Einstein viscosity increment

There are two molecular contributions to the intrinsic viscosity one from shape and the other from size or volume, as summarized by the following relation  

The viscosity increment Vg/i, is referred to as a universal shape function or Simha number [Table 2.2] it can be directly related to the shape of a particle independent of volume. For its experimental measurement, it does, however, require measurement of Vjp, v, d,po, and, of course, [ ]. 

A study of the viscosity of a solution of suspension of spherical particles [colloids] suggested that the specific viscosity 7]sp is related to a shape factor Vg/b ss follows  

As seen in Table 2.2, the values of P and Va/b are far away from the spherical form and are accurate to form rod-like, as pectin [159], alginate [160]. The hydration value accounts for the high water adsorption capacity for this polysaccharide and its great industrial potential application in highly viscous and thick solutions. The of Tara gum is between the values specified by Wu et al. [161]. 

The author thanks Universidad Nacional de San Luis [Project 2-81/11], FONCyT [PICT 2004-N°23-2548 and PICT 2008-N 21-84], CONICET [PIP 6324 Res. 1905/05] and PROIPRO 2-2414 [Regional Polysaccharides Purification and Physicochemical Characterization. Applications Analytics, Separative Processes and Food Industry] for the financial support. 

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While the suspended particles undergo diffusion in a solvent, the shear viscosity r]Q of the solvent is also modified by the particles to the shear viscosity rj of the whole solution. As was originally addressed by Einstein, the increment in viscosity is directly proportional to the volume fraction of the suspended particles, if the interparticle interactions are ignored. For a solution containing n particles of radius R in volume V, the result is... 

In 1906, Einstein worked out a theory of the viscosity of a liquid which contains, in suspension, spherical particles which are large compared with the size of molecules of the liquid. The predictions of the theory are found to be in good agreement with the measured values of the viscosity of liquids containing colloidal particles in suspension. The presence of these obstacles increases the apparent viscosity of the liquid, and Einstein found1 that the increment is proportional to the total volume v of the foreign particles in unit volume, that is to say, the sum of the volumes of the particles that are present in unit volume of the liquid thus,... 

To do this, we consider a dispersion of volume fraction 4> and examine the increment in viscosity dr) as a small amount of particles is added to the dispersion. If we take to be small enough that the Einstein equation, Equation (41), holds, the increment dr) that accompanies the addition of particles is then given by... 

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