Dispersion 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. 

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. 

A multiple emulsion provides a slightly different kind of volume fraction complication since the dispersed phase is itself an emulsion. A variation on the Mooney equation for double emulsions is... 

Knowing the silica content of a sol and the particle size one can calculate the volume fraction of the dispersed phase. jFor example. 1 ml of a 2% SiO, sol of 1.5 nm particles contains 0.022 ml of dispersed phase. From the Mooney equation (Figure 3.30) the value of/I, - 1 is 0.055. 

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] ... 

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 ... 

These equations are not valid at high concentrations of dispersed phase. A number of expressions have been discussed in detail by Sherman (27), Goodwin(28) and Frisch and Simha(29). One such equation, for a solid dispersed phase, is due to Mooney... 

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... 

An equation similar in form to Mooney s equation was derived by Kunnen [44], who proceeded from the additivity of the reciprocal values of the activation energy of the viscous flow for binary solutions, emulsions and dispersions ... 

Sherman concluded that in the 0/W systems a small fraction of the continuous phase was immobilized by the dispersed phase either by attractive forces or by flocculation. Therefore, the apparent volume fraction was greater than the actual volume fraction of that component. The equations he used to describe the viscosities of these emulsions further extended the approach of Mooney and took account of the particle diameter. 

A viscometric method for estimating the stability of W/O/W multiple emulsions has been described [189]. The dispersed phase consists of the inner aqueous phase (y,i) and the oil phase (0o). Using Mooney s equation in the form for Newtonian flow, where A is a crowding factor,... 

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