ₁/R ₂ (the radius ratio) in the range of small values of the Reynolds number,Re < 200. Water solutions of CMC and MC have been used as pseudoplastic liquids obeying the power law model. The results have been correlated with the Taylor and Reynolds numbers defined with the aid of the mean viscosity value. The stability limit of the Couette flow is described by a functional dependence of the modified critical Taylor number (including geometric factor) on the flow indexn. This dependence, general for pseudoplastic liquids obeying the power law model, is close to the previous theoretical predictions and displays destabilizing influence of pseudoplasticity on the rotational motion. Beyond the initial range of the Reynolds numbers values (Re>20), the stability of the helical flow is not affected considerably by the pseudoplastic properties of liquids. In the range of the monotonic stabilization of the helical flow the stability limit is described by a general dependence of the modified Taylor number on the Reynolds number. The dependence is general for pseudoplastic as well as Newtonian liquids.Nomenclature C _i concentration of reaction ions, kmol/m³ - d = R ₂ –R ₁ gap width, m - F _M () Meksyn's geometric factor (Eq. (1)) - F ₀ Faraday constant, C/kmol - i _l density of limit current, A/m³ - k _c mass transfer coefficient, m/s - n flow index - R ₁,R ₂ inner, outer radius of the gap, m - Re = V _m ·2d·/µ _m Reynolds number - Ta _c = _c ·d^3/2·R ₁ ^1/2 ·/µ _m Taylor number - Z _i number of electrons involved in electrochemical reaction - = R ₁/R ₂ radius ratio - µ apparent viscosity (local), Ns/m² - µ _m mean apparent viscosity value (Eq. (3)), Ns/m² - µ _i apparent viscosity value at a surface of the inner cylinder, Ns/m² - density, kg/m³ - _c angular velocity of the inner cylinder (critical value), 1/s