Development of a new mixing rheometer for studying rheological behaviour of concentrated energetic suspensions

The overall objective is to present a procedure based on a Couette analogy to quantitatively analyse torque/rotor speed data and extract viscosity/shear-rate curves using a non-conventional geometry. Diphasic flows of energetic concentrated suspensions of melt-cast insensitive explosives exhibit particular rheological properties. The characterization of these complex fluids may be a challenging task when conventional rheometers are used. Placing these dense suspensions in a classic cylindrical geometry may lead to a partial destruction of the internal fluid structure. To prevent that, a “RheoXF” a mixer-type rheometer has been developed: it consists of a mixing device with quite a complex geometry rotating in a cylindrical tank. To evaluate the rheological constants (virtual radius, virtual shear rate and stress constants) of thus mixing rheometer, we used five Newtonian fluids. After this calibration, the rheological characterizations were carried out on five formulations. The unique parameter which changes in these formulations is the batch's origin of a secondary explosive: the 3-nitro-1,2,4-triazole-5-one. These energetic particles differ by their morphology, maximum packing density and may be by their process synthesis. After having determined pseudoplastic parameters, a correlation has been made with the evolution of maximum packing density values calculated with De Larrard model.     

A specific slit die rheometer for extruded starchy products. Design,validation and application to maize starch

A novel in-line rheometer, called Rheopac, has been designed and built in order to study the rheological behaviour of starchy products or, more generally, of products sensitive to a thermomechanical treatment. It is based on the principle of a twin channel, using a balance of feed rate between each of them, in order to make local shear rate vary in the measuring section without changing the flow conditions into the extruder. A wide range of shear rate could be reached and measurements were performed more swiftly than with a classical slit die. The viscous behaviour of maize starch was studied by taking into account the influence of the thermomechanical history, which modified the starch degradation and thus led to important variations in the viscosity. Experimental results were satisfactorily compared to previously published models.Nomenclature E activation energy (J · mol^–1) - h channel depth (m) - h ₁ depth under the piston valve in channel 1 (m) - h ₂ depth under the piston valve in channel 2 (m) - K consistency (Pa·s ⁿ ) - K ₀ reference consistency (Pa·s ⁿ ) - L total channel length (m) - L _p length of the piston valve (m) - MC moisture content (wet basis) - n power law index - N screw rotation speed (rpm) - P ₀ entrance pressure (Pa) - P _e pressure at the entry of the piston valve (Pa) - Q ₁ flow rate in channel 1 (m3 · s^–1) - Q ₂ flow rate in channel 2 m³·s^–1) - Q _T total flow rate (m3 · s^–1) - R constant of perfect gas (8.314 J·mol^–1·K^–1) - SME specific mechanical energy (kWh · t^–1) - T temperature (°C) - T _a absolute temperature (K) - T _b barrel temperature (°C) - T _d die temperature (°C) - T _p product temperature (°C) - w channel width (m) - W energetical term (J·m^–3) - viscosity (Pa · s) - [gh ₀] intrinsic viscosity of native starch (ml·g^–1) - [] intrinsic viscosity (ml·g^–1) - shear rate (s^–1) - shear rate in measuring section (s^–1) - maximum shear rate (s^–1)     

Evaluation and comparison of routes to obtain pressure coefficients from high-pressure capillary rheometry data

A capillary rheometer equipped with a pressure chamber is used to measure the pressure-dependent viscosity of polymethylmethacrylate (PMMA), poly-α-methylstyrene-co-acrylonitrile (PαMSAN), and low-density polyethylene (LDPE). Data analysis schemes are discussed to obtain pressure coefficients at constant shear rate and at constant shear stress. It is shown that the constant shear stress pressure coefficients have the advantage of being shear stress independent for the three polymers. The constant shear rate pressure coefficients, on the other hand, turn out to depend on shear rate, which makes them less suitable for use, e.g., in process simulations. In addition to the commonly used superposition method, a direct calculation method for the pressure coefficients is tested. Values obtained from both methods are equivalent. However, the latter requires less experimental and calculational efforts. From the obtained pressure coefficients, it is clear that PMMA and PαMSAN have a very similar pressure dependence, while LDPE is less sensitive to pressure.     

The end correction for power-law fluids in the capillary rheometer

The finite element scheme developed by Nickell, Tanner and Caswell is used to compute the entry and exit losses for creeping flow of power-law fluids in a capillary rheometer. The predicted entry losses for a Newtonian fluid agree well with available experimental and theoretical results. The entry losses for inelastic power-law fluids increased with decreasing flow behaviour index and show an increasing deviation from available upper bound results as the flow behaviour index in the power-law decreases.The exit losses are found to be finite for inelastic power-law fluids and increase as the flow behaviour index decreases. The predicted die swell for Newtonian fluids agrees well with the available experimental data while the influence of shear thinning is to reduce the die swell.The end correction which is the sum of the entry and exit losses relative to twice the viscometric wall shear stress varies from 0.834 for n = 1 to 2.917 for n = 1/6. This figure reaches a very high value as n tends to zero. The experimental variation in the Couette correction factor in capillary rheometry is explained in terms of the shear thinning characteristics of the fluid. It is concluded that the exit flow is not viscometric, contrary to a common assumption.     

A dynamic U-tube rheometer of novel design for the study of weak gels and foams

A novel rheometer based on the U-tube technique of Saunders and Ward has been developed to determine the shear moduli of very weak gels and foams. The instrument is fully automatic and operates in both static and oscillatory modes. The change of the shear modulus, with the time, was monitored in three series of samples to illustrate the performance of the instrument. The first series comprised gelatinized maize starch aqueous suspensions ranging in starch concentration from 6% to 12%. The second was a series of gelatine aqueous solutions ranging in gelatine content from 2% to 12%. The third was two commercial samples of shaving foam. The results indicated that the instrument is particularly suitable for the study of the gelation mechanism in very weak gels as well as for the study of the stability of foams in relation to time.     

Design and operation of the free jet elongational rheometer

The controlled free jet instability is used for elongational rheometry of polymer solutions. The instantaneous elongational viscosity represents a convenient comparative parameter. Its dependence on the operating parameters and the conditions of operation will be discussed.     

A micromechanical model for porous materials with a reinforced matrix

In this study a micromechanical model is proposed for ductile porous material whose matrix is reinforced by small inclusions. The solid phase is described by a pressure sensitive plastic model. Based on works of Maghous et al. [6], a macroscopic plastic criterion is firstly obtained by using a two-step homogenization procedure. The effect of porosity at the mesoscale and the influence of inclusions at the microscale are taken into account simultaneously by this criterion. With a non-associated plastic flow rule, the micro-macro model is applied to modeling of mechanical behavior of a cement paste. In particular, we have considered at the microscopic scale the formation of calcite grains by carbonation process in the solid matrix. The studied cement paste is then seen as a reinforced matrix–pore system. Comparisons between numerical results and experimental data show that the proposed model is able to capture the main features of the mechanical behavior of the studied material.     

A parallel-plate rheometer for the measurement of steady-state and transient rheological properties

A parallel-plate rheometer (PPR) has been constructed for use with the Materials Test System (MTS) for the measurement of fast transient and steady-state responses of polymeric liquids. This particular combination exploits the versatility and capability of the MTS programmable drive system, while the design of the PPR ensures the ideal simple shearing configuration. Instrument compliance, material inertia and mechanical lag in both the input and output components of the system are minimal, thus avoiding defects of most existing rheometers. Reproducible data on a 20% polyisobutylene-in-decalin solution have been obtained for various complicated flow programs. This test system is thus suitable for extensive rheological characterization of complex viscous liquids.     

The rheological properties of solder and solar pastes and the effect on stencil printing

Solar and solder pastes are widely used in the electronics industry. Solder paste is the principal joining medium in the assembly of surface mount components, whilst solar paste is used in the manufacture of semiconductor solar cells in the photo-voltaic industry. The stencil printing of both solder and solar pastes is a very important and critical stage in the assembly process. With miniaturisation of components, this is likely to continue. The challenge in stencil printing at such dimensions is in achieving repeatable deposition of both solar and solder pastes from print to print. To meet this challenge requires an understanding of the flow behaviour of both solar and solder pastes. The rheological properties of solar and solder pastes have been evaluated through three different types of experiments. Existing models were applied to compare their rheological behaviour under these schemes. One striking difference was that solar paste showed a higher viscosity than solder paste. Both solar and solder pastes were found to be non-Newtonian materials, showing a decrease in viscosity with increasing shear rates. In this paper we investigate the rheological properties of both solder and solar paste under steady shear and creep-recovery tests. Received: 12 October 1999 Accepted: 11 July 2000     

The rheology of recycled EVA/LDPE modified bitumen

This paper describes linear viscoelasticity, at low and intermediate temperatures, and the flow behaviour, at high temperatures, of polymer modified bitumen (PMB) containing 5 and 9 wt% recycled EVA/LDPE. The relationship between flow behaviour and microstructure of the modified bitumen was also considered, by comparison of experiments carried out in capillary and rotational rheometers and photomicrographs taken using a microscopy system whilst the sample was being sheared. Blends of 60/70 penetration grade bitumen and waste plastic (EVA/LDPE) were processed in an open mixer using a four blade propeller. Rheological tests, differential scanning calorimetry (DSC) and microscopy showed that the bitumen performance was improved by adding the recycled polymer. As a consequence, the use of recycled EVA/LDPE in PMBs can be considered a suitable and interesting alternative from both an environmental and economical point of view. The experimental results also show that pure bitumen has shear-thinning characteristics. The blending of polymer into the bitumen modifies the melt processing characteristics of the blend, whilst the viscoelastic properties of the semi-solid composite are enhanced.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.     

The concept of a rotational rheometer with helical screw impeller

The paper is concerned with the development of an on-line rheometer for suspensions with settling particles. A new concept of a rotational rheometer with helical screw impeller is discussed. On the basis of model considerations a procedure for the flow curve determination of the investigated fluid has been proposed. Contrary to previous attempts, in the developed procedure no calibration of the instrument is necessary. The preliminary experimental verification of the developed approach proved its applicability.     

On-line measurement of elasticity and viscosity in flowing polymeric liquids

A new slit-die rheometer (the Stressmeter) for on-line and sample measurement of the viscosity, , and the first normal stress difference, N ₁, in steady shear flow for molten polymers and other high-viscosity liquids is described. Two liquid-filled transverse slots, located in one die wall near the center station, give pressures P ₂ and P ₃ from whose difference the wall shear stress is calculated. In the other die wall at a location opposite the center of the P ₂ slot is a flush-mounted transducer, giving a pressure P ₁. N ₁ is calculated from the hole pressure P ^* = P ₁–P ₂. A metering pump, used to measure the flow rate Q, is supplied with melt either from an extruder (online mode) or from a pressurized sample cylinder (sample mode). The wall shear rate is calculated from Q and ; the Weissenberg-Rabinowitsch correction and a new small-viscous-heating-correction algorithm (affecting ) are used. Viscous heating corrections are small; entrance and exit errors are negligible. The instrument is tested by comparing its results with those obtained from cone-plate and capillary rheometers. Measurement ranges extend to = 200 kPa, = 3000 s^–1, and temperature = 250°C.Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

Geometry dependence of the viscosity of a thermotropic LC-polymer measured by slit dies

This paper reports on geometry dependent viscosity curves of the biaxial thermotropic LC-Polymer Vectra B 950 measured with rectangular slit dies. The geometry dependence of the flow behaviour originates from the flow of two layers. The layer near the wall is highly flow oriented and free from defects. The layer in the bulk has an ordered texture. The thickness of the wall layer decreases with wall shear stress. Based on the Frank theory and the assumption that the core of a moving disclination is the smallest radius of distortion, the wall layer thickness is predicted and compared with experimental data.     

Development and laboratory evaluation of a rheometer for soil visco-plastic parameters

A motorized rheometer was developed for determining soil visco-plastic parameters that works on the principle of torsional shear applied to a standard vane with controlled strain rate. Rheological measurements were carried at different soil moisture contents (10%, 13%, 17% and 20% dry basis (gravimetric)) and soil compaction levels (100, 150, 200, 300 and 400 kPa) to find their effects on soil viscosity and yield strength. The values of viscosity of the clay loam soil (29% clay, 24% silt and 47% sand) were found to spread in the range of 53–283 kPa s, and yield stress variation had a span of 4–28 kPa. Increase in soil compaction was accompanied by a sharp increase in soil viscosity, while moisture content affected soil viscosity negatively. Effect of both these parameters was statistically significant (95% confidence interval). Yield stress was positively related to soil compaction and the effect was statistically significant. However, it was negatively related to moisture content and the effect was not statistically significant for the levels of moisture content tested.     

A novel geometry for rheological characterization of viscoelastic materials

A novel geometry for generating a viscometric flow presents advantages of both cone and plate and parallel plate geometries, regarding uniform shear field and adjustable range of measurement. Kinematics and dynamics of the generated flow have been described mathematically utilizing an orthogonal curvilinear coordinate system based on the shapes of the shearing surfaces which are similar to the surface that generates the flow. Simple equations that allow the calculation of quantities of experimental interest in the rheological characterization of liquid materials, namely, shear rate, shear stress and two normal stress differences, have also been derived.The geometry, called pseudosphere, was tested with two types of fluids (Newtonian and pseudoplastic). Results show that the geometry can be used with low viscosity liquids (Newtonian liquids) by only adjusting the gapH. The behavior of pseudoplastic fluids for both low and moderately high viscosity could also be studied with this geometry. Very reproducible results were obtained when compared with those obtained with cone and plate geometry. Regions of lower shear rate could be studied using only the pseudosphere geometry.     

Effect of capillary pressure on the approach to residual saturation

The approach to residual oil saturation during the immiscible displacement of oil as predicted by the multiphase Darcy equations is studied. It is well known that when the capillary pressure term is neglected, one arrives at the Buckley-Leverett formulation according to which the inlet face attains residual oil saturation instantaneously. This result may, however, be strongly influenced by the inclusion of the capillary pressure term. In this paper it is shown that when the relative permeability and capillary pressure functions have power law dependencies on the saturation deviation from residual oil condition, the long time solution exhibits a power law decay toward residual saturation. Moreover, the power law decay solution is found to be unique and independent of the initial condition. The relationship of this solution to the classical Buckley-Leverett result is shown. Finally, generalization to the time varying flow rate case is addressed. As a verification of the theoretical conjectures, the power law solution is compared with direct numerical simulation of the two phase flow equations.     

The rheological characterization of HPG gels: Measurement of slip velocities in capillary tubes

Measurements are reported for the properties of two hydroxypropyl guar (HPG) gels. The flow curves are composed of three distinct regions: a yield value at low stress levels, a quasi-linear region at intermediate stress or deformation rate levels, and a broad region at high deformation rate levels in which the flow is entirely dominated by slip phenomena.     

A procedure to determine the viscosity function from experimental data of capillary flow

The accurate calculation of the viscosity η as function of the shear rate &γdot; from capillary viscometry is still a matter of debate in the literature. In fact, this problem involves the inversion of an integral equation, which leads to multiple solutions due to the unavoidable noise present in the experimental data. The purpose of this work is to develop an efficient procedure to determine the viscosity function from experimental data of capillary flow without presenting the difficulties inherent in other methods discussed previously in the literature. The system identification procedure is used here to estimate the parameters of a viscosity model, which is appropriately selected for the fluid under study through preliminary calculations involving the apparent shear rate – shear stress data. Once the model is chosen by satisfying criteria for the fit goodness and its parameters are evaluated, a smooth and continuous function η(γdot;) is obtained in the range of experimental shear rates. The procedure proposed is also applicable to fluids in shear flow that present two Newtonian plateaus, as it is typically found in macromolecular dilute solutions. The mean value theorem of continuous functions is used to reduce significantly the computational time. Received: 15 November 1999 Accepted: 7 November 2000     

The effect of step-stretch parameters on capillary breakup extensional rheology (CaBER) measurements

Extensional rheometry has only recently been developed into a commercially available tool with the introduction of the capillary breakup extensional rheometer (CaBER). CaBER is currently being used to measure the transient extensional viscosity evolution of mid to low-viscosity viscoelastic fluids. The elegance of capillary breakup extensional experiments lies in the simplicity of the procedure. An initial step-stretch is applied to generate a fluid filament. What follows is a self-driven uniaxial extensional flow in which surface tension is balanced by the extensional stresses resulting from the capillary thinning of the liquid bridge. In this paper, we describe the results from a series of experiments in which the step-stretch parameters of final length, and the extension rate of the stretch were varied and their effects on the measured extensional viscosity and extensional relaxation time were recorded. To focus on the parameter effects, well-characterized surfactant wormlike micelle solutions, polymer solutions, and immiscible polymer blends were used to include a range of characteristic relaxation times and morphologies. Our experimental results demonstrate a strong dependence of extensional rheology on step-stretch conditions for both wormlike micelle solutions and immiscible polymer blends. Both the extensional viscosity and extensional relaxation time of the wormlike micelle solutions were found to decrease with increasing extension rate and strain of the step-stretch. For the case of the immiscible polymer blends, fast step-stretches were found to result in droplet deformation and an overshoot in the extensional viscosity which increased with increasing strain rates. Conversely, the polymer solutions tested were found to be insensitive to step-stretch parameters. In addition, numerical simulations were performed using the appropriate constitutive models to assist in both the interpretation of the CaBER results and the optimization of the experimental protocol. From our results, it is clear that any rheological results obtained using the CaBER technique must be properly considered in the context of the stretch parameters and the effects that preconditioning has on viscoelastic fluids.