懸濁液の粘度について

抄録

The presence of a set of rigid particles in a Newtonian liquid raises the viscosity of the liquid to a value η_s which is higher than the viscosity η₀ of the liquid itself. The nondimensional ratio η_s/η₀, which is known as the relative viscosity η_r of the suspension, might be a function of the fraction of the total volume of the suspension φ_v comprizing the particles.
The most widely known expression for η_r, first obtained by Einstein, has the form of the equation 1. But this equation does not agree with the experimental results except for the case in which the concentration is very dilute. So many theoretical relationships, derived by Guth, Simha, Vand, Brinkman and others, for higher concentration, however, do not agree with the observed data in the range higher than 8-10 volume percentage, either. Now, Robinson considered that the specific viscosity in higher concentration was not only proportional to the volume fraction of solid, but to the reciprocal of free liquid volume fraction, and obtained the empirical equation in Table 1.
Taking into account this consideration by Robinson and the observation by Bingham that the particles in the same stratum had the same velocity and did not change their mutual distances, the following theoretical relationship for the relative viscosity of general suspension system has been derived by the authors.
(16)'
where, d is the effective average diameter of particles, Sr is the volume specific surface, φ_v is the volume concentration and φ_vc is the limiting concentration at the full-packed state, where steady flow can occur without any deformation, fracture or grinding of particles.
From this formula, the physical meanings of the two empirical constants k and S' in Robinson's equation can be explained as follows:
in which, k is a function of particle shape, whose value becomes 3 for spherical particles, φ_vc, the limiting concentration, may be a function of particle shape and its size distribution.
In a special case when the suspended particles are spherical and have equal size, the obtained formula becomes as follows, provided the value of φ_vc is assumed to be equal to 0.52, which is the volume fraction of solid in cubic packing of spheres of equal size.
This formula agrees quite well with the observed values given by different writers over a wide range of concentration as shown in Figure 4. Figure 6 indicates the systematic variation of relative viscosity with changes in the relative fraction of large and small spheres in the suspensions. The plotted data are the experimental values by Eveson, Ward and Whitmore for the suspensions consisting of methyl methacrylate polymer spheres in an aqueous lead nitrate-plus-glycerol solution. The real lines are the theoretical results calculated by means of the equation (16)', using Furnas chart, Figure 5, for φ_vc. According to the equation 16, when 1/_ηsp is plotted against 1/φ_v on condition that and 1/φ_v are constants, the graphs must be linear, and its intercepts are equal to 2/d·S_r and 1/φ_vc respectively. All the data reported were examined and they proved to agree approximately with this consideration as shown in Figs. 9-15. It is especially interesting to note that in Figure 14, the value of φ_vc is approximately equal to the concentration of the cake produced in the centrifuge.