Rheology of two-phase systems

Excellent reviews [30-33] and a book on the subject of polymer blends [34] may be referred to for a deeper understanding. There are extensive reviews available in literature on the rheology of blends [35-38]. These are well supplemented by the fairly comprehensive chapter on the rheology of two-phase systems by Han [39]. The various blends which have received the attention of rheologists to date [40-58] have been summarized in Table 1.8. 

General definitions and relations for the rheological properties of two-phase systems, mainly dilute. 

Studies on the rheology of two-phase particulate systems suggest the existence of a deformation threshold that depends on the concentration of particles in the composite. Below this threshold (—68 vol.% for spherical particles), deformation occurs primarily by the flow of the composite matrix. Particles increase the effective viscosity of the matrix by absorbing energy and by forming clusters. 

The fourth chapter presents some constitutive theories and equations for suspensions. Suspension rheology normally deals with the flow behavior of two-phase systems in which one phase is solid particles like fillers but the other phase is water, organic liquids or pol)oner solutions. Literature on suspension rheology does not include flow characteristics of filled polymer systems. Neverttieless, ttiis chapter needs to be included as the foimdations for understanding ttie basics of filled polymer rheology stem from the flow behavior of suspensions. In fact, most of the constitutive theories and equations that are used for filled polymer systems are borrowed firom those that were initially developed for suspension rheology. 

Han, C.D., Kim, Y.W. Studies on melt spinning. 5. Elongational viscosity and spinnability of two-phase systems , J. Appl. Polym. Sci. 18(9) (1974), 2589-2603 Munstedt, H., Steffi, T., Malmberg, A. Correlation between rheological behaviour in uniaxial elongation and film blowing properties of various polyethylenes , Rheol. Acta 45(1) (2005), 14-22... 

In the early works by Soviet scientists (primarily the followers of P. A. Rebinder and G. V. Vinogradov) and Western investigators (H. C. Booij, R. I. Tanner, J. M. Simmons, T. Kataoka, R. Osaki, et al.) published between 1966 and 1968, the vibration was proven to produce a powerful effect on rheological properties of two-phase disperse systems, filled polymers, rubbers as wellas dissolved and molten polymers. 

At some volume fraction, mostly around

phase inversion occurs around this value, A and B are both continuous. This may, however, also happen at other values of (p, depending on the rheological behaviour of the components. Moreover, cocontinuity is possible at any volume fraction (see in 9.1.4 the remark on SBS). For the properties of a co-continuous two-phase system an expression has been derived by Nielsen ... 

Indirectly related to the cell models of this section is the work of Davis and Brenner (1981) on the rheological and shear stability properties of three-phase systems, which consist of an emulsion formed from two immiscible liquid phases (one, a discrete phase wholly dispersed in the other continuous phase) together with a third, solid, particulate phase dispersed within the interior of the discontinuous liquid phase. An elementary analysis of droplet breakup modes that arise during the shear of such three-phase systems reveals that the destabilizing presence of the solid particles may allow the technological production of smaller size emulsion droplets than could otherwise be produced (at the same shear rate). 

The rheological properties of a two-phase system depend not only on the rheological behavior of the components, but also on the size, size distribution, and the shape of the discrete phase droplets dispersed in the continuous matrix phase. Flow affects morphology in two different ways. 

Direct measurements of and indicate a parallel dependence of both these functions plotted vs. ( ), even when these have a sigmoidal form. Considering the steady shear flow of a two-phase system, it is generally accepted that the rate of deformation may be discontinuous at the interface, and it is more appropriate to consider variation of the rheological functions at constant stress than at constant rate, i.e., = Nj(Oj2). 

An appreciable amount of resin is required to modify the elastomer s rheological properties sufficiently have "good" tack. If one plots resin content versus a specific adhesive property such as tackr the curve increases sharply to a maximum, then decreases sharply to very low levels. The drop in properties occurs when the resin becomes the dominant or continuous phase in a distinctly two-phase system or when the modulus of the composition is sufficiently high to prevent it from wetting the substrate in other systems. The level of resin at the maximum tack value depends upon the solubility and/or compatibility of the particular resin chosen with the particular elastomer used. In solvent-based adhesives this level has been on the order of 60% resin to 40% elastomer. 

Owing to experimental difficulties, steady-state shear measurements of Ni and 0 2 are relatively rare. Their rate of shear gradients, Ni/y,r] = 012/y usually show a similar dependence ]322]. The value of the complex viscosity ist] >t]. In the steady shear flow of a two-phase system, the stress is continuous across the interphase, but the rate of deformation is not. Thus, for polymer blends, plots of the rheological functions versus stress are more appropriate than those versus rate, that is, a Ni = Ni oi2) plot is similar to G = G (G"). 

Han, C.D. (1971) Measurement of the rheological properties of polymer melts with slit rheometer. I. Homopolymer systems n. Blend systems ni. Two phase systems - higfi impact polystyrene and ABS resins, /. Appl Polym. Set., 15,2567-77,2579-89, 2591-6. 

Han, C. D., Measurement of the rheological properties of polynm melts with slit rheometer. I. Homopolymer Systems. II. Blend Systems. IB. TWo Phase Systems— High Impact Polystyrene and ABS Resins, J. Appl Pofym. ScL, IS, 2567-2577 (I), 2579-2589 (II), 2591-2596 (IB) (1971). 

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