New laboratory tests to measure rheological properties of paper coatings in transient and steady-state flows

The paper describes pertinent laboratory tests to characterize the rheological properties of paper coatings with regard to blade coating over a very wide range of shear rates in both transient and steady-state shear flows. Shear rates as high as 10⁶ s^–1 can be reached by means of a gas-driven capillary rheometer. Examples for the evaluation of end effects, wall effects, and coating thixotropy are given. A stiff and fast Couette rheometer is used to determine flow curves and the shear stress overshoot in step shear rate tests. The primary normal stress difference can be measured up to 10⁴ s^–1 by means of a high shear cone-plate rheometer with piezo transducer. A correct evaluation of the measurements has to take into account inertia contributions to the normal force. First results using a sinusoidal modulation of the shear rate are presented.Paper presented at: International Symposium on Pigment Coating Structure and Rheology, Helsinki, Febr. 8–9, 1989     

Comportement rheologique de sols d'acide polysilicique. II. Etude de la gélification

Résumé L'analyse du comportement rhéologique de sols d'acide polysilicique en solution aqueuse de concentration supérieure à 7 g 1^–1 de silice en fonction du pH entre 6 et 11 et de la température entre 25 et 45 °C a permis de situer la gélification dans un domaine de pH compris entre 8 et 10. Ce processus prend une intensité maximale à 30°C. Le comportement rhéofluidifiant à bas gradients de cisaillement et antithixotrope donne naissance sur les rhéogrammes à un point d'inversion à pH = 9. L'ionisation des groupes silanols à la surface des particules colloïdales permet la réorganisation du milieu après cisaillement. Un état d'ionisation trop élevé est responsable d'un effet electro-répulsif à pH = 10. L'influence de la concentration et de la température sur ces processus est discutée.

---

The rheological behavior of polysilicic acid in aqueous solutions at higher concentrations than 7 g 1^–1 of silice is studied for pH between 6 and 11 with temperature varying from 25° to 45°C. This study indicates that gelification takes place between pH 8 and 10. The process of gel formation attains the highest intensity at 30°C. The shear-thinning behavior at low shear rate gives rise to an inversion point at pH = 9 in shear stress—shear rate curves. The state of ionization at the surface of colloïdal silice particles after shear involve shear thickening observed at pH = 9. A high ionization degree causes an electrostatic repulsion at pH = 10. The concentration and temperature effects upon the organization of network are discussed.

     

Viscosity of some clay-based coating colors at high shear rates

The shear viscosity of clay-based coating colors containing latex and carboxymethyl cellulose (CMC) has been measured over a relatively large shearrate region. In the shear-rate range of 50–1500 s^–1 the measurements were performed using a rotational viscometer and, at higher shear rates extending into the region 10⁵ – 10⁶ s^–1, a high pressure capillary viscometer was employed. The viscosity of the clay colors increased with increasing CMC-concentration, but the influence of the CMC-content was less pronounced at higher shear rates. The apparent shear-thinning behavior of the investigated colors could, in part, be attributed to the shear-thinning of the corresponding polymer (CMC) solution constituting the liquid phase of the color, but the influence of another factor was also indicated. At low shear rates, the interaction between the color components can produce relatively high viscosity levels, but in the high shear rate region these interactions appear to be less important for the viscosity level. It is also of interest to note that the viscosity dependence on the solids content in the high shear-rate region could be described with reasonable accuracy using an empirical equation neglecting interactions between the color components.     

Shear creep and recovery of a technical polystyrene

The torsional creep and recoverable bahaviour of a technical polystyrene is reported over seven orders of magnitude of the value of the compliance from 10^–8 to 10^–1 Pa^–1 and over more than seven decades in time. The results for the recoverable compliance J_R (t) reveal a dispersion region seen between the glass transition and the steady-state recoverable compliance J_e. The limiting value of the final dispersion J_e = 4.7 · 10^–4 Pa^–1 indicates a broad molecular-weight distribution. The steady-state recoverable compliance J_e is independent of the temperature. The temperature dependence of the final dispersion was found to be indistinguishable from that of viscous flow. However, this temperature dependence differs significantly from that of the glass-rubber transition. A proposal has been made for the construction of creep compliance and recoverable compliance over an extended time scale.     

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)     

Drilling fluid shear stress overshoot behavior

Shear stress overshoot behavior was studied in four drilling fluid systems and ten bentonite dispersions. These overshoot properties, also described by the American Petroleum Institute as gel strengths, were measured after gelation times of 10 s to 24 h at temperatures of 20–80 °C. Two different rheometers were used to measure overshoot behavior. Gel strength development with time followed a first-order model. Gel development rates at 20 °C varied from 0.005 to 0.01 min^–1 for drilling fluid systems and from 0.0004 to 0.02 min^–1 for bentonite dispersions. Increasing the gelation temperature for each drilling fluid system caused an increase in the gelling rate constant. Comparison of gel strengths in bentonite dispersions were made using a Fann 35 A viscometer and a Weissenberg Rheogoniometer. Higher gel strength values observed using the Rheogoniometer were believed to be due to differences in instrument spring stiffness and fixture inertia.     

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.     

Viscosity measurements with a magnetoviscometer in the zero-shear and transition region of polypropylenes

Streaming of a non-Newtonian fluid around a sphere is of special importance not only for measuring viscosities with falling spheres, but also for many problems connected with polymer processing. Using the mentioned measuring principle, attention has to be paid to the following points: The sphere is moving in a fluid (melt) of finite extension which requires the application of wall and perhaps end corrections. These are possibly not the same for Newtonian and non-Newtonian fluids. To calculate the viscosity with the help of Stokes law the steady-state velocity is necessary, and it is essential, how long it takes the sphere to reach it. To compare our results with other data, an average shear rate has to be calculated, since there is no uniform shear rate around the sphere. Velocities being very low in our experiments result in very small Reynolds numbers (Re < 10^–3), which allows the application of Stokes law practically without corrections.The experiments were performed at zero shear and in the transition region above. It turned out, that it is usually not possible to extrapolate from shear-dependent viscosity data to zero-shear viscosity.Dedicated to Prof. A. Neckel on the occasion of his 60th birthday     

The peculiar rheo-optical behavior of bisphenol A-polycarbonate and polymethylmethacrylate

The rheological and stress-optical behavior of the melts of several grades ob bisphenol-A-polycarbonate (PC) and polymethylmethacrylate (PMMA) is investigated. Pertinent flow birefringence measurements are carried out in a remodelled cone-plate apparatus [1]. The shear stress in the polymer melt is calculated from the dynamic moduli, which are determined separately. It is shown that the linear stress optical rule is obeyed. In this way, the stress-optical coefficient C of the melt can be determined. The low-Mw polycarbonates all behave as Maxwellian fluids. The main stress direction does not deviate significantly from 45°. In the temperature range from 160° to 260°C the stress-optical coefficients of the different grades lie between 3 and 4×10^–9 Pa^–1 and show a weak temperature dependence. The stress-optical coefficient of PMMA is about a factor of 100 lower and shows a peculiar temperature-dependence, changing its sign at 144°C. The results are discussed in terms of the anisotropy of the polarizability of the polymer chain.     

Rheological properties of skim milk gels at various temperatures; interrelation between the dynamic moduli and the relaxation modulus

The rheological properties of rennet-induced skim milk gels were determined by two methods, i.e., via stress relaxation and dynamic tests. The stress relaxation modulusG _c (t) was calculated from the dynamic moduliG andG by using a simple approximation formula and by means of a more complex procedure, via calculation of the relaxation spectrum. Either calculation method gave the same results forG _c (t). The magnitude of the relaxation modulus obtained from the stress relaxation experiments was 10% to 20% lower than that calculated from the dynamic tests.Rennet-induced skim milk gels did not show an equilibrium modulus. An increase in temperature in the range from 20° to 35 °C resulted in lower moduli at a given time scale and faster relaxation. Dynamic measurements were also performed on acid-induced skim milk gels at various temperatures andG _c (t) was calculated. The moduli of the acid-induced gels were higher than those of the rennet-induced gels and a kind of permanent network seemed to exist, also at higher temperatures. G storage shear modulus,N·m^–2; - G loss shear modulus,N·m^–2; - G _c calculated storage shear modulus,N·m^–2; - G _c calculated loss shear modulus,N·m^–2; - G _e equilibrium shear modulus,N·m^–2; - G _ec calculated equilibrium shear modulus,N·m^–2; - G(t) relaxation shear modulus,N·m^–2; - G _c (t) calculated relaxation shear modulus,N·m^–2; - G ^*(t) pseudo relaxation shear modulus,N·m^–2; - H relaxation spectrum,N·m^–2; - t time,s; - relaxation time,s; - angular frequency, rad·s^–1. Partly presented at the Conference on Rheology of Food, Pharmaceutical and Biological Materials, Warwick, UK, September 13–15, 1989 [33].     

A slit viscometer for the measurement of the viscosity of aqueous systems at high temperatures

A slit viscometer has been constructed to measure the viscosity of aqueous systems at temperatures up to 140 °C. Liquid is forced backwards and forwards through the slit by the use of varying air pressure. The flow rate is obtained from the time for the liquid to pass conductivity probes located in liquid reservoirs either side of the slit. The pressure difference between two points on the slit wall is determined using a differential pressure transducer. By varying the slit height measurements can be made on liquids with viscosities in the range 10 to 10^–3 Pa s. Shear rates from 10 to 10⁴ s^–1 can be achieved. A simple microcomputer control system enables the shear stress to be automatically increased and decreased stepwise. Representative data on polysaccharide solutions and strach suspensions are presented. The viscometer is particularly well-suited for following temperature-dependent biopolymer transitions and the thermal depolymerisation of water soluble polymers.     

Rheology of concentrated microgel solutions

Viscosity, modulus, and yield stress for 0–6 wt% aqueous solutions of Carbopol 941 were investigated using constant shear rate, constant shear stress, and dynamic oscillatory experiments. The microgel character of the polymer was evident from the solid-like behavior of the solutions above 1 wt%. Yield stress increased with concentration, but yield occurred at a critical shear strain of 40%, independent of concentration. The static stress-strain relationship became non-linear at ~ 25% strain, in fair agreement with the onset of non-linear response in the storage modulus at ~ 10% strain. Small strain moduli from static and low frequency measurements agreed rather well; modulus values obtained from the recoverable strain after yielding were 30–40% smaller. Solutions flowed at near-constant stress in the low shear rate regime; at higher rates the stress increases with shear rate more rapidly. The viscosity did not obey the Cox-Merz rule. Steady-state viscosity scaled with polymer concentration to the 3/4 power. Results were interpreted using a cellular, deformable sphere model for the polymer, in analogy to emulsions and foams.     

Instabilities in multi-hole converging flow of viscoelastic fluids

Studies of the onset of instabilities were conducted on single hole and multi-hole contractions using laser speckle visualization. A well characterized elastic fluid was used with constant viscosity of 13.1 Pa · s and elasticity characterized by a longest relaxation time constant of 2.233 s. The onset of instabilities was characterized in terms of the Deborah number and the contraction ratio. Three types of instabilities were observed: pulsing vortices, azimuthally rotating vortices, and swirling vortices. For the single hole contractions the critical Deborah number for instability increased from 4.4 to 5.07 to 5.25 as the contraction ratio increased from 4: 1 to 8: 1 to 12: 1. The magnitude of the instabilities was much greater for the 4: 1 contraction than for the other two contraction ratios. For the multi-hole contraction a square array of nine holes was used and the ratio of the hole diameter to hole spacing was varied. The height of the vortices is very similar for the single hole and multi-hole contractions at low Deborah numbers. At high Deborah numbers the effect of adjacent holes is to reduce the height of the vortices by a factor of three. For the 4: 1 spacing no secondary vortex was observed below a Deborah number of De = 3.7. Secondary vortices occurred for the 8:1 and 10:1 spacing at all Deborah numbers. Unstable pulsing vortices appeared for all spacings at a critical Deborah number around 5.5. Adjacent holes decreased the strength of the unsteady vortex motions. The centerline velocities were measured for the multi-hole contraction at shear rates of 5, 30, and 300 s^–1. The elongational strain rates are similar at a low shear rate of 5 s^–1. As shear rate is increased the onset of stretching occurs closer to the plane of the contraction for the smaller contraction ratios.     

An automated dynamic viscometer with air bearing and inductive transducers for angular displacement detection

A dynamic viscometer is described, with which the dynamic moduli in the frequency range from 2 × 10^–3 to 10 Hz can be determined for liquids with 10^–3 Pa< |G ^* | <10² Pa. Due to the application of an air bearing and inductive transducers for the detection of the angular displacement of both the drive and the measuring cylinder a sensitive apparatus has been made. Very small strains (₀ 10^–3) can be applied and only a small amount of sample (4 ml) is needed. The operation of the apparatus is fully computer-controlled, thus, long runs at various frequencies and temperatures are possible without operator intervention. The theoretical background, calibration procedure, and operation window are described. A presentation of some measurements on two polyisoprene/polystyrene triblock copolymer solutions concludes the work.     

Rheological determination of peptizing agents in bentonite clays

This paper presents the results of an evaluation of the rheological properties of commercial bentonite suspensions made from peptized and unpeptized clay samples collected over a six year time span. The rheological properties of these suspensions were measured between shear rates of 5.11 to 1022 s^–1 at concentrations of 15, 30, 45, 64.2 and 70 kg/m³. Bingham, power-law and Casson models were then fitted to the shear stress and shear rate values. Parameters derived from these models were then subjected to further analyses. Four rheological methods (termed peptization index tests) were developed to differentiate between peptized and unpeptized bentonite samples.     

The rheology of a smectic main-chain polymer

The rheology of a smectic main-chain polymer shows that the activation energy is high (275 kJ mol^–1) and that the viscosity is more than two orders of magnitude higher than in the isotropic phase. The recoverable strain in the smectic phase is largely due to the reformation of the smectic layers after cessation of shear.     

Taylor-Couette stability analysis for a Doi-Edwards fluid

The stability of Taylor-Couette flow of entangled polymeric solutions to small axisymmetric stationary disturbances is analyzed using the Doi-Edwards constitutive equation in the small gap limit. A previous analysis of Karlsson, Sokolov, and Tanner for the general K-BKZ equation, of which the Doi-Edwards equation is a special case, reduces the problem to one of numerically evaluating seven viscoelastic functions of the shear rate in the gap. Of these seven, only three — two of which are related to the second normal stress difference, and one of them to shear thinning — significantly affect the flow stability. The negative second normal stress difference of the Doi-Edwards fluid stabilizes the flow at low values of the Weissenberg number ₁ , while shear thinning produces strong destabilization at moderate Weissenberg number. Here ₁ is the longest relaxation time. Non-monotonic effects of viscoelasticity on Taylor-Couette stability analogous to those predicted here have been observed in experiments of Giesekus. The extreme shear thinning of the Doi-Edwards fluid is also predicted to produce a large growth in the height of the Taylor cells, a phenomenon that has been seen experimentally by Beavers and Joseph.     

Driven torsion pendulum for measuring the complex shear modulus in a steady shear flow

To investigate the viscoelastic behavior of fluid dispersions under steady shear flow conditions, an apparatus for parallel superimposed oscillations has been constructed which consists of a rotating cup containing the liquid under investigation in which a torsional pendulum is immersed. By measuring the resonance frequency and bandwidth of the resonator in both liquid and in air, the frequency and steady-shear-rate-dependent complex shear modulus can be obtained. By exchange of the resonator lumps it is possible to use the instrument at four different frequencies: 85, 284, 740, and 2440 Hz while the steady shear rate can be varied from 1 to 55 s^–1. After treatment of the theoretical background, design, and measuring procedure, the calibration with a number of Newtonian liquids is described and the accuracy of the instrument is discussed.Notation a radius of the lump - A geometrical constant - b inner radius of the sample holder - c constant - C ₁, C ₂ apparatus constants - D damping of the pendulum - e _x , e _y , e _z Cartesian basis - e _r , e , e _z orthonormal cylindrical basis - E geometrical constant - E _t , ⁰ E _t , _t relative strain tensor - f function of shear rate - F _t relative deformation tensor - G (t) memory function - G ^* complex shear modulus - G Re(G ^* ) - G Im(G ^* ) - h distance between plates - H ^* transfer function - , functional - i imaginary unit: i ²= – 1 - I moment of inertia - J _exc excitation current - J ₀ amplitude of J _exc - k ^* = k – ik complex wave number - K torsional constant - K fourth order tensor - l length of the lump - L mutual inductance - M _dr driving torque - M _liq torque exerted by the liquid - ⁰ M _liq, _liq steady state and dynamic part of Mliq - n power of the shear rate - p isotropic pressure - Q quality factor - r radial position - R,R ₀, R _c Re(Z ^*, Z ₀ ^* , Z _c ^* ) - s time - t, t time - T temperature - T, ⁰ T, stress tensor - u velocity - U lock-in output - ₀ velocity - V _det detector output voltage - V _sig, V _cr signal and cross-talk part of V _det - x Cartesian coordinate - X , X ₀, X _c Im(Z ^*, Z ₀ ^* , Z _c ^* ) - y Cartesian coordinate - z Cartesian coordinate, axial position     

Stress optical measurement of the third normal stress difference in polymer melts under oscillatory shear

Results are reported for the dynamic moduli,G andG, measured mechanically, and the dynamic third normal stress difference, measured optically, of a series bidisperse linear polymer melts under oscillatory shear. Nearly monodisperse hydrogenated polyisoprenes of molecular weights 53000 and 370000 were used to prepare blends with a volume fraction of long polymer, _L, of 0.10, 0.20, 0.30, 0.50, and 0.75. The results demonstrate the applicability of birefringence measurements to solve the longstanding problem of measuring the third normal stress difference in oscillatory flow. The relationship between the third normal stress difference and the shear stress observed for these entangled polymer melts is in agreement with a widely predicted constitutive relationship: the relationship between the first normal stress difference and the shear stress is that of a simple fluid, and the second normal stress difference is proportional to the first. These results demonstrate the potential use of 1,3-birefringence to measure the third normal stress difference in oscillatory flow. Further, the general constitutive equation supported by the present results may be used to determine the dynamic moduli from the measured third normal stress difference in small amplitude oscillatory shear. Directions for future research, including the use of birefringence measurements to determineN ₂/N ₁ in oscillatory shear, are described.     

The steady shear viscosity of filled polymeric liquids described by a linear superposition of two relaxation mechanisms

Filled polymeric liquids often exhibit apparent yielding and shear thinning in steady shear flow. Yielding results from non-hydrodynamic particle—particle interactions, while shear thinning results from the non-Newtonian behavior of the polymer melt. A simple equation, based on the linear superposition of two relaxation mechanisms, is proposed to describe the viscosity of filled polymer melts over a wide range of shear rates and filler volume fraction.The viscosity is written as the sum of two generalized Newtonian liquid models. The resulting equation can describe a wide range of shear-thinning viscosity curves, and a hierarchy of equations is obtained by simplifying the general case. Some of the parameters in the equation can be related to the properties of the unfilled liquid and the solid volume fraction. One adjustable parameter, a yield stress, is necessary to describe the viscosity at low rates where non-hydrodynamic particle—particle interaction dominate. At high shear rates, where particle—particle interactions are dominated by interparticle hydrodynamics, no adjustable parameters are necessary. A single equation describes both the high and low shear rate regimes. Predictions of the equation closely fit published viscosity data of filled polymer melts. n power-law index - n ₁,n ₂ power-law index of first (second) term - shear rate - steady shear viscosity - ₀ zero-shear rate viscosity - _{0, 1}, _{0, 2} zero-shear rate viscosity of first (second) term - time constant - ₁, ₂ time constant of first (second) term - µ _r relative viscosity of filled Newtonian liquid - ₀ yield stress - ø solid volume fraction - ø _m maximum solid volume fraction