ABSTRACT
I. INTRODUCTION So far in this book we have examined the rheology of single-phase polymer melts and polymer solutions. i.n the remainder of the book we discuss the hovv ol' twophase systems. such as suspensions. emulsions. and foams. The introduction of a dispersed phase within the matrix of a continuous polymer phase not only leads to a consideration of new variables but also results in new complications. The new variables include. among others. the relative amounts of the two phases and the shape. size. and size distribution of the dispersed phase. The complications arise from the very nature of a two-phase system and the need to measure true material properties uninfluenced by the nature of the flow field. the kind of instrument chosen. or the fixture geometry employed. If the densities of the two phases are not matched. composition nomtniformities can arise in the material over the time scale of measurement. due either to sedimentation or creaming of the dispersed phase: in an extreme situation. there can be complete separation of the two phases. Concentrated two-phase systems are structured fluids. and this structure can endow the 11uid with a yield stress. lf the magnitude of the yield stress is larger than the force of adhesion between the fluid and the viscometer wall, the application of a stress that is smaller in value than the yield stress can result in slip of the fluid a1 a solid surface rather than deformation in the bLtlk of the material. lf adhesion is restored rapidly. and this happens commonly in the flow of gels, the phenomenon of stick-slip may be witnessed [ 1]. Here the motion of
a solid boundary causes fluid that is in contact with it to deform elastically, building up stress. The stress overcomes the force of adhesion, resulting in loss of contact between the fluid and the solid surface. This, in tum, makes the stress in the fluid relax and restores fluid-solid contact and adhesion. Once this happens, the cycle begins anew. If adhesion is not restored quickly, there can be complete separation at the solid boundary. This is illustrated in Fig. 9.1 for the torsional flow of a food emulsion in a parallel-plate viscometer [2]. A thin, vertical line is painted on the outer surface of the sample, and it makes contact with both the plates. On rotating the lower plate, there is a progressive decrease in the slope of the marker line because material adheres to both solid surfaces. At a later time, however, there is a separation of the marker at the upper boundary; the emulsion still sticks to the moving lower plate but slips on the upper one. The loss of adhesion is accompanied by a reduction in strain, with a concomitant increase in the slope of the marker line. Upon increasing the speed of rotation, material slips at the lower boundary as well and merely rotates as a solid body. This same phenomenon also manifests itself in concentric cylinder instruments, where the
"SINGLE" SUP
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FIGURE 9.1 Macroscopic slip of a food emulsion in a parallel-plate viscometer.
