Constant force and constant velocity experiments in concentrated suspensions

Homogeneous materials are characterized by intrinsic properties such as density, thermal conductivity, and viscosity that are independent of sample size and of the state of stress of the material. For example, experiments with a test sphere traversing in a homogeneous Newtonian fluid would determine the same viscosity by measuring the force on the test sphere traveling at a constant velocity or by measuring the velocity of the test sphere under a constant force.

Recent theoretical calculations have shown that a test sphere settling in suspensions of neutrally buoyant spheres will experience a larger resistance to motion traveling at a constant velocity through a region in the cylinder free of end effects than moving under a constant force when the spheres are of similar size or the test sphere is much smaller than the suspending spheres. Hence, constant force and constant velocity experiments would measure different apparent viscosities even in a suspension at infinite dilution. The objective of this paper is to examine this surprising prediction using concentrated suspensions of neutrally buoyant particles in viscous Newtonian liquids under conditions such that only hydrodynamic forces exert an appreciable effect.

Experiments have been performed to explore the difference between the apparent viscosity of a suspension as determined by a constant gravitational force applied to a test sphere (falling-ball rheometry) and the apparent viscosity of the same suspension measured with a non-rotating test sphere towed (pulling-ball rheometry) with uniform velocity through the suspension and extrapolated to zero string length. The relative viscosity is the apparent viscosity of the suspension relative to that of the pure suspending fluid, çr, The model suspensions used in these experiments were made from large, monomodal, neutrally buoyant particles in viscous Newtonian fluids. These experiments were conducted using cylinders of sufficient length that end effects were unimportant in the center section of the column.

When tested against Newtonian test fluids both pulling ball and falling ball experiments produce accurate measurements of the relative viscosities. For the same size balls and suspensions, çr measured in the pulling-ball experiments was larger than those measured in the falling-ball experiments. The ratio of the two viscosities increases linearly as the volume fraction of solids in the suspension, ö, increases from 0.1 to 0.5. The ratio of the two relative viscosities is not a strong function of the ratio of the size of the suspended balls to the test sphere.