Theoretical Rheology

Advances in constitutive laws for engineering materials (meeting). Fan J, Elsevier, 

Advances infinite deformation problems in materials processing and structures, 

Chandra M, Amer. Soc. Mech. Eng, 1992, 74 Applications of supercomputers in engineering fluid flow and stress analysis applications Vol 2, Bebbia C.A, Comp. Mechanics, 1989, 69 

Constitutive laws of plastic deformation and fracture (meeting), Krausz A.S, 

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HurrON, i. F., Pearson, J. R. A. and Walters, K. (eds) Theoretical Rheology (Applied Science Publishers, London, 1975). 

Reiner M (1949). Deformation and Flow. An Elementary Introduction to Theoretical Rheology, HK Lewis Co, London. 

R3. M. Reiner, Lectures on Theoretical Rheology, North Holland, Amsterdam, three editions (1943), (1949), (1960). 

Theoretical Rheology, Polymeric Systems, Blood, Food, Other Specific Systems, Drag Reduction, Other Meetings, Geological Subjects —and titles appear within each section in alphabetical order. The abbreviations used for publishers names are well known in the book trade, and the information supplied should be sufficient for any reputable book supplier to obtain copies of the books listed. 

Then, An Introduction to Rheology for me marks my gratitude to Prof. Ken Walters FRS, one of my co-authors of that book. He introduced me to the world of theoretical rheology as a postgraduate student at the University of Wales, Aberystwyth and thereby gave me of a wide appreciation of most aspects of rheology. Over 5000 copies of An Introduction. .. have now been sold and this present book has been written, in effect, as an introduction to An Introduction. ... ... 

Sheriff M, Warburton B. 1974. Measurement of dynamic rheological properties using the principle of externally shifted and restored resonance. Polymer 15 253-254. Sheriff M, Warburton B. 1975. The theory of a universal oscillatory rheometer for the study of linear viscoelastic materials using the principle of normalized resonance. In Theoretical Rheology. London Applied Science Publishers, pp 299-316. Shinoda K, Yoneyama T, Tsutsumi H. 1980. Evaluation of emulsifier blending./Disper Sci Technol 1(1) 1-12. 

Filler particle si2e distribution (psd) and shape affect rheology and loading limits of filled compositions and generally are the primary selection criteria. On a theoretical level the influence of particle si2e is understood by contribution to the total energy of a system (2) which can be expressed on a unit volume basis as ... 

In contrast to static properties, where LP and GM reveal generally the same behavior as that of conventional polymers, due to the self-assembling nature of the breakdown process the transport properties of GM are much more complex. Like conventional polymers, these materials are highly viscoelastic [73,74] and their novel rheology has been intensively studied recently, both experimentally [75,76] and theoretically [11,31,77-79]. A theoretical model... 

The paper contains a review with original theoretical and experimental data on the basis of the rheological behavior of gas-containing systems — thermoplastic melts — during extrusion. 

Here is a brief account of the main experimental and theoretical results obtained in the analysis of the rheological properties of low-molecular (Newtonian) liquids with gas bubbles ... 

We would like to think that this work will stimulate theoretical and experimental interest in this sphere of rheology, which is vitally important for polymer processing. 

Flow-induced degradation is intimately related to the nonequilibrium conformation of polymer coils and any attempt to interpret the process beyond the phenomenological stage would be incomplete without a sound understanding of chain dynamics. To make the paper self-contained and to provide a theoretical basis for the discussion, we have included some fundamental models of polymer dynamics in the next section which may also serve as a guideline for future work in the field of polymer degradation in flow. For the first-time reader, however, this section is not absolutely necessary. Further, any reader familiar with molecular rheology or interested only in experimental results can skip this section, only to go back whenever a reference is needed. 

To address these challenges, chemical engineers will need state-of-the-art analytical instruments, particularly those that can provide information about microstmctures for sizes down to atomic dimensions, surface properties in the presence of bulk fluids, and dynamic processes with time constants of less than a nanosecond. It will also be essential that chemical engineers become familiar with modem theoretical concepts of surface physics and chemistry, colloid physical chemistry, and rheology, particrrlarly as it apphes to free surface flow and flow near solid bormdaries. The application of theoretical concepts to rmderstanding the factors controlling surface properties and the evaluation of complex process models will require access to supercomputers. 

The mechanisms of static friction and stick-slip motion, as discussed in the last section, are supposed to be a good description of dry friction. Another case, perhaps more general in engineering practices, to be addressed in this section is lubricated sliding where liquid lubricant, consisting of a few molecule layers, is confined between two solid walls. Both experimental and theoretical studies indicate, as we have discussed in Chapter 5, that there are substantial changes in rheology of the confined lubricant, and the liquid may transit practically to a solid-like state when film thickness becomes molecularly thin [32,33]. 

Melt spinning of the E-plastomers has been the source of a commercial development directed to woven cloth of cross-linked E-plastomers [16]. Recent work on the rheological and theoretical estimation of the spinnability of polyolefins is a part of this development. 

The theoretical basis for spatially resolved rheological measurements rests with the traditional theory of viscometric flows [2, 5, 6]. Such flows are kinematically equivalent to unidirectional steady simple shearing flow between two parallel plates. For a general complex liquid, three functions are necessary to describe the properties of the material fully two normal stress functions, Nj and N2 and one shear stress function, a. All three of these depend upon the shear rate. In general, the functional form of this dependency is not known a priori. However, there are many accepted models that can be used to approximate the behavior, one of which is the power-law model described above. 

The discussion above that led to Eqs. (4.2.6 and 4.2.7) assumes that the no-slip condition at the wall of the pipe holds. There is no such assumption in the theory for the spatially resolved measurements. We have recently used a different technique for spatially resolved measurements, ultrasonic pulsed Doppler velocimetry, to determine both the viscosity and wall slip velocity in a food suspension [2]. From a rheological standpoint, the theoretical underpinnings of the ultrasonic technique are the same as for the MRI technique. Flence, there is no reason in principle why MRI can not be used for similar measurements. 

Other schemes have been proposed in which data are fit to a lower, even order polynomial [19] or to specific rheological models and the parameters in those models calculated [29]. This second approach can be justified in those cases when the range of behavior expected for the shear viscosity is limited. For example, if it is clear that power-law fluid behavior is expected over the shear rate range of interest, then it would be possible to calculate the power-law parameters directly from the velocity profile and pressure drop measurement using the theoretical velocity profile... 

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