###
To the rheology of suspensions: a scale effect in fine-filled suspensions for the friction account between particles and liquid

Belov P.A., Lurie S.A., Lykosova E.D.

#### Abstract:

In the paper, we investigate viscosity models of suspensions based on the “classical” Reiss averaging of the viscosity and taking into account the dynamic friction of the liquid on the particle. It was found that the allowance of friction determines the scale effect, which manifests itself in the fact that viscosities of both liquid and “dry” particles in the composition have larger values than outside of the composition. For finely dispersed suspensions with a non-zero coefficient of dynamic friction, the characteristic thickness of the boundary layer is commensurable with the distance between the particles, and the scale effect makes a significant correction to the viscosity of the suspension in comparison with the “classical” Reiss averaging. By analogy with the hypotheses of averaging the elastic moduli in the theory of composites, in the hydrodynamics of suspensions, the corresponding hypotheses for averaging dynamic viscosities are proposed. The hypotheses of effective inclusion, effective liquid, effective volume fraction and hypothesis of three phases, allowing to take into account scale effects of the first order in the Navier-Stokes hydrodynamics associated with friction of a liquid and particles, are formulated. The statements of all the above hypotheses are different forms of the same solution for the Navier-Stokes equations with boundary conditions that take into account the friction of the liquid on the particles. The appearance of a turbulent flow specific for suspensions associated with friction at the boundary of a particle with a liquid (nonideal slip of a liquid) is established. The size of the vortices of this flow is directly related to the characteristic thickness of the boundary layer and, correspondingly, to the coefficient of dynamic friction. This fact allows us to propose a new method for determining the coefficient of dynamic friction based on the known viscosity of the suspension and the characteristic thickness of the boundary layer.

0