A three-parameter model describing the experimental relation between shear stress and shear rate for laminar flow of aqueous polymer solutions

1981 ◽  
Vol 20 (3) ◽  
pp. 270-279 ◽  
Author(s):  
P. J. Hamersma ◽  
J. Ellenberger ◽  
J. M. H. Fortuin
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Laminar Flow ◽  
Polymer Solutions ◽  
Aqueous Polymer ◽  
Experimental Relation

Heat Transfer in Internal Flows of Non-Linear Fluids: A Review

2006 ◽  
Author(s):  
Dennis A. Siginer ◽  
Mario F. Letelier
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Heat Transfer Enhancement ◽  
Polymer Solutions ◽  
Single Mode ◽  
Secondary Flows ◽  
Transfer Enhancement ◽  
Experimental Heat ◽  
Aqueous Polymer ◽  
Non Linear

A survey of the developments in heat transfer studies of non-linear inelastic as well as elastic fluids in tubes is given. Experimental findings concerning heat transfer enhancement characteristics of viscoelastic aqueous polymer solutions are very significant. Specifically, it is reported that heat transfer results for viscoelastic aqueous polymer solutions are drastically higher than those found for water in laminar flow in rectangular ducts. A number of investigators suggested that the high experimental heat transfer values were due to secondary flows resulting from the elasticity of the fluids. In this context recent results concerning the fully developed thermal field in constant pressure gradient driven laminar flow of a class of viscoelastic fluids characterized by single mode, non-affine constitutive equations in straight pipes of arbitrary contour ∂D is reviewed. Heat transfer enhancement due to shear-thinning is identified together with the enhancement due to the inherent elasticity of the fluid. The latter is the result of secondary flows in the cross-section. Increasingly large enhancements are computed with increasing elasticity of the fluid as compared to its Newtonian counterpart. Large enhancements are possible even with dilute fluids. Isotherms for the temperature field are presented and discussed for several non-circular contours such as the ellipse and the equilateral triangle together with heat transfer behavior in terms of the Nusselt number Nu.

Laminar Flow of Non-Newtonian Fluids in Concentric Annuli

1963 ◽  
Vol 3 (04) ◽  
pp. 274-276 ◽  
Author(s):  
Robert D. Vaughn
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Laminar Flow ◽  
Power Law ◽  
Experimental Work ◽  
Newtonian Fluids ◽  
Horizontal Line ◽  
Parallel Plates ◽  
Bingham Plastic ◽  
Fluid Behavior

The limiting cases of non-Newtonian fluids flowing inside a concentric annular duct are developed without using a model of the fluid behavior. The solutions provide limits with which to test the various models of fluid behavior such as the power law and Bingham plastic models. The results of previous theoretical work are discussed in terms of limiting cases. This limiting case study also shows that experimental work on flow of non-Newtonian fluids in annular ducts should be confined to ducts for which the ratio of the radius of the inner wall to that of the outer wall is less than 0.3 and preferably less than 0.2. Introduction During the last 10 years the problem of laminar flow of non-Newtonian fluids in concentric annuli has received much attention largely because of its application to the hydrodynamics of the wellbore. Recently solutions utilizing the power law and Bingham plastic models have been published.In this paper the method of limiting cases, which has been successfully applied to laminar-flow heat transfer will be applied to the problem of flow of non-time dependent, non-Newtonian fluids through annuli. This method permits solutions for the limiting cases to be made without using a model of unknown validity. The solutions, therefore, provide limits with which to test the various models which have been or will be proposed. A pertinent conclusion concerning the region of experimental work is also provided. DEVELOPMENT OF LIMITING CASES The limiting cases for the axial flow of fluids in concentric annuli may be defined with reference to Fig. L It is possible to define two limiting cases which pertain to the physical dimensions of the annulus. First, the annulus must degenerate to a circular pipe as the radius of the inner wall decreases or, as K = (KR/R) - 0. Second, the annulus must approach the limit of parallel plates of infinite extent as the spacing between the inner and outer tubes becomes small in comparison with the radius R of the annulus, or as K - 1. It is also possible to ascertain three limbing cases which pertain to fluid behavior. With reference to Fig. 2, as a fluid becomes progressively more pseudoplastic, the shear stress- shear rate relationship progressively approaches the indicated horizontal line more closely. At this limit the shear stress becomes independent of the shear rate. At the other extreme of increasingly dilatant behavior, the vertical asymptote is approached. Intermediate between these two limiting cases lies the case of the Newtonian fluid. Fluids which exhibit a yield shear stress also approach the limbing case of "infinite" pseudoplastic behavior. SPEJ P. 274^

Rheometric Tests and Extrusion

1951 ◽  
Vol 24 (3) ◽  
pp. 520-540
Author(s):  
Silvio Eccher
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Laminar Flow ◽  
Experimental Determination ◽  
Power Law ◽  
Reasonable Agreement ◽  
Straight Line ◽  
Flow Through ◽  
The Relationship

Abstract A cylindrical rheometer of the Couette type, suitable for the experimental determination of the rheological properties of extruded materials, was designed to provide data which could not be obtained with existing plastometers. The purpose of this study was strictly practical, as the work was performed in connection with a study of extruders. The results obtained on twenty-five different materials—natural and synthetic rubbers and compounds of both with various fillers—are reported; measurements fall within shear rate limits from 1 to 100 seconds−1. In this interval the relationship between logD (rate of shear) and logτ (shear stress) is nearly a straight line. It may, therefore, be analytically interpreted by the power law : D=−(τ/c)n, where n and c are parameters characteristic of the material. As the power law is known to be of limited validity, attempts were made to ascertain the limits of its application in laminar flow through a cylindrical hole. The results of measurements carried out on a 2-inch extruder and employing the same materials as were tested by the rheometer are reported. Measurements of pressure and flow were made, using discharge holes of various diameters and operating the screw at various speeds. Reasonable agreement was found between values of flow and pressure determined with an extruder and those calculated from parameters n and c determined with the cylindrical rheometer.

1990 Max Jakob Memorial Award Lecture: Viscoelastic Fluids: A New Challenge in Heat Transfer

1992 ◽  
Vol 114 (2) ◽  
pp. 296-303 ◽  
Author(s):  
J. P. Hartnett
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Friction Factor ◽  
Power Law ◽  
Polymer Solutions ◽  
Rectangular Channel ◽  
Viscoelastic Fluids ◽  
Transfer Coefficients ◽  
Aqueous Polymer ◽  
Dimensionless Heat

A review of the current knowledge on the fluid mechanics and heat transfer behavior of viscoelastic aqueous polymer solutions in channel flow is presented. Both turbulent and laminar flow conditions are considered. Although the major emphasis is on fully established circular pipe flow, some results are also reported for flow in a 2:1 rectangular channel. For fully established turbulent channel flow, it was found that the friction factor, f, and the dimensionless heat transfer factor, jH, were functions of the Reynolds number and a dimensionless elasticity value, the Weissenberg number. For Weissenberg values greater than approximately 10 (the critical value) the friction factor was found to be a function only of the Reynolds number; for values less than 10 the friction factor was a function of both Re and Ws. For the dimensionless heat transfer coefficient jH the corresponding critical Weissenberg value was found to be about 100. The heat transfer reduction is always greater than the friction factor reduction; consequently, the heat transfer per unit pumping power decreases with increasing elasticity. For fully established laminar pipe flow of aqueous polymer solutions, the measured values of the friction factor and dimensionless heat transfer coefficient were in excellent agreement with the values predicted for a power law fluid. For laminar flow in a 2:1 rectangular channel the fully developed friction factor measurements were also in agreement with the power law prediction. In contrast, the measured local heat transfer coefficients for aqueous polymer solutions in laminar flow through the 2:1 rectangular duct were two to three times the values predicted for a purely viscous power law fluid. It is hypothesized that these high heat transfer coefficients are due to secondary motions, which come about as a result of the unequal normal stresses occurring in viscoelastic fluids. The anomalous behavior of one particular aqueous polymer solution—namely, polyacrylic acid (Carbopol)—is described in some detail, raising some interesting questions as to how viscoelastic fluids should be classified. In closing, a number of challenging research opportunities in the study of viscoelastic fluids are presented.

scholarly journals Quantification of shear viscosity and wall slip velocity of highly concentrated suspensions with non-Newtonian matrices in pressure driven flows

2021 ◽  
Author(s):  
Patrick Wilms ◽  
Jan Wieringa ◽  
Theo Blijdenstein ◽  
Kees van Malssen ◽  
Reinhard Kohlus
Keyword(s):  
Shear Stress ◽  
Liquid Phase ◽  
Shear Rate ◽  
Shear Viscosity ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Wall Slip ◽  
Flow Index ◽  
Concentrated Suspensions

AbstractThe rheological characterization of concentrated suspensions is complicated by the heterogeneous nature of their flow. In this contribution, the shear viscosity and wall slip velocity are quantified for highly concentrated suspensions (solid volume fractions of 0.55–0.60, D4,3 ~ 5 µm). The shear viscosity was determined using a high-pressure capillary rheometer equipped with a 3D-printed die that has a grooved surface of the internal flow channel. The wall slip velocity was then calculated from the difference between the apparent shear rates through a rough and smooth die, at identical wall shear stress. The influence of liquid phase rheology on the wall slip velocity was investigated by using different thickeners, resulting in different degrees of shear rate dependency, i.e. the flow indices varied between 0.20 and 1.00. The wall slip velocity scaled with the flow index of the liquid phase at a solid volume fraction of 0.60 and showed increasingly large deviations with decreasing solid volume fraction. It is hypothesized that these deviations are related to shear-induced migration of solids and macromolecules due to the large shear stress and shear rate gradients.

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