Elongational Viscosity Measurements Using a Semi-Hyperbolic Die

Abstract The lubricated semi-hyperbolic die has been proposed as a technique for generating uni-axial extensional flow and, hence, as a device for measuring elongational viscosity. Two methods for extracting extensional viscosity data for polymer melts in laminar flow from this device have been proposed and are evaluated here. Following the approach proposed by Collier and coworkers, values of the transient extensional viscosity, ηe+, obtained from a non-lubricated semi-hyperbolic (SHPB) die for several polyethylene (PE) melts were found to be considerably higher than values obtained by means of the Münstedt-type device. Furthermore, the values of ηe+ obtained from the SHPB die were considerably higher than the strain averaged values of ηe+ which Everage and Ballman proposed would be obtained from a lubricated SHPB. The pressure drop across a SHPB die was estimated assuming resistance was all due to wall shear (using the lubrication approximation) for two PE resins. In the case of low density PE (LDPE) the values agreed to within 20% of the measured values suggesting that shear effects at the die wall were dominating the pressure drop and not extensional stresses. An analysis was carried out which showed that in the presence of lubrication the conditions for which the values of ηe+ obtained from the SHPB would be relatively accurate (Hencky strains > 5.0).

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Newtonian and Non-Newtonian Fluids: Velocity Profiles, Viscosity Data, and Laminar Flow Friction Factor Equations for Flow in a Circular Duct

Volume 9: Engineering Education and Professional Development ◽

10.1115/imece2008-67611 ◽

2008 ◽

Cited By ~ 1

Author(s):

Melissa M. Simpson ◽

William S. Janna

Keyword(s):

Fluid Flow ◽

Pressure Drop ◽

Laminar Flow ◽

Friction Factor ◽

Newtonian Fluid ◽

Velocity Profiles ◽

Newtonian Fluids ◽

Viscosity Data ◽

Circular Duct ◽

Flow Friction

Newtonian fluid flow in a duct has been studied extensively, and velocity profiles for both laminar and turbulent flows can be found in countless references. Non-Newtonian fluids have also been studied extensively, however, but are not given the same attention in the Mechanical Engineering curriculum. Because of a perceived need for the study of such fluids, data were collected and analyzed for various common non-Newtonian fluids in order to make the topic more compelling for study. The viscosity and apparent viscosity of non-Newtonian fluids are both defined in this paper. A comparison is made between these fluids and Newtonian fluids. Velocity profiles for Newtonian and non-Newtonian fluid flow in a circular duct are described and sketched. Included are profiles for dilatant, pseudoplastic and Bingham fluids. Only laminar flow is considered, because the differences for turbulent flow are less distinct. Also included is a procedure for determining the laminar flow friction factor which allows for calculating pressure drop. The laminar flow friction factor in classical non-Newtonian fluid studies is the Fanning friction factor. The equations developed in this study involve the Darcy-Weisbach friction factor which is preferred for Newtonian fluids. Also presented in this paper are viscosity data of Heinz Ketchup, Kroger Honey, Jif Creamy Peanut Butter, and Kraft Mayonnaise. These data were obtained with a TA viscometer. The results of this study will thus provide the student with the following for non-Newtonian fluids: • Viscosity data and how it is measured for several common non-Newtonian fluids; • A knowledge of velocity profiles for laminar flow in a circular duct for both Newtonian and non-Newtonian fluids; • A procedure for determining friction factor and calculating pressure drop for non-Newtonian flow in a duct.

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Approximate Calculation of Pressure Drop in Laminar Flow of Generalized Newtonian Liquid Through Channel of Noncircular Cross Section

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19940603 ◽

1994 ◽

Vol 59 (3) ◽

pp. 603-615 ◽

Cited By ~ 1

Author(s):

Václav Dolejš ◽

Ivan Machač ◽

Petr Doleček

Keyword(s):

Pressure Drop ◽

Laminar Flow ◽

Numerical Solution ◽

Cross Section ◽

Approximate Calculation ◽

Newtonian Liquid ◽

Straight Channel ◽

Suggested Procedure ◽

Noncircular Cross Section ◽

Calculation Results

The paper presents a modification of the equations of Rabinowitsch-Mooney type for an approximate calculation of pressure drop in laminar flow of generalized Newtonian liquid through a straight channel whose cross section forms a simple continuous area. The suitability of the suggested procedure of calculation of pressure drop is demonstrated by the comparison of calculation results with both the published and original results of numerical solution and experiments.

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Applicability of the Cox-Merz Rule to High-Density Polyethylene Materials with Various Molecular Masses

Polymers ◽

10.3390/polym13081218 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1218

Author(s):

Raffael Rathner ◽

Wolfgang Roland ◽

Hanny Albrecht ◽

Franz Ruemer ◽

Jürgen Miethlinger

Keyword(s):

Molecular Weight ◽

Pressure Drop ◽

High Molecular Weight ◽

High Density Polyethylene ◽

Parallel Plate ◽

Empirical Relationship ◽

Polymer Processing ◽

High Density ◽

Viscosity Data ◽

Molecular Masses

The Cox-Merz rule is an empirical relationship that is commonly used in science and industry to determine shear viscosity on the basis of an oscillatory rheometry test. However, it does not apply to all polymer melts. Rheological data are of major importance in the design and dimensioning of polymer-processing equipment. In this work, we investigated whether the Cox-Merz rule is suitable for determining the shear-rate-dependent viscosity of several commercially available high-density polyethylene (HDPE) pipe grades with various molecular masses. We compared the results of parallel-plate oscillatory shear rheometry using the Cox-Merz empirical relation with those of high-pressure capillary and extrusion rheometry. To assess the validity of these techniques, we used the shear viscosities obtained by these methods to numerically simulate the pressure drop of a pipe head and compared the results to experimental measurements. We found that, for the HDPE grades tested, the viscosity data based on capillary pressure flow of the high molecular weight HDPE describes the pressure drop inside the pipe head significantly better than do data based on parallel-plate rheometry applying the Cox-Merz rule. For the lower molecular weight HDPE, both measurement techniques are in good accordance. Hence, we conclude that, while the Cox-Merz relationship is applicable to lower-molecular HDPE grades, it does not apply to certain HDPE grades with high molecular weight.

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Thermohydraulics of Laminar Flow Through Rectangular and Square Ducts With Transverse Ribs and Twisted Tapes

Journal of Heat Transfer ◽

10.1115/1.2345432 ◽

2006 ◽

Vol 128 (10) ◽

pp. 1070-1080 ◽

Cited By ~ 43

Author(s):

Debashis Pramanik ◽

Sujoy K. Saha

Keyword(s):

Heat Transfer ◽

Pressure Drop ◽

Laminar Flow ◽

Laminar Flows ◽

Short Length ◽

Full Length ◽

Twisted Tape ◽

Twisted Tapes ◽

Square Ducts ◽

Better Than

The heat transfer and the pressure drop characteristics of laminar flow of viscous oil through rectangular and square ducts with internal transverse rib turbulators on two opposite surfaces of the ducts and fitted with twisted tapes have been studied experimentally. The tapes have been full length, short length, and regularly spaced types. The transverse ribs in combination with full-length twisted tapes have been found to perform better than either ribs or twisted tapes acting alone. The heat transfer and the pressure drop measurements have been taken in separate test sections. Heat transfer tests were carried out in electrically heated stainless steel ducts incorporating uniform wall heat flux boundary conditions. Pressure drop tests were carried out in acrylic ducts. The flow was periodically fully developed in the regularly spaced twisted-tape elements case and decaying swirl flow in the short-length twisted tapes case. The flow characteristics are governed by twist ratio, space ratio, and length of twisted tape, Reynolds number, Prandtl number, rod-to-tube diameter ratio, duct aspect ratio, rib height, and rib spacing. Correlations developed for friction factor and Nusselt number have predicted the experimental data satisfactorily. The performance of the geometry under investigation has been evaluated. It has been found that on the basis of both constant pumping power and constant heat duty, the regularly spaced twisted-tape elements in specific cases perform marginally better than their full-length counterparts. However, the short-length twisted-tape performance is worse than the full-length twisted tapes. Therefore, full-length twisted tapes and regularly spaced twisted-tape elements in combination with transverse ribs are recommended for laminar flows. However, the short-length twisted tapes are not recommended.

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The extensional flow capillary as a new method for extensional viscosity measurement

Nature ◽

10.1038/273213a0 ◽

1978 ◽

Vol 273 (5659) ◽

pp. 213-215 ◽

Cited By ~ 29

Author(s):

A. E. EVERAGE ◽

R. L. BALLMAN

Keyword(s):

Extensional Flow ◽

Viscosity Measurement ◽

Extensional Viscosity ◽

New Method ◽

Flow Capillary

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The interpretation of transient extensional viscosity data

Journal of Non-Newtonian Fluid Mechanics ◽

10.1016/s0377-0257(96)01513-3 ◽

1997 ◽

Vol 68 (2-3) ◽

pp. 241-257 ◽

Cited By ~ 13

Author(s):

J Ferguson ◽

N.E Hudson ◽

M.A Odriozola

Keyword(s):

Extensional Viscosity ◽

Viscosity Data

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Numerical Prediction of Heat Transfer Characteristics of Nanofluids in a Minichannel Flow

Journal of Energy ◽

10.1155/2014/307520 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 5

Author(s):

Arjumand Adil ◽

Sonam Gupta ◽

Pradyumna Ghosh

Keyword(s):

Heat Transfer ◽

Brownian Motion ◽

Pressure Drop ◽

Laminar Flow ◽

Computational Model ◽

Flow Regime ◽

Cfd Simulation ◽

Computational Results ◽

Heat Transfer Characteristics ◽

Simulation Process

CFD simulation of the heat transfer and pressure drop characteristics of different nanofluids in a minichannel flow has been explained using FLUENT version 6.3.26. Different nanofluids with nanoparticles of Al2O3, CuO, SiO2, and TiO2have been used in the simulation process. A comparison of the experimental and computational results has been made for the heat transfer and pressure drop characteristics for the case of Al2O3-water nanofluid for the laminar flow. Also, computations have been made by considering Brownian motion as well as without considering Brownian motion of the nanoparticles. After verification of the computational model with the experimental results for Al2O3-water nanofluid, the simulations were performed for the same experimental readings for different nanofluids in the laminar flow regime to find out the heat transfer and pressure drop characteristics.

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Drag Reduction of Polymer Solutions in a Pipe With a Highly Water-Repellent Wall

10.1115/imece1999-1160 ◽

1999 ◽

Author(s):

Keizo Watanabe ◽

Hiroshi Udagawa

Keyword(s):

Pressure Drop ◽

Laminar Flow ◽

Drag Reduction ◽

Polymer Solutions ◽

Tap Water ◽

Acrylic Resin ◽

Water Repellent ◽

Number Range ◽

Surfactant Solutions ◽

Laminar And Turbulent Flow

Abstract By applying a highly water-repellent wall pipe in the drag reduction of polymer solutions, a flow system in which drag reduction is obtained in both laminar and turbulent flow ranges has been realized. Experiments were carried out to measure the pressure drop in pipes with a highly water-repellent wall and an acrylic resin wall by means of a pressure transducer. The diameter of the pipe was 6mm. The polymer solutions tested were PE015 aqueous solutions in the concentration range of 30ppm∼1000ppm. The drag reduction ratio for laminar flow was about 11∼15%. To understand this effect, the pressure drop was measured by using surfactant solutions and degassed water, and by pressurizing tap water in the pipeline. It was shown that the laminar drag reduction does not occur in the case of surfactant solutions although degassed water and pressurizing tap water in the pipeline have no effect on the reduction. In the laminar flow range, the friction factor of a power-law fluid with fluid slip was analyzed by applying the modified boundary condition on fluid slip at the pipe wall, and the analytical results agree with the experimental results in the low Reynolds number range.

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