The Einstein coefficient of suspensions in generalized Newtonian liquids

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Abstract
A new, theoretically more satisfactory, definition for relative viscosities of suspensions in generalized Newtonian media is presented, which according to the viscosities of suspensions and pure liquids should be compared to equal averaged squared strain rates gamma-L2 in the liquid phases. Comparison of this quantity (eta-r(L) is made with two definitions currently in use, in which viscosities are compared either at equal macroscopic stresses-tau or at equal macroscopic squared strain rates gamma-L2. Interrelations between the three different relative viscosities have been derived in the case of dilute suspensions of particles of arbitrary shape in generalized Newtonian liquids. Values for limiting viscosity numbers (Einstein coefficients K(E)) have been derived from experimental data on suspension viscosities both as obtained by the authors and as obtained from other sources. The data cover suspensions of spherical particles in liquids with power-law exponents n between 0.07 and 1.O. According to the new definition the Einstein viscosity coefficient K(E) = lim-phi --> 0 (d ln-eta)/(d-phi) is constant with a value of 2.5 over the whole range of n. According to the other definitions, K(E) is 2.5 only for n = 1; with n decreasing to zero, K(E) decreases linearly to 0.75 (eta-r under equal strain rate) or rises exponentially to infinity (eta-r under equal strain stress). The values of K(E), as deduced from experiments, obey the theoretical interrelations derived. There are strong indications that the value of n has no influence on the inhomogeneity in rate of strain in dilute suspensions.

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