Mooney functional analysis

Using functional analysis, Mooney (5i) derived the following equation for concentrated suspensions ... 

Using functional analysis similar to Mooney, Kreiger and Dougherty (53) derived the following equation ... 

For the analysis of experimental force-deformation data, it is necessary to use a suitable constitutive equation for the material under test. The constitutive equation relates the stresses and strains that are generated in the wall during compression, and therefore relates the tensions and stretch ratios. For example, Liu et al. (1996) used a Mooney-Rivlin constitutive equation to investigate the compression of polyurethane microcapsules and the functions f, /2 and fa are produced in... 

Experiments were carried out in a background buffer solution that was chosen as a simple model of natural surface waters, with a monovalent and divalent cation and a background electrolyte to allow pH adjustment without changing ionic strength. The concentration of the cation calcium, was selected after the analysis of the Mooney Mooney Dam surface water. The composition of this water is shown in Appendix 1. The composition of the model system is summarised in Table 4.1. This background solution was used in all experiments, if not otherwise indicated. The species in solution as a function of solution chemistry is described in Appendix 5. 

However, there is a condition which must be fulfilled for the above analysis to be valid. It is that the shear rate at a given radius in the tube is a unique function radius. This will normally be so if the tube radius is large compared with the molecular dimension of the polymer. However, for very narrow capillaries, this may not be the case and the solution may become depleted in polymer molecules close to the capillary wall through the depleted layer effect (see Chapters 6 and 7). Thus, the concentration may vary across the capillary, and hence the constitutive model relating rj and y must also depend on local concentration and there is not a unique inversion of the rj/y relationship. This will be discussed in detail in Chapter 6, which will refer back to the development of the Mooney-Weissenberg-Rabinowitsch equations in this context (Sorbie, 1989, 1990). 

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