Search

Work done during the past twenty years on the physics of fibre bonds in paper and the behaviour of paper under mechanical strain is reviewed. The first major section of the article illustrates the chemical nature of the cohesion in paper and reports the results of direct observations on fibre-to-fibre bonds. A statistical theory of the geometry of fibrous networks is shown to be a basis for the characterization of fibre bonding in paper. The second major section is concerned with the mechanical behaviour of paper. This is shown to be a complex subject because paper exhibits almost every known rheological property. Direct, conventional rheological methods, molecular theories and the concept of elastic networks are discussed in this context. Further complications arise from any changes in the water content of the environment. Such effects are conveniently thought of as a competitive process wherein cellulose and water compete for hydrogen bonds for their hydroxyl groups. Not least among the rheological phenomena that paper exhibits is mechanical fracture. This is a discontinuous process that is found to be intimately connected with the mechanical work done on the specimen and is principally governed by its geometrical distortion.

It is established that when a uniform film of liquid is pressed against the surface of a material through rolling, the depth of the deepest part of surface which can be coated is equal to the initial thickness of the film. The total coated area, which may be determined by the change in diffuse reflectance of the material, varies with film thickness but is shown to be independent of the rheological properties of the liquid. These observations are utilized in a treatment developed to determine the topographical structure of a surface. Results show that the surface structure of paper can be described by the Gaussian distribution of the logarithm of depression. The surface structure is sensitive to both load and velocity of rolling, but tends to become stabilized at high load or low velocity. It is suggested that the maximum of the pressure distribution in rolling matters most, but its effect may be complicated by the varying number of stress-bearing sites on the surface and by the interaction between them and their neighbours. The effect of velocity is attributed primarily to the viscoelastic nature of paper and secondarily to the number of stress-bearing sites.

The effect of the amount and type of latex on the mechanical properties of the paper-polymer combinations is described in detail. The treatment with latex increases the wet and dry strength properties of the paper considerably, together with improving the folding and tearing resistance. If the polymer in latex is below its film-forming temperature, however, the beneficial effects of latex treatment are absent. Limitations to varying the rheological properties of plasticpaper combinations are imposed by the comparatively inextensible nature of the paper matrix. Methods of improving the extensibility of paper, including the use of synthetic fiber papers, are discussed, and the time-dependent nature of the properties are outlined.

The explanation of rheological properties of paper and pulp sheets in terms of their structure has hitherto been considered to be very difficult, seeing that they are composed of a lot of macroscopic elements or fibers, though it seems rather easier than those of other materials composed of microscopic elements or molecules. Therefore, rheological studies in this field have not been very actively made in spite of practical importance of these materials. In this article, the rheological studies by the author, especially those on non-destructive elastic and viscoelastic properties, have been reviewed along with the related studies by other investigators.There are two distinct lines in the theories relating the rheological and other physical properties of paper to its structure. Nissan's works are typical of the first of the two. He assumes that the strain of paper under stress is derived from the extension of hydrogen bonds. The author and several others, assuming that paper consists of randomly arranged three-dimensional array of fibers, have put forward theories for elastic and other properties, assuming also that the deformation of paper arises from the bending, stretching and shearing of the fiber segments between the bond sites. The latter theories can presuppose many important facts, some of which have been known experimentally or empirically, though imperfectly yet.Paper is a typically orthotropic material, and its Young's modulus and tensile strength in an arbitrary direction are well represented by the Horio-Onogi equations (8) and (9), which describe a peculiar elastic property of paper, as was pointed out by Campbell and Craver and Tayler. The correlation between the density and modulus of elasticity, the effects of humidity and several manufacturing variables such as beating, wet press, screening and drying on rheological properties of papers and pulp sheets are also discussed. The viscoelastic data reported by the author reveal that paper has essentially the same viscoelastic properties as cellulosic fibers such as viscose and Bemberg rayons if, and only if, they are corrected for the density. This indicates that the junctions between the constituent fibers are very strong and similar to those between the cellulose molecules as was assumed in the above theories, while the macroscopic structural factor should also be taken into account.

Among the color pulps used for coating paper, there are some that bear the reputation of giving difficulty on the coating machine, while others run perfectly under the same apparent conditions. Since Bingham first called attention to the plastic flow of solids in suspensions, a great deal of work has been done on the flow of dry pigments dispersed in oily vehicles. By applying similar methods of study to pigment pulps used in an aqueous medium, some light has been thrown on a bothersome coating problem which has hitherto defied solution.

Since articular cartilage is the principal wear resisting tissue in animal joints, an understanding of its physical behaviour is of particular importance in studies of animal joint lubrication. This review is concerned with the physical factors involved in rheology of cartilage. Particular attention is paid to the physico-chemical properties of its matrix and to the nature of forces acting between its liquid and solid components. The experimental work reviewed includes studies of the interrelations between stress, strain, fluid flow, and time during compression and swelling of the tissue, and of transport of liquid through the matrix. The mechanism which controls the behaviour of cartilage during compression and swelling is discussed.

In order to predict the behaviour of lubricating fluids which are to be operated under elastohydrodynamic conditions, the designer requires to know the rheological properties of the lubricant at the pressure, temperature, and rate of shear encountered in practice. A review is given of the available evidence aimed at establishing a formal connection between the rate of shear behaviour and that observed under alternating shear stress. It is shown that the viscoelastic properties of liquids in oscillatory shear can be successfully predicted on the basis of a new phenomenological model and that complete results are available from oscillatory experiments. Possible correlation of these results with rate of shear behaviour is suggested.

Publisher Summary This chapter focuses on the time-dependent prerupture response of paper to stresses and strains. It also focuses on stress relaxation, creep, and dynamic properties on application of periodic strain. One of the reasons for the shortcoming of the theoretical models for portraying the flow properties of paper is the limited accumulation of experimental data yielded by the investigations of the relevant processes such as relaxation and creep, a deficiency that becomes more striking when comparison is made with the mass of data obtained for other polymers or for metals. Another reason is that the rheological behavior of paper cannot be attributed to properties and movement of specific structural elements or defects. Whereas dislocations in crystals or the movement of polymer molecules in the rubbery state constitute an accepted basis for the understanding of the flow of metals or amorphous polymers, there is no such basis for paper, even though it is recognized that cellulose, being a semicrystalline polymer, may behave in a more complicated manner than metals or amorphous polymers.

The rheological properties of pulps during acetylation process were discussed by using the rotationalviscometer. Cotton linter, commercial wood pulp for acetyl-cellulose and Viscose, purified wood pulps which were treated by hot alkali, cold alkali or acid hydrolysis, and pentosan were used. The rheological properties which were estimated from their rheogram is different by pulps respectively. And viscosities of their acetylation products were also examined.Higher reactive pulps for acetylation changes, generally, their flow properties from non-newtonian flow to Bingham flow at early stage of acetylation than poorer one. Cotton linter changes most rapidly his flow properties and also have lower apparent viscosity of acetylation mixture than any pulps., But wood pulp which was hydrolyzed with mild condition and xylan do not change their non-newtonian flow properties during acetylation. And also wood pulp which was mercerized and then hydrolyzed with hard condition, did not exhibit the non-newtonian flow and always took a Bingham flow from beginning to end.From these results, it seems that this difference of rheological behavior between cotton linter and wood pulps may depend upon the difference of their fine structure and the presence of non-cellulosic materials in them. And on account of these differences wood pulp may take a poorer dispersity of his acetylation bath.This poorer dispersity of the acetylation bath of wood pulp causes higher viscosity than cotton linter for their accetylation products in the same solvent. It is said that wood pulp has a higher viscosity ratio (27%/7%) than linter. This difference of their viscosity ratio may depend also upon the poorer dispersities of wood pulps in the acetylation mixture.

Numbers of spinning tests were made on the viscoses prepared from various types of dissolving pulps varying in sulphite or prehydrolysis sulphate, soft wood or hard wood, and high or low in viscosity and alpha-cellulose content.The results were evaluated with regard to the effects attributable to the characteristics of the pulp.So far as the comparisons were made within the analogous, types of pulp, it was recognized that the important strength properties such as the wet-dry ratio in tensile strength and the bending endurance are difficult to be developed to higher level with increased amount of low DP cellulose fractions expressed as beta-or gamma-cellulose in aged alkali cellulose.The measurements of the spinnability of viscose solution which should be an index of the rheological characteristics of it, have shown that the spinnability will be of great importance to obtain the rayon fibers of satisfactorily high levels in the qualities.Many other aspects concerned with the pulp characteristics, including the analytical results, the sulphidation resistance, the filterability of viscose and the colloid chemical changes during ripening of viscose were also investigated and discussed in connection with the strength properties of the rayon.

Experimental results are given for the influence of wood extractives fromteak andAcacia catechu on the rheological properties of casein-NaOH-water systems.

Bromhexine was compared with a placebo in a double-blind clinical trial in bronchitic inpatients with mucoid sputum. Oral bromhexine 16 mg. thrice daily for 11 days compared with placebo resulted in a significant increase in sputum volume and significant decrease in sputum viscosity, and changed markedly the rheological characteristics of the sputum. There was, however, no improvement in ventilatory capacity or in the overall respiratory state as assessed by the patients themselves or their clinician. No patient having the drug had side-effects and there was no change in laboratory findings attributable to it.

This paper deals with the effects of contact pressure and temperature on the shear strength of thin organic films. The experimental method involves depositing the material as thin films (ca. 3 nm to 500 nm) on smooth glass surfaces. The film is sheared by sliding over it indenters of fired glass. By varying the indenter radius from 4 μm to 2.5 mm and the load from 10 mg to 20 g, the contact pressure may be varied from 107 Pa (1.4 × 103 P.s.i.) to 8 × 109 Pa (12 × 105 p.s.i.). The temperature dependence of the shear strength is also studied. Two types of organic materials have been investigated. These range from simple low molecular weight compounds such as stearates, to more complex high molecular weight polymers, for example P.M.M.A. The shear strength of these films has been compared with the bulk shear properties and consideration has been given to the molecular processes occurring during shear. Presented as an American Society of Lubrication Engineers paper at the ASLE/ASME Lubrication Conference held...

Processing involves complex polymer flow problems, either in the melt or in solution. Rheologists have developed many studies with the aim of correlating polymer structure with flow properties and polymer processing. Most of these studies, however, have had relatively little impact on practical processing because of the difficulty in solving the mathematical equations involved. Recently, a relatively few papers have been published with the aim of bridging the gap between theoretical rheology and technology. The first part of the paper presents an account of works which have dealt with the process of filling a mold cavity. The second part discusses briefly some experimental results which provide a correlation between moldability and rheological properties. By analogy with the terms “electrology” and “electrotechnics,” the term “rheotechnics” is suggested for this new area of study.

This paper reports results of studies of birefringence (Δ) in ABS systems and in two component materials, measurements which reveal information about the orientation and response of these materials to deformation. Continuous measurements of (Δ) at strain rates (e) from 8.5×10−5 to 3.3×10−3 sec−1 were carried out with a He–Ne laser light source on polystyrene (PS), poly(styrene‐acrylonitrile) (SAN), and two clear ABS polymers. Measurements at constant e were related to mechanical response of the materials in creep, and two tests for the invariance of the stress optical coefficient were developed. These were achieved through comparison of computer‐generated plots of appropriate rheo‐optic functions with rheological counterparts derived from previous creep measurements via the convolution procedure of Hopkins and Hamming. Such comparisons indicated nearly identical constant time dependences for the respective logarithmic plots of (Δ/e) and (stress/e) vs time (t) for the PS and SAN polymers. Comparison of other functions confirmed the constant value of the stress optical coefficient (SOC) implied above, |(SOC)| being 1.0×10−12 cm2/dyn. This paper also presents results which indicate that the onset of yielding in the ABS systems can be studied by these optical techniques. It was observed that the increase in Δ in the two ABS systems was followed by the onset of a high degree of scattering which produced a maximum (M) in each plot of apparent Δ vs t, the height of M decreasing with increasing e. The relevance of this latter phenomenon to the study of impact strength and yielding in ABS systems is discussed.

In this paper a three-dimensional continuum model of a mammalian left ventricle is formulated. The stresses in the model satisfy the conditions of zero stress on the outer (epicardial surface-representing) boundary. The strains of the model are obtained from the actual dynamic geometry measurements (obtained from cineangiocardiography). Since the left ventricular muscle is incompressible, the dilatational strain is zero and hence the (three-dimensional) deviatric stress components are related to the corresponding strain components by Maxwell and Voigt rheological model analogues of one-dimensional systems; the parameters of the model are series and parallel elastic (SE, PE) elements and the contractile element (CE) (representing the sarcomere). The incorporation of the rheological features of the cardiac muscle into the three-dimensional constitutive equations (for the three-dimensional continuum model of the left ventricle) is a feature of this paper. A procedure is presented to determine the parameters of the constitutive equations (i.e., the SE, PE, and the parameters of the force-velocity relation for the CE) for the left ventricle of a subject from data on the dimensions and chamber pressure of the left ventricle. The values of these parameters characterize the rheology of the left ventricular muscle of the subject. In order to demonstrate clinical application of the analyses, in vivo data of the subjects' left ventricular pressure and dimensions are obtained, and the analyses are applied to the data to determine (for each subject) the values and characteristics of the elastic elements and CEs.

This paper is based upon data for the thixotropy of paints given in the previous paper of this series. The data will not be repeated here but reference will be made to it when necessary.

Characterization of Starches with Respect to their Application in the Industry, especially in the Textile and the Paper Industry. After a short review of the economical importance of starch in the textile and the paper sector the author shows how he characterizes the industrial starches: water content (after the French Standard AFNOR V. 03602), microscopic examination (normal and polarized light, phase contraste, 100 × or 250 × magnification), nitrogen content (Kjeldahl), ash content (AFNOR V. 03605), color, pH-value of water extract, and particulary rheological behaviour. At this point the following is accentued: 1 Starch/water systems are not true Newtonian. They have not one viscosity alone but an infinity of apparent viscosities in relation with the rheological conditions. To give one value even in arbitrary units without precise informations about shear rate and shear stress is meaningless. 2 The preparation of the starch paste is a multiphenomene and needs a non-laminar stirring. That means that it is illusive to obtain reproducible torque value by rotation at constant speed from one apparatus to another. 3 Only rheometers with coaxial cylinder permit an absolute characterization of the before prepared starch/water system.

This report deals primarily with the deformation problem in classical sense of this word, i. e., with changes of geometrical characteristics of the considered medium, but also at the certain level, with changes of hydraulic characteristics of this medium, being expressed primarily by conductivity K. The deformations are considered due to two characteristic conditions: a) without change of masses between phases which are transported in the interspace of the solid matrix; b) with change of masses (especially subsoil, mechanic and chemical erosion, and, briefly seepage). In the first case, the water action has essentially a dynamic nature being determined by filtration force which is generated by flow. This force represents a term in the generalized Navier's equation (Eq. 1) which is discussed in this paper. The generalized Navier's equation contains also the effective stresses whose relationship to the deformation is determined by rheological models. This relationship has, in general case, to involve elasto-visco-plastic properties of the considered medium. A model, proposed by Brzosky (1969), describing all these characteristics including the action of filtration water too, is treated briefly in this paper. The practical application of such a generalized model is faced with numerous difficulties both experimental and mathematical. Because of this, some simplifications of rheological model used have been introduced (Tabl. 1) considering soil either as an elasto-plastic body (small deformations) or as a rigid-perfectly plastic body (big deformations) or even as a perfectly elastic body (small deformations) using sometimes modified material constants. The problem of the medium stability is treated from the standpoint of view of continuum mechanics as a limiting case of big deformation where the system is transforming into a mechanism kinematically labile. The medium model has to be essentially different than this one at the flow without mass changes, since the compression as well as the reduction of effective stresses can appear here (shown by a series of examples, see Figs 4 and 5, obtained at the Hydraulic Laboratory, Fac. of Civil Eng., Belgrade). In the scope of the analysis of chemical erosion, the influences of clay and suspension characteristics to the nature of the process, adding some original experiences, have been considered.

In a paper of 1928 the author dealt with the factors which interfere with the flow of mixtures of gas and liquid in vertical channels, and again in English in 1929. In these two papers a cause of intermittency was already mentioned, viz., that although there may be sufficient gas to establish the mist condition as described below, when the rate of speed of this fluid is smaller than the differential velocity of gas and liquid, drops of liquid cannot be lifted by the gas. Liquid then, if continuously supplied, collects at the bottom and can only be lifted when enough of it has been gathered so that for some time a foam is formed.

HILLER, K.H., CALIFORNIA RESEARCH CORP., LA HABRA, CALIF. Abstract A rotational viscometer has been designed which permits the measurement of the rheological properties of drilling muds and other non-Newtonian fluids under conditions equivalent to those in a deep borehole (350F, 10,000 psi). The important mechanical features of this instrument are described, and its design criteria are discussed. The flow equations for the novel configuration of the viscometer are derived and the calibration procedures are described.The date and their interpretation, resulting from measurement of the flow properties and static gel strengths of homoionic montmorillonite suspensions at high temperatures and pressures, are presented. Data are also presented for the flow behavior of typical drilling fluids at high temperatures and pressures. The pressure losses in the drill pipe and the annulus depend critically upon the flow parameters of the drilling fluid. This work demonstrates the need to measure these parameters under bottom-hole conditions in order to obtain a reliable estimate of the pressure losses in the mud system. Introduction The rheological properties of drilling fluids are affected by temperature and pressure, but the extent of these effects on the dynamic flow properties is not well known. Measurements of changes of the flow properties of clay-water drilling muds with temperature have been reported by Srini-Vasan and Gatlin. The temperatures reported did not exceed 200F, a limitation imposed by the apparatus used by these authors. The rheological properties of clay suspensions were measured at temperatures up to 100C by Gurdzhinian. Neither the nature of the exchange ions in the clay suspensions nor the degree of purity were defined in his work, nor were the measurements extended to currently used drilling fluids.The lack of systematic measurements of dynamic flow properties at high temperatures and pressures seems the more surprising since during the last decade the importance of the control of the hydraulic properties of drilling fluids has come to be widely recognized. Very good mathematical treatments of the friction losses in drill pipe and annulus have been developed. These treatments are based on the assumption that drilling fluids behave as Bingham plastic fluids. Quite often this assumption is justified, while in other cases a power law equation produces better fit than the Bingham model does. For convenience in applying viscometer data to pressure-drop calculations, the Bingham plastic flow equation is preferable and, therefore, has been applied to the data reported in this paper, although other equations may fit these data more accurately. In a Bingham plastic fluid the relationship between the shearing stressand the rate of shear D is given by the following equation: ..............................(1) where is the plastic viscosity and the yield point. If =, the equation for simple Newtonian flow, =, is obtained. Two empirical constants are required for the description of laminar flow of a Bingham plastic fluid, and calculations of the flow behavior at high temperatures and pressures cannot be better than is permitted by the accuracy with which these constants are known.For this reason a high-pressure, high-temperature rheometer has been designed to measure the plastic viscosity, the yield point, and the static gel strength Sg at pressures up to 10,000 psi and temperatures up to 350F. The important features of its design will be described. The results of measurements on homoionic clay slurries will be discussed insofar as they are relevant to an understanding of the general flow behavior of clay-water drilling fluids. The results of measurements on some typical drilling fluids will be presented also, and their practical implications will be briefly discussed. DESCRIPTION OF EQUIPMENT MECHANICAL FEATURES A viscometer designed to measure the plastic viscosity, yield point and gel strength of non-Newtonian fluids must permit the measurement of the shearing stress at any given rate of shear D. This is possible only if and D are approximately uniform throughout the entire sheared sample. A Couette apparatus is the most convenient method of realizing this condition, as has been pointed out by Grodde.The "high-pressure, high-temperature rheometer" described in this paper is basically a rotational Couette viscometer that is immersed in a cell in which pressure and temperature can be controlled over the range of interest. Fig. 1 shows schematically the important features of the pressure cell and associated equipment. The heart of the instrument is the rotating cup. It is shown more clearly in Fig. 2, which represents the lower one-third of the pressure cell (below the input drive shaft shown in Fig. 1), and it is shown in detail in Fig. 3. JPT P. 779^

Abstract A rheological equation for viscoelastic fluids is derived as an expansion of Noll's functional for sample fluids. The present expansion is developed in terms of the deformation rate referred to a co-rotational material frame. The resulting series of approximations for stress differs significantly from those proposed previously by Green and Rivlin and by Coleman and Noll. Applications to both simple-extensional and viscometric flow are considered. For viscometric flows the present model exhibits non-Newtonian effects similar to those observed in real fluids, with relatively few terms in the functional expansion. The first term in the expansion yields a "first-order" fluid similar to that proposed by Pao. Expressions are also given for the viscometric material functions of the present "third-order" fluid. As with higher-order fluids, these functions are Fourier integrals of certain hereditary or memory functions for the fluid. Introduction In a previous paper it was shown how one could construct an inverse for the co-rotational or Jaumann derivative. This is operation, termed "Jaumann integration" was then used in a somewhat intuitive manner to derive a rheological model for viscoelastic fluids, by means of a Boltzmann superposition integral. As discussed in the above paper, the resulting fluid model is essentially a generalization of the "Quasilinear" model proposed earlier by Oldroyd. Moreover, the rheological equation bears some resemblance to certain others which have been derived from molecular considerations. However, while the model was shown to exhibit some of the features of real-fluid behavior, including shear-dependent viscosity and normal-stress functions, both related to the linear-viscoelastic "memory" function, it was concluded that the model was in general not sufficient to describe nonlinear viscoelastic effects in their entirety. The present work is first of all an attempt to provide the above model with a somewhat more rigorous continuum-mechanical basis, by deriving it from Noll's general theory of materials with a "memory". More importantly, the intent of the present paper is to arrive systematically at certain improvements on the "quasi-linear" model previously proposed and, then, to relate the resulting fluid models to the "higher-order" fluids proposed by Green and Rivlin and by Coleman and Noll. Finally, it is hoped that the present work might suggest other types of functional expansions and perhaps stimulate investigation of the convergence of such expansions, as it relates to the physical properties of fluids. FORMULATION OF THE RHEOLOGICAL EQUATION The Material Matrizant For the present work it will be convenient to recall the notion of a material matrizant, which was introduced in an earlier paper. Thus, for a given second-order tensor field(x,t) and a material velocity field the material matrizant of A relative to v is a tensor field Mtt [A] which is to satisfy ........................................(2.1) where I is the unit [metric] tensor or idem factor and D/Dt is the material derivative: ........................................(2.2)

The first two sections of this paper deal with the necessity for amending the classical Newtonian equations by assuming a nonlinear stress-strain curve in order to account for the presence of a considerable amount of second harmonic of the test frequency in the restoring forces in a rubber, in both forced-vibration and positive-displacement dynamic testers. The nonlinear stress-strain curve is applied also to a damped free-vibration curve of the Yerzley type, and is shown to account for the asymmetry of the envelope of the vibration curve. The latter part of the paper obtains a relationship between the dynamic modulus of loaded rubbers and amplitude of vibration, leading to equations analogous to those used in rheology to deal with rate of shear effects in non-Newtonian liquids, and to explain the effects of fillers on the static modulus and hardness of vulcanized rubbers. A resonance curve from a resonant vibrator is analyzed and the variation of modulus with amplitude is shown to exhibit the typical thixotropic effect associated with loaded rubbers subjected to vibrations. The last section discusses how the decrease of modulus with increasing amplitude can be attributed to two different mechanisms: (1) thixotropic breakdown of filler structure, (2) in compression, nonlinearity of the stress-strain curve.

This paper describes the results of the traction measurements obtained in the experiment discussed in the companion paper entitled “Fluid Rheological Effects in Sliding Elastohydrodynamic Point Contacts With Transient Loading: I.—Film Thickness.” Under the conditions investigated, the traction values appear to be primarily a function of the sliding velocity. Large variations in fluid composition and inlet viscosity had little influence on the tractive force. It was also found that rapid application of the normal load had a negligible effect on the traction.

Abstract Inasmuch as the differentiation and integration methods represent different modes of rheological analyses, a dual scheme of analysis using both methods should lead to a generalized method of data analysis. A dual differentiation. integration method of analysis is applied here to the Poiseuille flow of a variety of ideal Generalized Newtonian and viscoplastic models. Using machine processing techniques, the result is a spectrum of response patterns which are expressed in terms of certain derivative functions. It is shown that these characteristic functions form the basis of a highly-sensitive analytic technique for optimizing the selection of the most appropriate functional relationship between shear rate and shearing stress. Introduction In the first paper of this series, Savins, Wallick and Foster presented an historical review of the salient features of the differentiation method of rheological analysis in Poiseuille flow, and also indicated how the method could be applied to problems involving plane Poiseuille flow. It was shown that the differentiation and integration methods, although basically not incompatible, do represent different modes of rheological analysis. This suggests that valuable background information regarding the probable response characteristics of real data obtained with the differentiation method can be obtained from an integration method-differentiation method analysis of the response of a variety of ideal rheological models. The present paper describes how this dual method of analysis has been applied to suites of idealized models representing a wide variety of Generalized Newtonian and viscoplastic behavior which have received attention at various places in the literature. THEORETICAL CONSIDERATIONS NEWTONIAN LIQUID For a liquid of constant viscosity .............................(1) By substituting Eq. 1 in Eq. 9 of Ref. 1 and integrating, it is easily shown that for Poiseuille flow .......................(2) and, hence, ....................(3) ...........................(4) GENERALIZED NEWTONIAN SYSTEMS Odd Power This model is of the form ......................(5a) Note that it represents a Maclaurin-type series expansion, based on the Newtonian model, which is restricted to the odd powers of the stress. SPEJ P. 309^