Dispersion Rheology "Interlude" Addition of a particulate phase to a liquid increases its viscosity in proportion to the volume fraction o of the dispersed phase: dispersed-phase volume total volume However,the hydrodynamically-effective volume fraction,f is often not the same as the formulated volume fraction o
Dispersion Rheology "Interlude" Addition of a particulate phase to a liquid increases its viscosity in proportion to the volume fraction o of the dispersed phase: dispersed-phase volume total volume However,the hydrodynamically-effective volume fraction,efe is often not the same as the formulated volume fraction o
Effective Volume Fraction e Φef can be made greater thanΦby: Increasing the hydrodynamic radius of the dispersed particle through adsorption of polymeric stabilizer particle surface electrical charge Flocculating the dispersion,trapping liquid phase within the flocs (volume of floc volume of particles contained)
The viscosity of suspensions Einstein showed that single particles increased the viscosity of a liquid (n)as a simple function of their phase volume () 7=7,(1+2.5p) There is no effect of particle size,nor of particle position, because the theory neglects the effects of other particles. This equation works for <10%
The viscosity of suspensions Einstein showed that single particles increased the viscosity of a liquid (s) as a simple function of their phase volume (), s1 2.5 There is no effect of particle size, nor of particle position, because the theory neglects the effects of other particles. This equation works for < 10%
More concentrated suspensions Higher order terms: 7=7.(+2.50+620+00》 or the Krieger and Dougherty equation =-0 where [n]is the intrisnic viscosity (2.5 for spheres) and is the maximum packing fraction
More concentrated suspensions Higher order terms: =s 1 2.5 6.2 2 O 3 or the Krieger and Dougherty equation =s 1 m m where is the intrisnic viscosity (2.5 for spheres) and m is the maximum packing fraction
The maximum packing fraction of various Arrangements of monodisperse spheres Arrangement Maximum packing fraction Simple cubic 0.52 Hexagonally 0.605 Body-centered 0.68 Face-centered 0.74
The maximum packing fraction of various Arrangements of monodisperse spheres Arrangement Maximum packing fraction Simple cubic 0.52 Hexagonally 0.605 Body-centered 0.68 Face-centered 0.74
The values of [n]andm for a number of suspensions of asymmetric particles,obtained by fitting experimental data to eqn.(7.7) System I 中m [n]中m Reference Spheres (submicron) 2.7 0.71 1.92 de Kruif et al.(1985) Spheres (40 um) 3.28 0.61 2.00 Giesekus(1983) Ground gypsum 3.25 0.69 2.24 Turian and Yuan(1977) Titanium dioxide 5.0 0.55 2.77 Turian and Yuan(1977) Laterite 9.0 0.35 3.15 Turian and Yuan (1977) Glass rods 9.25 0.268 2.48 Clarke (1967) (30×700m) Glass plates 9.87 0.382 3.77 Clarke(1967) (100×400um) Quartz grains 5.8 0.371 2.15 Clarke (1967) (53-76um) Glass fibres: axial ratio-7 3.8 0.374 1.42 Giesekus(1983) axial ratio-14 5.03 0.26 1.31 Giesekus(1983) axial ratio-21 6.0 0.233 1.40 Giesekus(1983)
Effect of Particle Shape 30 皇 20 10 0 0 10 20 30 40 50 Phase volume,φ Viscosity as a function of phase volume for various particle shapes
Effect of Particle Shape
4 月正天 3 2 = 0 0 10 20 30 40 Phase volume,.φ Viscosity as a function of phase volume for various aspect ratio of fibres
Effect of the viscosity of the internal phase -25294） where n=the viscoisty of the internal or the dispersed phase Several limiting cases: =[n]=2.5 the Einstein case (hard sphere) 7:=7[7]=1.75 7,=0;[]=1 the situation for gas bubbles
2.5 i 0.4s i o where i the viscoisty of the internal or the dispersed phase Several limiting cases: i ; 2.5 the Einstein case (hard sphere) i s; 1.75 i 0; 1 the situation for gas bubbles Effect of the viscosity of the internal phase