Viscoelasticity soft spheres

This chapter is an in-depth review on rheology of suspensions. The area covered includes steady shear viscosity, apparent yield stress, viscoelastic behavior, and compression yield stress. The suspensions have been classified by groups hard sphere, soft sphere, monodis-perse, poly disperse, flocculated, and stable systems. The particle shape effects are also discussed. The steady shear rheological behaviors discussed include low- and high-shear limit viscosity, shear thinning, shear thickening, and discontinuity. The steady shear rheology of ternary systems (i.e., oil-water-solid) is also discussed. 

Viscoelasticity Colloid and polymer solutions both generally show shear thinning. The frequency dependences for the dynamic moduli of colloid and polymer solutions, written as G (a>)fco and G" co)/co, are qualitatively the same, namely at smaller co the moduli follow an exponential or stretched exponential in co and at larger co the moduli follow a power law in >. At very large frequencies, the dynamic moduli of polymer solutions sometimes show additional features, an additive secondary relaxation or additive baseline or a second power-law decay, that are not seen with colloidal spheres. However, the secondary relaxations apparent for the moduli of soft sphere melts, as studied by Antonietti, ct a/. (11), are only apparent at frequencies considerably larger than those that have been reached experimentally... 

Time and frequency do not enter the above calculations. However, the solutionlike-meltlike transition suggested a structure for fixed points of the Altenberger-Dahler renormalization group. An ansatz extending the structure from a single concentration variable to a two-variable concentration-time plane indicated a possible form for the complex viscosity(14). Chapter 13 successfully compares the ansatz predictions with experiment. This two-parameter temporal scaling approach has since been applied successfully to describe viscoelastic functions of linear polymers and soft-sphere melts(15), of star polymers(16), and of hard-sphere colloids(17). 

Rolling friction is often found to be proportional to the velocity, but more complex relationships may be observed, depending on the combination of the bodies. For a soft, viscoelastic sphere on a hard substrate, Brilliantov et al. [464] predicted a linear dependence of rolling friction on speed. For a hard cylinder on a viscous surface, a much more complex behavior was found [465,466], At lower speeds, the rolling friction increases with speed to reach a maximum value and then decreases at higher speeds. The reason is an effective stiffening of the substrate at higher speeds. 

On rolling a hard sphere over a soft material, the friction results almost entirely from energy loss through deformation of the soft material. Thus, the friction depends on the viscoelastic properties of the material that the sphere is rolled over. If the deformation only results from pressure (and not from shear stress), then the frictional coefficient is given as... 

Here ri r]c is the relevant Miesovicz viscosity, and v is the velocity of the sphere. The situation is quite different for semi-infinite and finite barriers, where permeation is necessarily involved in the flow, leading to undulation of layers and arrays of defects. Since it is very difficult to trap and stabilize a sphere vdth a size smaller than the film thickness, as far as we know, the flow of smectics aroimd a sphere has never been studied experimentally. However, experiments when finite particles are moving in the liquid crystal medium, which is at rest far from the particles has been carried out very recently, and it was indeed found that the flow of beads in smectic A and smectic C liquid crystals is purely viscous at sufficiently high speeds. Such technique is analogous to the one-bead micro-rheology ° developed recently to monitor the mechanical properties of viscoelastic soft materials, especially biological systems. i... 

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