<p>An analytical expression for the effective viscosity of a liquid with solid particles near a plane wall has been obtained. The effective viscosity of the liquid with solid particles was determined by the average stress in the system with regard for the hydrodynamic interaction of the particles with the plane wall and without regard for the interaction of the particles with each other and, consequently, in the linear approximation for the volume concentration of particles in the liquid. The calculations were performed using the analytical data obtained for the distribution of the velocity of the particles in a shear flow of the liquid and the distribution of the pressure around them with account of the presence of the plane wall. Since the indicated distributions are dependent on the distance between each particle and the plane wall, the effective viscosity of the system was determined by averaging over this parameter with regard for the distribution of particles in the liquid. It was found that the effective viscosity of the system changes from a maximum value near the plane wall to the characteristic minimum value corresponding to the absence of wall. The results obtained conform qualitatively with the known calculated data on the effective viscosity of a thin near-wall layer of a liquid containing particles.</p>

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Effective Viscosity of Liquid with Particles near a Plane Wall

  • S. I. Martynov

摘要

An analytical expression for the effective viscosity of a liquid with solid particles near a plane wall has been obtained. The effective viscosity of the liquid with solid particles was determined by the average stress in the system with regard for the hydrodynamic interaction of the particles with the plane wall and without regard for the interaction of the particles with each other and, consequently, in the linear approximation for the volume concentration of particles in the liquid. The calculations were performed using the analytical data obtained for the distribution of the velocity of the particles in a shear flow of the liquid and the distribution of the pressure around them with account of the presence of the plane wall. Since the indicated distributions are dependent on the distance between each particle and the plane wall, the effective viscosity of the system was determined by averaging over this parameter with regard for the distribution of particles in the liquid. It was found that the effective viscosity of the system changes from a maximum value near the plane wall to the characteristic minimum value corresponding to the absence of wall. The results obtained conform qualitatively with the known calculated data on the effective viscosity of a thin near-wall layer of a liquid containing particles.