Simha suspension viscosity

Frisch, H. L., and Simha, R., Viscosity of colloidal suspensions and macromolecular solutions, in Rheology, Vol. 1, Eirich, E. R.,Ed., Academic Press, New York, 1956. 

Guth, E., and A. R. Simha. 1936. Viscosity of suspensions and solutions. KoIIoid-Z, 74, 266. Quoted in Wasp, E. J., J. P. Kenny, and R. L. Gandhi. 1977. Solid-Liquid Flow—Slurry Pipeline Transportation. AedermaniBdorf, Switzerland Trans. Tech. Publications. 

The effect of concentration on viscosity of suspensions of spheres was first modeled by Guth and Simha [30]. They again began with Eq. 2.5, but considered the hydrodynamic interaction of other spheres on the velocity field. This led to an enhancement of the viscous dissipation and to an increase in suspension viscosity of form... 

Frisch,H.L., Simha.R. The viscosity of colloidal suspensions and macromolecular solutions, Vol. 1, Chapter 14. In Eirich,F.R. (Ed.) Rheology. New York Academic Press 1956. 

According to the Einstein theory, the intrinsic viscosity of a spherical particle suspension is 2.5. However, for a colloidal suspension of nonspherical particles, [r ] > 2.5. Jeffery [112] obtained the viscosity of an ellipsoidal particle suspension under shear. Incorporating Jeffery s results of velocity fields around the particle, Simha [113] obtained expressions for two explicit limiting cases of ellipsoids. Kuhn and Kuhn [114] also obtained an expression for intrinsic viscosity for the full range of particle aspect ratio (p) by taking an approach similar to Simha s method. 

Frisch, H. L and R- Simha Viscosity of colloidal suspensions and macro-molecular solutions. In Rheology, Vol. I, pp. 525—-613. edited by F. Eirich, New York Academic Press 1956. 

Consider a concentrated suspension of porous spheres of radius a in a liquid of viscosity rj [27]. We adopt a cell model that assumes that each sphere of radius a is surrounded by a virtual shell of outer radius b and the particle volume fraction 4> is given by Eq. (27.2) (Eig. 27.3). The origin of the spherical polar coordinate system (r, 6, cp) is held fixed at the center of one sphere. According to Simha [2], we the following additional boundary condition to be satisfied at the cell surface r = b ... 

Simha (1940) employing Eq. (10) solved the equation for the viscosities of solutions of ellipsoids of revolution for the limiting case a —> 0. Under this condition the distribution of the particles can be regarded as almost completely random. Simha also found that for large axial ratios the viscosity increment at a0 for very dilute solutions or suspensions (i.e., 4> —> 0) can be approximately represented by... 

Relative Viscosity of Suspensions One of the most interesting derivations of the T vs. (() dependence (covering the full range of concentration) was published by Simha [1952]. He considered the effects of concentration on the hydrodynamic interactions between suspended particles of finite size. (Note that previously the particles were simply considered point centers of force that decayed with cube of the distance.) Simha adopted a cage model, placing each solid, spherical particle of radius a inside a spherical enclosure of radius b. At distances x < b, the presence of other particles does not influence flow around the central sphere and the Stokes relation is satisfied. This assumption leads to a modified Einstein [1906, 1911] relation ... 

Figure 7.7. Relative viscosity of hard-sphere suspension in Newtonian fluid as a function of the volume fraction. Thomas curve represents the generalized behavior of suspensions as measured in 19 laboratories. The remaining curves were computed from Simha s, Mooney s and Krieger-Dougherty s relations assuming Einstein value for intrinsic viscosity of hard spheres, [T ] = 2.5, but different values for the maximum packing volume fraction, ([) = 0.78, 0.91, and 0.62 respectively.

The relationships between 17 and ( ) have been derived for suspensions of monodispersed hard spheres in Newtonian liquids. However, most real systems are polydispersed in size, and do not necessarily consist of spherical particles. It has been found that here also Simha s Eq 7.24, Mooney s Eq 7.28, or Krieger-Dougherty s Eq 7.8 are useful, provided that the intrinsic viscosity and the maximum packing volume fraction are defined as functions of particle shape and size polydispersity. For example, by allowing ( ) to vary with composition, it was possible to describe the vs. ( ) variation for bimodal suspensions [Chang and Powell, 1994]. Similarly, after values... 

Guth, E., and Simha, R., Untersuchungen ilber die Viskositat von suspensionen und Losungen 3. tiber die Viskositat von Kugelsuspensionen [Investigations of the viscosity of suspensions and solutions Part 3. The viscosity of spherical suspensions], Kolloid Z, 74, 266-275... 

In 1940, Simha derived dependencies for [ j] of the freely rotating monodispersed ellipsoids. The derivation considered the viscosity increase due to the disorienting influence of the thermal motion. At the limit of the shear rate to the rotational diffusion coefficient ratio, y/Dr 0, [ j] of the prolate and oblate ellipsoid suspension with high aspect ratio, p 1, was derived as, respectively [Simha, 1940 ... 

Jamieson, A. M., Simha, R., Newtonian viscosity of dilute, semi-dilute and concentrated polymer solutions. Chapter 1, in Polymer Physics From Suspensions to Nanocomposites and Beyond, Utracki L. A. and Jamieson A. M., Editors, J. Wiley Sons, New York (2010). 

Simha, R., Somcynsky, T The viscosity of concentrated spherical suspensions. Journal of Colloid Science, 20 (3), pp. 278-281 (1965). 

Benoit and coworkers demonstrated that it is possible to use a set of narrow polymer standards of one chemical type to provide absolute molecular weight calibration to a sample of a different chemical type (19,20). To understand how this is possible, one must first consider the relationship between molecular weight, intrinsic viscosity, and hydrodynamic volume, the volume of a random, freely jointed polymer chain in solution. This relationship has been described by both the Einstein-Simha viscosity law for spherical particles in suspension,... 

A collection of classic papers is given in Hermans, J. J., (ed.) Polymer Solutions Properties II, Hydrodynamics and Light Scattering. Dowden Hutchinson Ross Inc., Stroudsburg, Pa. (1978). Also a history of the development of the theory of suspensions is described in Frisch, H. L., and Simha, R., The viscosity of colloidal suspensions and macromolecular solutions, in Rheology Vol 1 (ed. F. R. Eiiidi). Academic Press, New York (1956). 

Here, [t)] is the shape-dependent intrinsic viscosity, viz. [t ] = 2.5 for spheres and is the maximum packing volume fraction. Owing to < )-dependent rotation and orientation of particles, the flow of suspensions with anisometric particles is more complex. Here also Simha s equation is applicable, but experimental values of the two parameters, [t ] and < ) should be used. 

Numerous other equations have been developed to even more accurately predict the viscosity behavior of spheres in more concentrated suspensions, but these have generally not been tested on sols. These include studies by Simha (209), Vand (210), and Ford (211). 

Attempts were also made to extend the Einstein law to higher concentration, both experimentally and theoretically. Eirich succeeded on the experimental side and Simha on the theoretical side. The work was extended to suspensions of elhpsoids and the dramatic increase in viscosity with elongation at constant volume fraction was derived by Simha and by Kuhn. The actual dependence of the intrinsic viscosity for a rod on length (and hence M) was as the square, not the linear dependence asserted by Staudinger. Another key figure in polymer science appears in this discussion Maurice L. Huggins (1897-1981). A more thorough... 

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