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

摘要

A dispersion is prepared by vigorous agitation for large particles of radius r or volume v larger than its critical rc or v_c.The viscosity #eta# is several Pa s and will be large compared with the viscosity of the solvent #eta#_o of 10~(-3) Pa s.As a typical case,cement paste was studied by Hattori-Izumi who showed a gradual increase in #eta# with time t.It was explained by collisions followed by cohesion,but gradual sedimention 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 W_(sed),whereas dynamic viscosity #eta# is expressed as exponential functions of W_(sed).Molar concentration W_(sed)/v increases with the density of particles p,but decreases with the viscosity of solvent.The #eta# value decreases by addition of water and fly ash.#zeta#-potetial promotes dispersion.Contrary to an ordinary cocept,cohesion heat may not act except in the coagulated state. 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 sedimentation energy due to viscous resistance and finally relaxation by coagulation.The second stage is expressed as In #eta# approx=#PHI#(W_c/v_cRT)(t/t),where W_C/v_cRT=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#_o~(0.5)/#DELTA#p~(3/4) and #tau#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 u_o like thermal expansion with a coefficient #beta# and #eta# is expressed as #eta#=A exp (W_(wed)/#beta#u_oRT).This type of equation for polymeric material is known as Doolittle's equation,#eta#=A exp(B/v_f),v_f being a free volume fraction.