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SUSPENSION RHEOLOGY

DOI: 10.1615/ICHMT.1988.20thAHT.60
pages 71-113

H. Brenner
Carnegie-Mellon University, Pittsburgh, U.S.A.

Abstract

The science of rheology is concerned with establishing constitutive relations connecting the dynamical and kinematical responses of materials. It deals, in essence, with general relations existing between the states of stress and strain in a substance undergoing deformation. Paradoxically, the great generality of these constitutive relationships represents both the principal strength and weakness of the science. The strength resides in the fact that the fundamental precepts underlying the theory of rheological constitutive equations are so broadly applicable as to be capable of embodying virtually any conceivable type of behavior, from the elementary to the bizarre. The weakness stems from the fact that the general theory by itself, being purely formal, furnishes no insight into which particular constitutive relation applies to a given substance. This poses a dilemma for the experimentalist who seeks, in an objective and unbiased fashion, to embed his data into a particular constitutive formulation. How is he to choose, especially in the initial phases of his search, among the myriad rheological formalisms mat have been proposed?
In this sense, modern rheological theories tend to be sterile, at least in proportion to the heavy theoretical investment that has entered into their creation and subsequent development. A non-professional rheologist* like myself cannot help but feel stifled, indeed bewildered, by the endless array of contravariant and tensor affices that characterize the formal aspects of the discipline. The successful application of such theories to real substances depends, in large measure, upon the ability to supplement these formal rheological schemes with simple, but reasonably detailed, physical models of the phenomena, into which are incorporated the principal structural features of the substance under investigation. It is only through the use of such models that one can hope to understand and interpret the rich variety of rheological responses manifested by various classes of materials. It is only through the use of such models that one can hope to understand and interpret the rich variety of rheological responses manifested by various classes of materials. These models may merely constitute analogies as, for example, in the case of Maxwellian or Kelvin-Voigt spring-dashpot models of viscoelastic fluids or elasticoviscous solids. In other cases the model may represent an attempt at a more faithful portrayal of the detailed geometrical microstructure characterizing the system. Such is the case with the rheology of suspensions, the subject of this lecture.
Suspension rheology is a highly developed discipline in terms of the quantity and quality of knowledge currently available in the field. This is equally true of both the experimental and theoretical facets of the subject. Apart from the pioneering work of Einstein, concerned essentially with developing a kinetic theory of the liquid state, the impetus for the rapid development of the subject over the past thirty years came about largely from the needs of polymer science, where the "suspended" particles are macromolecular in size. Other applications of interest exist in the areas of emulsion rheology, slurry transport in pipelines, paint technology, ferrofluid rheology, blood flow, and a host of other areas involving non-Newtonian technology. In a survey lecture of the type demanded by the heterogeneous nature of the audience in attendance at this symposium, attention will be directed only to the fundamental, theoretical aspects of the subject. An equivalent version of essentially this same lecture will be published elsewhere.

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