Volume fraction, effective

Viscosity. Because a clump of particles contains occluded Hquid, the effective volume fraction of a suspension of clumps is larger than the volume fraction of the individual particles that is, there is less free Hquid available to faciHtate the flow than if the clumps were deagglomerated. The viscosity of a suspension containing clumps decreases as the system becomes deagglomerated. This method is not very sensitive in the final stages of deagglomeration when there are only a few small clumps left. 

Following the idea of van Laar, Chueh expresses the excess Gibbs energy per unit effective volume as a quadratic function of the effective volume fractions. For a binary mixture, using the unsymmetric convention of normalization, the excess Gibbs energy gE is found from6... 

Increasing the bound mbber content increases the effective volume fraction of filler by intimately bonding polymer to the filler. This polymer is no longer available to contribute to viscous flow. As a consequence, the viscosity of the compound increases. 

Tjo is the viscosity of the unfilled polymer ( eff is the effective volume fraction of filler... 

By relating the endpoint of crushed DBF absorption to the void space within and between equivalent spheres of aggregates, and assuming the spheres to be packed at random, Wang et al. obtained the following equation for the effective volume fraction of carbon black ... 

The term pair potential that contains only the attractive potential, because the repulsion effects have been allowed for by the effective volume fraction and hard sphere diameter. The new potential can be defined as... 

Figure 1 The shear stress relaxation function, C(t), obtained from a molecular dynamics simulation of500 SRP spheres at a reduced temperature of 1.0 and effective volume fraction of 0.45. Note that n = 144 and 1152 (from Equation (1)) cases are superimposable with the analytic function of Equation (4) ( Algebraic on the figure) for short times, t (or nt here)...

In summary of these points, it is seen that the isolation of particles from the epoxy matrix, the effective volume fraction of the elastomeric phase, and strength of the interface interact to control modulus. The morphology which a particular siloxane modifier promotes determines the contribution of any or all of these three factors to the modulus of the modified resin. 

Colloidal interactions between emulsion droplets play a primary role in determining emulsion rheology. If attractions predominate over repulsive forces, flocculation can occur, which leads to an increase in the effective volume fraction of the dispersed phase and thus increases viscosity (McCle-ments, 1999). Clustering of milk fat globules due to cold agglutination increases the effective volume fraction of the milk fat globules, thereby increasing viscosity (Prentice, 1992). 

A grafted layer of polymer of thickness L increases the effective size of a colloidal particle. In general, dispersions of these particles in good solvents behave as non-Newtonian fluids with low and high shear limiting relative viscosities (fj0 and rj ), and a dimensionless critical stress (a3aJkT) that depends on the effective volume fraction = (1 + L/a)3. The viscosities diverge at volume fractions m0 < for mo < fan < 4>moo> the dispersions yield and flow as pseudoplastic solids. 

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.

At very low shear rates (i.e., flow velocities), particles in a chemically stable suspension approximately follow the layers of constant velocities, as indicated in Fig. 2. But at higher shear rates hydro-dynamic forces drive particles out of layers of constant velocity. The competition between hydrodynamic forces that distort the microstructure of the suspension and drive particles together, and the Brownian motion and repulsive interparticle forces keeping particles apart, leads to a shear dependency of the viscosity of suspensions. These effects depend on the effective volume fraction of... 

The viscosity in the low shear regime depends mainly on the effective volume fraction of the particles in the suspension. There are many expressions given in the literature which relate the low shear viscosity of a suspension rjo to the viscosity of the suspending fluid ris. Two formulas which are independent of parameters specific... 

The viscosity and the shear dependency of the viscosity both increase with growing effective volume fraction of particles. For very low shear rates there is usually a low shear plateau jo and for high shear rates a high shear plateau joo exists. These features are not described by the power model, but a more elaborate model such as the cross model is needed ... 

Shear thickening in colloidal suspensions is governed by particle size and surface roughness, in addition to the effective volume fraction of sohds. The onset of shear thickening depends on the effective particle radius, R in the hterature two relations for this dependency are formd. The first is the Peclet nmnber ... 

To summarize, problems with the application of ceramic suspensions with inkjet printers grow with the (effective) volume fraction... 

Effect of Particle Rotation on the Effective Volume Fraction The rotation of particles cause the effective volume fraction of an anisotropic particle to be much laiger than that of the volume fraction of the particle itself. For example, the volume of the effective sphere of revolution divided by the particle volume is given by... 

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