Rheological characteristics of suspensions

Einstein considered a suspension of spherical particles which were far enough apart to be treated independently where 0 is defined by 

The suspension could be assigned an effective viscosity, ry, given by 

A charged particle in suspension with its inner immobile Stern layer and outer diffuse Gouy (or Debye-Hiickel) layer presents a different problem than a smooth and small non-polar sphere. Such particles when moving experience electroviscous effects which have two sources (i) the resistance of the ion cloud to deformation (ii) the repulsion between particles in close contact. When particles interact, for example, to form pairs in the system the new particle will have a different shape from the original and will have different flow properties. The coefficient 2.5 in Einstein s equation (9.11) applies only to spheres asymmetric particles will produce coefficients greater than 2.5. 

Other problems in deriving a priori equations result from the polydisperse nature of pharmaceutical suspensions. The particle size distribution will determine fj. Experimentally a polydisperse suspension of spheres has a lower viscosity than a similar monodisperse suspension. It is obvious that a simple undifferentiated volume fraction (f) cannot be expected to be of value in this situation. 

Structure formation during flow is an additional complication. Structure breakdown occurs also and is evident particularly in clay suspensions, which are generally flocculated at rest. Under flow there is a loss of the continuous structure and the suspension exhibits thixotropy and a yield point. The viscosity decreases with increasing shear stress. 

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