A simple model is presented to describe both first (shear) and second (bulk) viscosity coefficients for quiescent suspensions of fine spherical particles flow-induced fluctuations of which may be ignored. Components of the shear viscosity coefficient are distinguished that must be associated with mean flow of the continuous and dispersed phase. In dilute, and also moderately concentrated suspensions, the shear viscosity component attributed to the continuous phase is by far larger than that related to the dispersed phase. In dense suspensions whose concentration approaches that for the state of close packing, it is the shear viscosity of the dispersed phase that plays a dominant role. This viscosity characterizes shear stresses that are transmitted through a transient fluctuating network of occasional interparticle contacts. It is essentially dependent on the particle Peclet number, that is, on relative intensity of Brownian motion of the suspended particles. This dependence is ultimately responsible for the shear-thinning of suspensions, and it is can be described with the help of a reasonable semi-empirical approach. In accordance with the developed model, the bulk suspension viscosity must be wholly attributed to the dispersed phase, and it should not depend on the Peclet number.

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