Volume 12, Issue 1, March 1968
Index of content:
12(1968); http://dx.doi.org/10.1122/1.549097View Description Hide Description
The problem of determining the shear rate in a non‐Newtonian fluid sheared between rotating coaxial cylinders has eluded exact solution, although many approximations and solutions in infinite series form are available. The present paper shows that certain of the infinite series which appear in Krieger and Elrod’s solution [J. Appl. Phys., 24, 134 (1953)] can be summed in closed form, leading to an expression for the shear rate in which the dominant term is identical to the local power‐law approximation, and the correction terms take account of deviation from power‐law behavior. As a consequence, point‐by‐point application of the power law is shown to give an excellent approximation to the true shear rate in Couette flow, with a small and readily calculable error.
12(1968); http://dx.doi.org/10.1122/1.549098View Description Hide Description
A study was made of the rheological behavior of dilatant fluids. It was found that such behavior is particularly sensitive to size, shape, and surface characteristics of particles used in dilatant systems. Dilatant behavior was found to take place with a number of different suspensions of corn starch in various fluids. These fluids were ethylene glycol, ethylene glycol‐glycerine, ethylene glycol‐glycerine‐water, and ethylene glycol‐water. The power law held for flow curves of these fluids from 20 to Effect of temperature on power‐law parameters was determined. It was found that n, flow behavior index, was relatively insensitive to temperature while K, consistency index, was a function of temperature according to an Arrhenius relation. The power‐law parameter relation to suspension concentration was also determined. It was found that n increased with increasing concentration while K decreased with increasing concentration.
12(1968); http://dx.doi.org/10.1122/1.549099View Description Hide Description
A theory for the rheological behavior of dilatant (shear‐thickening) fluids was developed. The theory based on physical‐chemical principles was shown to overcome the shortcomings of existing theories. In addition, it was found that the theory predicted the rheological behavior of dilatant (shear‐thickening) fluids as affected by particle size, suspending medium characteristics, temperature, and concentration.
12(1968); http://dx.doi.org/10.1122/1.549092View Description Hide Description
Stress‐birefringent patterns were determined for a viscoelastic fluid (14 wt‐% polystyrene in Aroclor) flowing into a sharp‐edged channel entrance. The final data are point‐by‐point shear stresses and differences in normal stresses. Independent shear and normal stress data were obtained on the Weissenberg Rheogoniometer. In developed straight channel flow, the experimental shear stresses are in quantitative agreement with those calculated from the rheogoniometer data; the normal stresses are of the correct magnitude but the agreement is not quantitative. Very good detail of the stresses at the corners and in the entrance region is available. The entrance regions are of the order of one large channel width upstream and one small channel width downstream, as judged by the approach of the stresses to within a few per cent of their developed values. The accelerating region upstream of the entrance was treated theoretically with a simplified version of the theory of Bernstein, Kearsley, and Zapas, using the model of radial, plug flow. Although a reasonably good prediction of the normal stresses along the centerline is obtained, the predominance of the Newtonian term does not make the check a sensitive one.
12(1968); http://dx.doi.org/10.1122/1.549117View Description Hide Description
The dependence of the response of viscoelastic media upon the magnitude of the Deborah number describing the deformational process is predicted to be a strong one, with materials which are normally considered to be “solids” submitting readily to large‐scale, irreversible (fluid‐like) deformations at low Deborah numbers, and low viscosity (“fluid”) materials predicted to exhibit recoverable, strain‐dependent deformations of a solid‐like character in the asymptotic limit of a large Deborah number. This paper reports the results of investigations in which low viscositymaterials (3–20 cp) were deformed by means of sudden impacts with blunt objects. At the high Deborah number level of these experiments it is seen that these systems exhibit dramatically little evidence of a fluid‐like response, in contrast to their behavior in steady flows
12(1968); http://dx.doi.org/10.1122/1.549118View Description Hide Description
The purpose of this review is to inform those whose interests have been primarily in the rheology of organic polymers and simple liquids as to the similarities and differences between the inorganic glasses and these substances. The inorganic glasses act more like molecular liquids than like polymers; although there have been some reports of a yield stress for flow in the high‐viscosity range, these have not been widely confirmed, and the best available evidence is that the inorganic glasses are Newtonian liquids under the usual stress levels used to measureviscosity near, but above, In the transformation range the viscosity is time‐dependent as volume (or more generally structural) relaxation occurs. Study of these processes permit two conclusions: a single internal ordering variable is insufficient to describe the state, and the free volume concept for viscosity is inadequate, at least in its original form. Of the various equations for viscosity so far proposed, that due Adam and Gibbs appears to offer the widest range of satisfactory agreement. It is based on a reintroduction of the concept of an activation energy for flow, and in the author's view, such a picture offers the best hope of explaining not only the ordinary rheology of glass but the highly nonlinear and presumably related phenomenona of cold flow in polymers and plasticity in inorganic glasses.
12(1968); http://dx.doi.org/10.1122/1.549100View Description Hide Description
Up to now the constitutive equations for viscoelastic liquids have usually been formulated in connecting similar components of the stress and strain velocity tensors (one‐dimensional liquids). This is completely adequate if one assumes that both tensors have their axes parallel to each other (coaxial tensors). However, there is enough evidence, especially in finite shear in laminar flow, that this is not always the case. The stress and strain velocity tensors can have a finite angle between their principal axes. This angle in finite shear depends on the amount of shear. In such a case, not only the relation between the corresponding components has to be considered but also the influence of all the components of one tensor on each single component of the other tensor. This has been performed for laminar (two‐dimensional) shear for the Maxwell and the Rouse models and results in a non‐Newtonian viscosity for both models and a different behavior for the recoverable shear calculated from steady‐state and vibrational experiments. The results of the theory coincide closely with experimental findings.
12(1968); http://dx.doi.org/10.1122/1.549101View Description Hide Description
A theoretical analysis of the spherically symmetric growth of vapor bubbles in viscoelasticliquids of the Oldroyd type is presented. The momentum transfer process is described by a nonlinear integro‐differential equation for which analytical and numerical solutions have been obtained. The overall picture of bubble growth in such liquids compared to growth in a corresponding Newtonian liquid of the same shear viscosity is one of a high initial growth rate followed essentially by a cessation of growth when the bubbles interact to form thin liquid films. Furthermore, under certain conditions the analysis shows that because of the elastic nature of the liquid, tensile stresses can build up near the bubble surface in a rapid manner. This could lead to rupture of the liquid. Simplified methods are presented for the evaluation of elastic effects in expanding systems. This work sheds light on the general applicability of existing rheological models of viscoelasticliquids to engineering flow problems. Furthermore, it provides these existing models with critical tests which lie at the foundations of the conceptualization of viscoelasticliquids.
12(1968); http://dx.doi.org/10.1122/1.549102View Description Hide Description
Viscosity‐shear rate measurements have been made on two branched polyethylenes with molecular weights of 3300 and 8300 over a temperature range extending from above to below the nominal melting point and well into the region of partial crystallinity. Calculation of flowactivation energies at different shear rates shows several distinct temperature regions for flow of the polymer with molecular weight of 3300. The polymer with a molecular weight of 8300, above the entanglement composition, also shows distinct temperature regions of flow but with considerably different flowactivation energies. Certain activation energies are independent of shear rate within experimental error. Depolarized light intensity measurements and photomicroscopy confirm that physical changes occur at the temperatures where the flowproperties exhibit transitions.
On the Numerical Determination of Relaxation and Retardation Spectra for Linearly Viscoelastic Materials12(1968); http://dx.doi.org/10.1122/1.549103View Description Hide Description
Knowledge of the relaxation spectrum is important because (1) it provides an intrinsic characterization of the mechanical properties for linearly viscoelastic materials and (2) it offers a rational way to derive the coefficients for a Prony or Dirichlet series representation of the relaxation modulus of importance to some engineeringanalyses. A numerical solution based on Simpson quadrature leads to an unstable solution in the sense that a decrease in integration intervals produces a progressively worse solution which oscillates between positive and negative values. This difficulty may be overcome by requiring that the curvature of the relaxation spectrum with respect to the relaxation times be minimized. The method is tested on the modified power law and good agreement with the exact and numerically determined relaxation spectrum is obtained. However, when the same method is used to determine the retardation spectrum, only the unstable solution is obtained, although the form of the integral equation is the same. This different behavior is attributed to the difference in the characteristics of the relaxation and retardation spectral functions.
12(1968); http://dx.doi.org/10.1122/1.549104View Description Hide Description
Some current simple integral theories of the Lodge type are compared in simple shearing, small sinusoidal shearing, combined simple and sinusoidal shearing, cessation and start of simple shearing, finite amplitude sinusoidal shearing, and simple elongational motions. Of the simpler models only the recently proposed network‐rupture theory shows a realistic response in elongational flows; in the other flows it gives a reasonable prediction of experimental results from poly‐isobutylene‐cetane solutions.
A Modified Pochettino Viscometer for the Measurement of the Viscoelastic Properties of High Polymer Melts12(1968); http://dx.doi.org/10.1122/1.549105View Description Hide Description
A modified Pochettino viscometer has been developed for the measurement of fundamental viscoelastic properties of polymer melts. The calculation and evaluation of various viscoelastic constants and functions from experimental stress‐strain and stress relaxation curves are discussed. The terminal zone relaxation spectra for three polyethylenes of similar melt index are presented.