A Thermodynamic Theory of Suspension II. Kinetic Theory for Viscosity of Suspension

Abstract

Abstract A dispersion is prepared by vigorous agitation for large particles of radius r or volume v larger than its critical rc or vc. The viscosity η is several Pa s and will be large compared with the viscosity of the solvent η0 of 10-3 Pa s. As a typical case, cement paste was studied by Hattori-Izumi who showed a gradual increase in η with time t. It was explained by collisions followed by cohesion, but gradual sedimentation seems more likely to be the origin. The author proposes a dynamic theory of viscosity. The static viscosity is proportional to the energy of sedimentation Wsed, whereas dynamic viscosity η is expressed as exponential functions of Wsed. Molar concentration Wsed/v increases with the density of particles ρ, but decreases with the viscosity of solvent. The η value decreases by addition of water and fly ash. ζ-potential promotes dispersion. Contrary to an ordinary concept, cohesion heat may not act except in the coagulated state. Time-dependent viscosity is caused by the relaxation of agitation energy Wag through three stages: rapid stage relaxation by collision of particles, slow stage relaxation by the consumption of Wc i.e., internal sedimentation energy due to viscous resistance and finally relaxation by coagulation. The second stage is expressed as ln η ≈ φ (Wc/vcRT)(t/τ), where Wc/vcRT = 1, vc = (rc/r)3, rc = 30 nm, r = 1 μm, τ = C0.5 (rc/r)2, C = η00.5/Δρ3/4 and τ is about 1 h. For the case of very large particles e.g., fluidized bed, the relative volume v of the bed expands with the velocity of gas stream u0 like thermal expansion with a coefficient β and η is expressed as η = A exp (Wsed/β u0RT). This type of equation for polymeric material is known as Doolittle's equation, η = A exp (B/vf), vf being a free volume fraction.