Theoretical and experimental work on the rheology of suspensions of slender fibres is reviewed. This is an area of enormous importance in applications such as the manufacture of fibre reinforced polymeric materials and the fabrication of articles out of reinforced plastic. The particular features of suspension rheology when the suspended particles are long and slender, notably the response in extensional flows, are also of fundamental scientific interest in their own right and the issues we shall be surveying are of interest to both theorists and experimenters.The published literature relevant to this topic is vast; one of us has listed well over 300 references [l]. In the rheological literature, attention is drawn to useful sections in a number of books [2, 3, 4]. Note that for suspensions of fibres and for solutions of long rigid polymers the theoretical approach, and indeed many theoretical results, are identical. Review articles which can be recommended include the comprehensive theoretical study by Brenner [5] and a review by Batchelor [6] which focus on the fundamental aspects of the topic. This contrasts with the more pragmatic approach of Jinescu [7]. A valuable contribution to bridging the gap between theory and practice was produced by Jeffrey and Acrivos [8]. More specifically devoted to fibre suspensions are the reviews by Maschmeyer and Hill [9] and by Ganani and Powell [10]. The behaviour of fibre suspensions in extensional flow has been recently reviewed in [11]. The starting point for theoretical work has to be the dynamics of a single particle suspended in a flowing fluid. From there we trace the steps necessary for the construction of a model from which the macroscopic behaviour of a suspension may be predicted. The influence of non-Newtonian behaviour of the suspending fluid has been studied to a limited extent. The main practical drawback of dilute suspension theory is that, for long slender fibres, diluteness means that fibres have to be far apart on a scale based on the length of the fibres rather than their diameter, and so dilute means extremely dilute in terms of the volume fraction of solids in the suspension. Consideration of the hydrodynamic interaction between particles is obviously necessary. In the extreme case of suspensions that axe so concentrated that, in effect, the fibres have no choice but to lie parallel to one another we find the regime of liquid crystalline behaviour. The issue of wall effects, i.e. hydrodynamic or direct mechanical interaction between the suspended fibres and the walls of the container within which the suspension is flowing, is extremely important. There is much published experimental work on suspensions both in Newtonian liquids, which is of fundamental scientific interest, and in molten polymers, with obvious relevance to the processing of fibre-reinforced plastics. Suspensions of fibres in wellcharacterized non-Newtonian liquids have perhaps been studied less until recently and we discuss this area critically. We shall present in tabular form references to papers on both these areas and attempt to make clear the rheological content of the reports. Studies on fibre orientation and attempts at flow visualization are also of considerable interest and we offer a further tabulation of work in this area. The contribution of C J S Petrie was made possible by a Visiting Research Fellowship of the University of Melbourne and by support from the Departments of Mathematics and Chemical Engineering of the University of Melbourne. This support and the granting of a period of study leave by the University of Newcastle upon Tyne are gratefully acknowledged. Research in non-Newtonian fluid mechanics at the University of Melbourne is supported by the Australian Research Council.

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The rheology of fibre suspensions

The objective of this chapter is to introduce and to illustrate the frequent and wide occurrence of non-Newtonian fluid behaviour in a diverse range of applications, both in nature and in technology. Starting with the definition of a non-Newtonian fluid, different types of non-Newtonian characteristics are briefly described. Representative examples of materials (foams, suspensions, polymer solutions and melts), which, under appropriate circumstances, display shear-thinning, shear-thickening, visco-plastic, time-dependent and viscoelastic behaviour are presented. Each type of non-Newtonian fluid behaviour has been illustrated via experimental data on real materials. This is followed by a short discussion on how to engineer non-Newtonian flow characteristics of a product for its satisfactory end use by manipulating its microstructure by controlling physico-chemical aspects of the system. Finally, we touch upon the ultimate question about the role of non-Newtonian characteristics on the analysis and modelling of the processes of pragmatic engineering significance.

https://physics.iitm.ac.in/~compflu/Lect-notes/chhabra.pdf

Non-Newtonian Fluids: An Introduction

Rheology to understand and optimize processibility, structures and properties of starch polymeric materials

The steady-state and time-dependent flow transitions observed in a well-characterized viscoelastic fluid flowing through an abrupt axisymmetric contraction are characterized in terms of the Deborah number and contraction ratio by laser-Doppler velocimetry and flow visualization measurements. A sequence of flow transitions are identified that lead to time-periodic, quasi-periodic and aperiodic dynamics near the lip of the contraction and to the formation of an elastic vortex at the lip entrance. This lip vortex increases in intensity and expands outwards into the upstream tube as the Deborah number is increased, until a further flow instability leads to unsteady oscillations of the large elastic vortex. The values of the critical Deborah number for the onset of each of these transitions depends on the contraction ratio β, defined as the ratio of the radii of the large and small tubes. Time-dependent, three-dimensional flow near the contraction lip is observed only for contraction ratios 2 [les ] β [les ] 5, and the flow remains steady for higher contraction ratios. Rounding the corner of the 4:1 abrupt contraction leads to increased values of Deborah number for the onset of these flow transitions, but does not change the general structure of the transitions.

Nonlinear dynamics of viscoelastic flow in axisymmetric abrupt contractions

We consider the use of pressure measurements in contraction flows in the determination of the extensional viscosity behaviour of polymer solutions. The experimental data are interpreted on the basis of the recent theory of Binding. The resulting extensional viscosities are compared with those obtained from a commercial Spin Line Rheometer. We conclude that contraction flows provide a convenient means of determining the extensional viscosity of shear-thinning polymer solutions. The case is not so clear for constant viscosity Boger fluids. In the course of the experiments, it is shown that excess pressure losses in the contractions can be brought about by two distinct flow mechanisms in the case of Boger fluids. In the axisymmetric case, both vortex enhancement and excess pressure loss are observed, although there is not a strict one-to-one correlation between these phenomena. In the planar case, vortex enhancement is not conspicuously present, although there is still a substantial excess pressure loss at high flow rates. This excess must be associated with the ‘bulb’ flow field which essentially replaces the vortex-enhancement regime of the axisymmetric case.

On the use of flow through a contraction in estimating the extensional viscosity of mobile polymer solutions

We describe experimental results on the extensional viscosity of mobile polymer solutions obtained from two instruments, the first being a commercial Spin Line Rheometer and the second a custom-built lubricated-die Converging Flow Rheometer. The interpretation of data in terms of Trouton ratios is facilitated by a simple analysis for the Generalized Newtonian Fluid model.

D. M. Jones

Papers

On the extensional viscosity of mobile polymer solutions