Mahesh Padmanabhan

Extensional viscosity from entrance pressure drop measurements

Extensional rheological properties are important in characterization and processing of polymeric liquids. The use of entrance pressure drop to obtain extensional viscosity is particularly attractive because it can be applied to both low and high viscosity liquids using the Bagley correction obtained from a conventional capillary rheometer.Low density polyethylene of three different melt index values, including IUPAC-X (a different batch of IUPAC-A), and a high density polyethylene were tested using a commercial capillary rheometer. The entrance pressure drop (ΛPen) was obtained with a “zero-length” orifice die with an abrupt contraction. The contraction ratio was 12:1. Predictions from several approximate analyses to calculate the uniaxial extensional viscosity ηu (using an axisymmetric contraction) from ΔPen were compared. These comparisons are summarized in the appendices.Due to the transient nature of contraction flows, ηu is also a function of the strain (ɛ). This was examined by comparing ηu from ΔPen (Cogswells analysis was chosen for convenience) with transient extensional viscosity (ηu+) at different magnitudes of ɛ from fiber-windup technique (Padmanabhan et al., 1996). ηu+at ɛ≈ 3 was found to be close to ηu from ΔPen (using Cogswells analysis) for two LDPE samples that had fiber-windup data available. The magnitude of the strain in the contraction did not vary with strain rate.

Flow behavior and exit pressures of corn meal under high‐shear–high‐temperature extrusion conditions using a slit diea)

Corn meal and commercial low density polyethylene (LDPE) were extruded through a slit die using a laboratory model single‐screw extruder at various extrusion conditions. Flow curves for the corn meal showed severe shear thinning behavior (n≲0) at lower moisture contents; molecular degradation, pressure dependence of viscosity, viscous dissipation, slip, and yield stress were identified as the possible factors. Survey of the available literature and the behavior observed in this study indicates that molecular degradation is the major factor responsible for n≲0. A modified viscosity model that includes the die entrance pressure (barrel pressure) for molecular degradation effects was developed; such a model also accounts for the pressure dependence of viscosity. Negative exit pressures for LDPE and both positive and negative exit pressures for corn meal were obtained. Statistical analysis indicated large errors in the exit pressures predicted by the linear extrapolation. These errors originate from several s...

Measurement of extensional viscosity of viscoelastic liquid foods

Abstract Extensional rheology of foods can be important and helpful in various stages of food manufacture, starting from the initial stage of formulation to the final stage of sensory perception of the product by the consumer. Several new techniques have been developed over the last two decades to measure the extensional flow properties of polymeric liquids. Some of these techniques can be employed to measure the extensional viscosity of foods. Three such techniques are reviewed in this paper: the fiber wind-up and the entrance pressure drop technique for high viscosity liquids, and the opposed jets device for low viscosity liquids. The fiber wind-up technique requires a special set of fixtures which is attached to a conventional rotational rheometer. The entrance pressure drop technique requires a capillary rheometer. A large-diameter barrel capillary rheometer is useful to obtain data for wheat doughs. A commercial rheometer is available with the opposed jets configuration for low viscosity liquids (RFX). Extensional viscosity data from all these techniques are examined and their application to foods discussed. The transient extensional viscosity of a high viscosity polyisobutylene (a polymer melt at room temperature) obtained using the fiber wind-up technique over extension rates of 0.5–10 s−1, and up to strains of three is examined. The extensional viscosity of two different wheat flour-water mixtures estimated using the entrance pressure drop technique is presented. Both doughs showed extension-thinning behavior over the range of extension rates examined. The use of the opposed jets device to characterize polysaccharide solutions is discussed based on a study conducted by R. C. Clark in 1991 (Extensional viscosity of some food hydrocolloids. Paper presented at the Sixth International Conference on Gums and Stabilizers in the food industry, Wrexham, Wales, 15–19 July 1991).

Transient extensional viscosity from a rotational shear rheometer using fiber‐windup technique

The fiber‐windup technique, developed by Macosko and Lorntson [SPE Tech. Papers 19, 461–467 (1973)] for rotational shear rheometers, was re‐examined to obtain transient uniaxial extensional viscosity data. Macosko and Lorntson used a special force transducer to measure the tension in the filament being pulled. In contrast, in this study commercial rotational shear rheometers (Rheometrics Mechanical Spectrometer‐800 and Rheometrics Fluids Spectrometer‐II) with torque transducers were used to obtain the extensional viscosity. One end of the sample is clamped, while the other end is wound around a drum at a constant rotational speed, to achieve a given extension rate. Tests were conducted with a polyisobutylene sample at room temperature to verify reproducibility and were compared with published studies. Results for polyisobutylene and IUPAC‐X low density polyethylene were found to be in good agreement with published results. Hencky strains of up to 6 could be achieved. The technique can provide valuable ext...

In-line measurement of rheological properties of polymer melts

Shear viscosity (η), first normal stress difference (N1), and extensional viscosity (ηE) of polymer melts measured under processing conditions are important in process modeling, quality control, and process control. A slit rheometer that could simultaneously measure η, N1, and the planar extensional viscosity (ηp) was designed and tested by attaching it in-line to a laboratory model single-screw extruder. A tube (circular cross-section) rheometer to measure η and the uniaxial extensional viscosity (ηu) simultaneously was also designed and tested. Two commercial grades of LDPE (low density polyethylene) with melt index values of 6 and 12 were used as test materials for the study. Exit and hole pressure methods were used to estimate N1, and the entrance pressure drop method using the analyses of Cogswell, Binding, and Gibson (the last analysis used with the axisymmetric case only) was used to estimate ηE.The hole pressure method was considered better than the exit pressure method to estimate N1 (due to the greater susceptibility of the latter to experimental errors). From the hole pressure method N1 was obtained from 100 kPa to 500 kPa over a range of shear rates from 40 s−1 to 700 s−1. Among the analyses used to estimate the extensional viscosity, Cogswells is recommended due to its simpler equations without loss of much information compared to the other analyses. The range of extension rates achieved was 1 to 30 s−1. The combination of the hole pressure and entrance pressure drop methods in a slit rheometer is a feasible design for a process rheometer, allowing the simultaneous measurement of the shear viscosity, first normal stress difference and planar extensional viscosity under processing conditions. Similarly, combining the entrance pressure drop measurements with a tube rheometer is also feasible and convenient.

Effect of extrusion processing history on the rheology of corn meal

Abstract Slit and capillary dies attached in-line to an extruder are a popular configuration for obtaining the flow curves of food doughs during extrusion-cooking. However, it is demonstrated in this paper that the use of screw speed, especially for a single-screw extruder, to vary the shear rate through the die can result in erroneous flow curves for single-screw extruders. Furthermore, the use of a sidestream valve to vary the flow rate for a given screw speed is shown to result in flow curves that are different and better behaved. Such a procedure will be helpful in single-screw extruder systems, not only in obtaining the true flow curves of the food dough, but also in rheological measurements with in-line rheometers. Data for hole pressure (a measure of the first normal stress difference) are also presented to demonstrate the validity of using the sidestream valve and the error in using the screw speed to obtain rheological measurements during extrusion of starchy foods.

Single‐point correction for parallel disks rheometry

The nonhomogeneous nature of the flow in the parallel disks rheometer necessitates the differentiation of the measured quantities (torque and normal force) with respect to the shear rate at the disk rim. Commercial instruments do not calculate true material functions online, rather they report apparent Newtonian values, i.e., ones obtained assuming the material functions are constants. In this work, we present a single‐point correction technique to obtain approximate values for material functions without numerical differentiation. The advantage of the single‐point correction method is that it gives more accurate results than the apparent Newtonian values and it takes less time than numerical differentiation. This can, therefore, be useful in quality control laboratories and for process‐line measurements where reasonably accurate data are needed in a short time. A single‐point correction is applied to the parallel disks device for the shear viscosity and a new correction method for the normal stress coefficients is also developed. The accuracy of these approximate methods is tested with experimental results for a polymer melt and a polymer solution. The correction for both shear viscosity η and normal stress coefficient Ψ≡Ψ1−Ψ2 avoids the numerical differentiation of the data and can be easily implemented in software that provide online material functions.

Planar extensional viscosity of corn meal dough

Abstract The application of the entrance pressure drop method to evaluate the extensional viscosity of corn meal during extrusion-cooking was investigated. An approximate planar extensional flow was generated by forcing the dough from a circular channel barrel into a slit die. The pressure drop along the contraction was calculated to obtain the entrance pressure drop Δ P en . Both Cogswells and Bindings analyses were applied to estimate the apparent planar extensional viscosity η pa from Δ P en . The magnitude of η pa from Cogswells analysis was found to be much larger than that predicted by Bindings analysis. In addition, the severe extension-thinning behavior exhibited by the fluid introduced problems in the calculations of Bindings analysis for some cases. Calculation and interpretation of the Trouton ratios have to be done carefully when extrapolation of the viscosities is required. Moderate to large entrance corrections were obtained, with lower values obtained for the lower moisture contents and temperatures of extrusion. In all cases the entrance correction decreased with increasing flow rate.

Rheological measurement of fluid elasticity during extrusion cooking

Abstract The use of slit rheometers for on-line viscosity measurements of fluid foodstuffs has been gaining increasing popularity in recent years. However, the viscoelastic nature of fluid foodstuffs necessitates the measurement of their elastic properties, which will provide a better overall understanding of the behavior of the foodstuffs during processing. This review discusses the exit-pressure and hole-pressure methods for the on-line measurement of fluid elasticity, and the application of these methods to the control of the extrusion-cooking process. The potential application of the methods to the rheological characterization of viscoelastic fluid foodstuffs in general is also discussed.

Remarks on two available extensional viscosity measurement techniques

Two different experimental methods for measuring extensional viscosity are examined, the entrance pressure drop method and the opposed-nozzle approach. The velocity and stress fields for the flows that occur in these geometries have been obtained by integrating the corresponding governing equations. The Galerkin method with finite element basis functions was employed in the integration. An inelastic constitutive relation with a new viscosity function was used to relate the extra stress with the flow field. The pressure drop and force that are measured in the experimental techniques are evaluated here by using the calculated pressure and stress fields. These quantities are then used in conjunction with the working equations of each technique to determine apparent extension viscosities and extension rates. The thus obtained extensional viscosity functions are compared with the ones used in the constitutive equation, to give an assessment of the accuracy of each technique. Results show that the entrance pressure drop method underestimates the extension viscosity of extension-thinning fluids and overestimates this material function when the fluid displays extension-thickening. The opposed-nozzle method is quite reliable at low to moderate extension rates. At high rates, shear thinning becomes important and affects the measured force.