A thermodynamic theory of suspension II. Kinetic theory for viscosity of suspension

A dispersion is prepared by vigorous agitation for large particles of radiu s r or volume v larger than its critical r(c) or v(c). The viscosity eta is several Pa s and will be large compared with the viscosity of the solvent eta(0) of 10(-3) Pa s. As a typical case, cement paste was studied by Hatto ri-Izumi who showed a gradual increase in eta with time t. It was explained by collisions followed by cohesion, but gradual sedimentation seems more l ikely to be the origin. The author proposes a dynamic theory of viscosity. The static viscosity is proportional to the energy of sedimentation W-sed, whereas dynamic viscosity eta is expressed as exponential functions of W-se d. Molar concentration W-sed/v increases with the density of particles rho, but decreases with the viscosity of solvent The eta value decreases by add ition of water and fly ash. zeta-potential promotes dispersion. Contrary to an ordinary concept, cohesion heat may not act except in the coagulated st ate. Time-dependent viscosity is caused by the relaxation of agitation energy W- ag through three stages: rapid stage relaxation by collision of particles, slow stage relaxation by the consumption of W-c i.e., internal sedimentatio n energy due to viscous resistance and finally relaxation by coagulation. T he second stage is expressed as In eta approximate to phi (W-c/v(c)RT)(t/ta u), where W-c/v(c)RT = 1, v(c) = (r(c)/r)(3), r(c) = 30 nm, r = 1 mu m, tau = C-0.5(r(c)/r)(2), C = eta(0)(0.5)/Delta rho(3/4) and tau is about 1 h. For the case of very large particles e.g., fluidized bed, the relative volu me v of the bed expands with the velocity of gas stream mu(0) like thermal expansion with a coefficient beta and eta is expressed as eta = A exp (W-se d/beta u(v)RT). This type of equation for polymeric material is known as Do olittle's equation, eta = A exp(B/v(f)), v(f) being a free volume fraction.