Viscosity Mooney equation

Viscosity of Systems with Dispersed Phases. A large proportion of coatings are pigmented and, therefore, have dispersed phases. In latex paints, both the pigments and the principal polymer are in dispersed phases. The viscosity of a coating having dispersed phases is a function of the volume concentration of the dispersed phase and can be expressed mathematically by the Mooney equation (96), a convenient form of which is... 

If there is particle—particle interaction, as is the case for flocculated systems, the viscosity is higher than in the absence of flocculation. Furthermore, a flocculated dispersion is shear thinning and possibly thixotropic because the floccules break down to the individual particles when shear stress is appHed. Considered in terms of the Mooney equation, at low shear rates in a flocculated system some continuous phase is trapped between the particles in the floccules. This effectively increases the internal phase volume and hence the viscosity of the system. Under sufficiently high stress, the floccules break up, reducing the effective internal phase volume and the viscosity. If, as is commonly the case, the extent of floccule separation increases with shearing time, the system is thixotropic as well as shear thinning. 

Accepting the elastic floe model as a reasonable description of the structured suspension, it is possible to calculate a few more parameters from the experimental results. For example C p may be calculatedfrom which, in turn, may be obtained from the plastic viscosity, ripj using the Mooney equation (23),... 

By a different choice of e value, one can derive many existing viscosity equations (84). For example, when e - 2, equation 39 can lead to the Mooney equation 32. When e - 1, equation 39 reduces to equation 38 and hence leads to the Krieger-Dougherty equation. 

Equations 66 and 68 indicate that the droplet behaves like a solid particle only when the viscosity ratio of the dispersed phase to the continuous phase is large. For liquid-in-liquid dispersions, the modified Quemada equation, Krieger-Dougherty equation, and Mooney equation are still applicable provided that the maximum packing limit and the Einstein constant are left as adjustable parameters for a given system. 

The third term, which involves O (the volume fraction of silica), expresses the effect of increasing the silica concentration in decreasing the gel time. The expression 0/(1 - KO) is used instead of O itself as a concentration variable, since the particles will physically touch one another long before the silica volume fraction becomes one (corresponding to a 100% concentration). The constant in the denominator of this expression, which has the value of 2.58 for the particular sample of deionized Ludox used in these gelling experiments, is identical to the constant, which appears in the Einstein-Mooney equation for the viscosity of spherical colloidal particles. This will vary with the degree of hydration and aggregation, or the % solids in the dispersed phase, of the silica particles. 

Away to describe the relative viscosity of colloidal systems up to high concentrations is given by the Mooney equation [40]... 

Mooney equation (M. Mooney) n. An empirical modification of the Einstein equation applicable to higher solids concentrations, and relating the viscosity of a suspension of monodisperse spheres to that of the pure liquid r]o. 

The volume of microgel phase can be estimated from viscosity on the assumption that the microgel regions are spherical in shape and of approximately uniform size. The volume fraction of microgel phase (which is also the fraction of silica immobilized in gel) can be calculated from the Mooney equation (128a) ... 

Figure 3.30. Plot of the Mooney equation relating the volume-fraction of uniform spheres in suspensions to viscosity.

The apparent viscosity of a slurry can be related to the volume fraction of the solid, e by the Mooney-equation (Mooney, 1951) ... 

Clearly the more open the structure of the floe, the larger is the Cpp value. 0 may be calculated from the plastic viscosity, rjpp, using the Mooney equation (35),... 

The viscosity of a colloidal dispersion is a rheological property that measures the resistance to flow in response to the applied shear force. It is dependent on the hydrodynamic interactions between the particles and the continuous aqueous phase and interparticle interactions. The viscosity increases exponentially with increasing total solids content of the emulsion polymer, as shown schematically in Figure 1.7. This general feature can be described by the Mooney equation [73] ... 

For this analysis, the microgels are assumed to be spherical and pack in a close random manner with a maximum packing fraction of 0.637 [13]. Modeling the viscosity data using the Mooney equation and Einstein s... 

Figure 3 Viscosity data of a 5 wt% microgel suspension with a volume-averaged particle size of 10.28 pm in squalane modeled with the Mooney equation. Here, A represents data from the heating cycle, represents data from the cooling cycle, represents the Mooney equation with Re = 2.5,. .. represents the Mooney equation with ks = 2.5l(p sphere, and represents the Mooney equation with A = 2L/D.

The majority of investigators consider it permissible and convenient to use, when calculating the boundary layer thickness, the relationships describing the concentration dependence of viscosity in the high and medium concentration range (basically Mooney s equation) [67 — 71]. 

The type of chosen polymer and additives most strongly influences the rheological and processing properties of plastisols. Plastisols are normally prepared from emulsion and suspension PVC which differ by their molecular masses (by the Fickentcher constant), dimensions and porosity of particles. Dimensions and shape of particles are important not only due to the well-known properties of dispersed systems (given by the formulas of Einstein, Mooney, Kronecker, etc.), but also due to the fact that these factors (in view of the small viscosity of plasticizer as a composite matrix ) influence strongly the sedimental stability of the system. The joint solution of the equations of sedimentation (precipitation) of particles by the action of gravity and of thermal motion according to Einstein and Smoluchowski leads 37,39) to the expression for the radius of the particles, r, which can not be precipitated in the dispersed system of an ideal plastisol. This expression has the form ... 

All the above formulas are one-parameter equations, i.e. they relate the dispersion viscosity only to the volume fraction of particles contained in it. This limits the range of applicability of the equations to not very high dispersion concentrations. To take account of the influence of the structure of concentrated dispersions on their rheological behavior, Robinson [12] suggested that the viscosity of dispersions is not only propertional to the volume fraction of solid phase, but is also inversely proportional to the fraction of voids in it. (At about the same time Mooney [40], who proceeded from a hydrodynamic model, arrived, using theoretical methods, at the same conclusion). Robinson s equation contains the relative sedimentation volume value — S, which depends on the particle size distribution of the dispersion... 

The most widely used equation describing the dependence of viscosity on concentration is Mooney s formula [40] ... 

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