Viscosity coefficient colloidal dispersions

Viscosity A measure of the resistance of a liquid to flow. It is properly the coefficient of viscosity and expresses the proportionality between shear stress and shear rate in Newton s law of viscosity. Many equations have been used to predict the viscosities of colloidal dispersions see reference 2. 

Routh and Russel [10] proposed a dimensionless Peclet number to gauge the balance between the two dominant processes controlling the uniformity of drying of a colloidal dispersion layer evaporation of solvent from the air interface, which serves to concentrate particles at the surface, and particle diffusion which serves to equilibrate the concentration across the depth of the layer. The Peclet number, Pe is defined for a film of initial thickness H with an evaporation rate E (units of velocity) as HE/D0, where D0 = kBT/6jT ir- the Stokes-Einstein diffusion coefficient for the particles in the colloid. Here, r is the particle radius, p is the viscosity of the continuous phase, T is the absolute temperature and kB is the Boltzmann constant. When Pe 1, evaporation dominates and particles concentrate near the surface and a skin forms, Figure 2.3.5, lower left. Conversely, when Pe l, diffusion dominates and a more uniform distribution of particles is expected, Figure 2.3.5, upper left. 

Sometimes when dealing with a fluid that contains a dispersed particle phase that cannot be considered a component, we treat the suspension fluid as a continuum with a constitutive relation that is modified because of the presence of the particles. An example to be discussed in Chapter 5 is Einstein s modification of the Newtonian viscosity coefficient in dilute colloidal suspensions due to hydrodynamic interactions from the suspended particles. As with molecular motions, the modified coefficient may be determined from measurements of the phenomenon itself by using results from analyses of the particle behavior in the fluid as a guide. These ideas are further expanded upon in Chapter 9 where the behaviors of concentrated suspensions of colloidal and non-colloidal particles are examined. 

Fig. 19 Reduced flow curves for a core-shell dispersion at an effective volume fraction of ij>eff = 0.580 data from [33], analysis from [86]. Here Rg denotes the hydrodynamic radius and Dq the self diffusion coefficient of the colloidal particles IcgT is the themial energy. The solid line (red) shows the result for the fitted fi -model with = 2.0. The fitted parameters are e = -0.00042, 7c = 0.14, V(j = VOfcaT/Rg, F = 8()/J,-,/A j, and = (),394A [i7 The dashed line shows the corresponding result for the A-formula. The dotted line shows the inflection tangent of the numerically determined flow curve with a slope of p = 0.12. The inset shows the corresponding results for the viscosity...

In colloidal systems where the dispersion medium is solid all processes aimed at changing the degree of dispersion are retarded due to high viscosity of dispersion medium and small diffusion coefficients of components. 

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