Intrinsic viscosity suspensions

Smith,T.L Bruce, C.A. (1979) Intrinsic viscosities and other rheological properties of flocculated suspensions of non magnetic and magnetic ferric oxides. J. Colloid Interface Sci. 72 13-25... 

This is a well known result The intrinsic viscosity of a suspension of elastic dumb-bells is equal to that of another suspension containing rigid dumb-bells of uniform length equal to the root mean square end-to-end... 

Young, S.L. and Shoemaker, C.F. 1991. Measurement of shear-dependent intrinsic viscosities of carboxymethyl cellulose and xanthan gum suspensions. J. Appl. Polymer Sci. 42 2405-2408. 

Other modifications have been made for application to suspensions of aniso-metric particles such as clays. In this case the intrinsic viscosity tj, given by ... 

The irradiation dose was 12 Mrad/h from a source of total activity of 8000 Ci. The gels were prepared from 5% starch suspensions. Calculated from intrinsic-viscosity data determined in 90% aq. Me2SO. 

Shape effect of PFPE molecules or magnetic particles in suspension, including agglomeration phenomena at low concentration, interaction among these particles, and effects of floes can be examined via solution viscosity (r ) measurement. For a very dilute polymer solution [108], there is no interaction among polymer molecules, and the solution viscosity results from the contribution of the solvent plus the contribution of the individual polymer molecules. The intrinsic viscosity, therefore, is a measure of the hydrodynamic volume of a polymer molecule as well as the particle aspect ratio. Figure 1.24 shows the determination of the intrinsic viscosity for Zdol4000 in three different solvents. 

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. 

Ratio of Apparent Intrinsic Viscosity of Heated ([i)0]h) to Control ([T a]e) for Some Polysaccharide Suspensions... 

Fig. 37. The ratio of the equivalent hard sphere volume fraction based on the measured intrinsic viscosity as a function of for polyfmethyl methacrylate) spheres with grafted poly( 12-hydroxy stearic add) layers such that a/L = 4.7 (Mewis et ai, 1989). Open and closed circles correspond to the low and high shear limits of suspension viscosity.

Here [>7] is the intrinsic viscosity, which for suspensions is the dilute limit of the viscosity increment per unit particle volume fraction, divided by the solvent viscosity. Thus, it is a dimensionless quantity defined as... 

Brenner (1974) has presented numerical results for the suspension stresses in various flows. Figure 6-14 plots the intrinsic viscosity [defined in Eq. (6-6)] for oblate and prolate spheroids of various aspect ratios as functions of the Peclet number. Note that as the aspect ratio of the spheroid increases, the zero-shear viscosity increases, and the suspension shows more shear thinning. The suspension also becomes more elastic when the aspect ratio p for prolate or 1/ for oblate spheroids) is large see Fig. 6-15, which plots Ni N2 versus Pe for prolate spheroids of various aspect ratios p. Typically, N2 is roughly an order of magnitude less than Ni, so this plot of Nj, mainly reflects the behavior of V,. 

Figure 6.14 Intrinsic viscosity versus Peclet numberfor dilute suspensions of spheroidal particles of (a) oblate shape and (b) prolate shape, (From Macosko 1994, adapted from Brenner 1974, with permission from Pergamon Press.)...

Figure 6.17 Normalized intrinsic viscosity [r ]/[)7]o for a dilute solution of poly(y-benzyl-L-glutamate) (PBLG) = 208,000) in m-cresol. The line is a calculation for the rigid-dumbbell model, with the relaxation time t = lj6Dro adjusted to the value 10- sec to obtain a fit. The stress tensor for a suspension of rigid dumbbells is given by Eq. (6-36) with Cstr replaced by k T/Dro-(From Bird et al. 1987 data from Yang 1958, Dynamics of Polymeric Liquids, VoL 2, Copyright 1987. Reprinted by permission of John Wiley Sons, Inc.)...

Because the continuous phase or serum influences the rheological properties of suspensions, its characteristics, such as the intrinsic viscosity, are of interest. The magnitude of intrinsic viscosity can be determined by extrapolation techniques, such as with Huggins s equation (Equation 20), and from the slopes of straight lines of quantities based on relative viscosity (Equation 21) ( ). 

For a suspension of rigid spheroids, Leal and Hinch (102) determined the Einstein constant (intrinsic viscosity) for the limiting case of large axis (aspect) ratio, re = long axis/short axis - oo, as follows ... 

In a uniaxial elongational flow, the Trouton, or elongational viscosity of an anisometric particle suspension can be estimated by equation 59 as well with an intrinsic viscosity given by... 

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... 

An HPMC sample kindly supplied by Shin-Estu Chemical Co. was purified by the method described previously (5) and its molecular weight was determined to be 250x10 by the intrinsic viscosity measurement. PPG with the molecular weight of 725 was purchased from the Aldrich Chemical Co. and it was used without further purification. Silica suspensions were prepared by mechanically... 

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,... 

An optimum model-based predictive controller was developed to allow for control of molecular weight averages (intrinsic viscosities) and reactor temperatures in solid-state PET polymerizations, through manipulation of the inert gas temperatures and flowrates [ 199]. Simulation studies also showed that predictive controllers might lead to significant improvement of process operation in PVC suspension reactors, when temperatures are allowed to vary along the batch time [200]. Simulation studies performed for continuous styrene solution polymerizations showed that the closed-loop predictive control can also be used to stabilize the reactor operation at unstable open-loop steady-state conditions [201]. 

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