B. Jachimska, Z Adamczyk/Joumal of the European Ceramic Society 27 (2007)2209-2215 =1 Fig 3. Zetapotential of ZrO2 as a function of pH determined for 1=1x 10-3M. ig. 5. The dependence of the intrinsic viscosity [n]=ns /n of ZrO2 suspensions The broken line denotes the theoretical results calculated from Einstein formula and msus is the suspension mass. The weight fraction of zirco- n/n=1+2. 5 y and the solid line represent the linear regression fit nia was changed within the range 0-0.3 by taking appropriate assuming that the volume of the electrolyte remained the same 5.79 g/cm. The deviation is probably caused by the intrinsic upon mixing, the density of the zirconia/electrolyte mixture can porosity of zirconia particles. Some of the pores of primary par- be expressed by the formula ticles forming aggregates were probably closed, inaccessible for he solvent. By knowing the real density of particles, the volume pe (1) fraction can be calculated as v= wpss/Pp 1+u(pe/p-1) Typical experimental data presenting the dependence of the where pe is the solvent(electrolyte density)and P, is the density intrinsic viscosity (m =ns/n (where ns is the viscosity of the of zirconia oxide particles(dry). From Eq. (1)one can deduce that zirconia particle density in fraction of zirconia for the low concentration range(v <0.08 ion can be calculated from the depende are plotted in Fig. 5. It is interesting to note, that the weight frac tion of zirconia in these suspensions was much higher attaining 0.4 (for v=0.08). As can be seen, the dependence of [n] on (2) y of zirconia can well be fitted by a linear regression. How- where tg ais the slope of the pe/psus versus w dependence(which Einstein formula predicts. witten in the usual form results shown in Fig. 4 suggest that these dependencies can well be fitted by a linear regression line with the slope which gives b ns=1+ Cy Zirconia l oxide density 5.47 g/cm. This is slightly smaller than the value supplied by the producer for solid zirconia, equal were Cv is the dimensionless constant. In our case the slope was found equal 4.5, in stead of 2.5, which is 1. 8 times larger than predicted by the Einstein formula. The deviation from the Einstein formula occurring for the low volume fraction of suspensions rpreted in terms of the primary electroviscous effect stemming from shear induced deformations of ionic double layers surrounding suspended particles. This leads to increased dissipation of mechanical energy resulting in increased viscosity of suspensions over val- ues predicted by the Einstein model. This deviation is expressed in terms of the primary electroviscous function, expressed Cv=2.(1+p) 070050101202005 where p is the primary electroviscous function depending on the ionic strength and composition of the electrolyte 4. The dependence of Pe/psus on the weight fraction w of zrOz, determined In the case where the diffusion coefficients of ions forming the electrolyte do not differ too much, one can derive an analytical2212 B. Jachimska, Z. Adamczyk / Journal of the European Ceramic Society 27 (2007) 2209–2215 Fig. 3. Zeta potential of ZrO2 as a function of pH determined for I = 1 × 10−3 M. and msus is the suspension mass. The weight fraction of zirco￾nia was changed within the range 0–0.3 by taking appropriate mass of the zirconia powder and the solvent (electrolyte). By assuming that the volume of the electrolyte remained the same upon mixing, the density of the zirconia/electrolyte mixture can be expressed by the formula8: ρsus = ρe 1 1 + w(ρe/ρp − 1) (1) where ρe is the solvent (electrolyte density) and ρp is the density of zirconia oxide particles (dry). From Eq. (1) one can deduce that zirconia particle density in the suspension can be calculated from the dependence: ρp = ρe 1 + tg α (2) where tg α is the slope of the ρe/ρsus versuswdependence (which is negative in our case) that is expected to be a straight line. The results shown in Fig. 4 suggest that these dependencies can well be fitted by a linear regression line with the slope which gives for the zirconia oxide density 5.47 g/cm3. This is slightly smaller than the value supplied by the producer for solid zirconia, equal Fig. 4. The dependence of ρe/ρsus on the weight fraction w of ZrO2, determined for pH 10. Fig. 5. The dependence of the intrinsic viscosity [η] = ηs/η of ZrO2 suspensions on the volume fraction ΦV = wρsus/ρp determined for pH 10, I = 5 × 10−3 M. The broken line denotes the theoretical results calculated from Einstein formula ηs/η = 1 + 2.5ΦV and the solid line represent the linear regression fit. 5.79 g/cm3. The deviation is probably caused by the intrinsic porosity of zirconia particles. Some of the pores of primary par￾ticles forming aggregates were probably closed, inaccessible for the solvent. By knowing the real density of particles, the volume fraction can be calculated as ΦV = wρsus/ρp. Typical experimental data presenting the dependence of the intrinsic viscosity [η] = ηs/η (where ηs is the viscosity of the sus￾pension and η is the viscosity of the electrolyte) on the volume fraction of zirconia for the low concentration range (ΦV < 0.08) are plotted in Fig. 5. It is interesting to note, that the weight frac￾tion of zirconia in these suspensions was much higher attaining 0.4 (for ΦV = 0.08). As can be seen, the dependence of [η] on ΦV of zirconia can well be fitted by a linear regression. How￾ever, the slope of this line d[η]/dΦV was found larger than the Einstein formula predicts, written in the usual form: η¯ = ηs η = 1 + CVΦV (3) were CV is the dimensionless constant. In our case the slope was found equal 4.5, in stead of 2.5, which is 1.8 times larger than predicted by the Einstein formula. The deviation from the Einstein formula occurring for the low volume fraction of suspensions is interpreted in terms of the primary electroviscous effect stemming from shear induced deformations of ionic double layers surrounding suspended particles.15 This leads to increased dissipation of mechanical energy resulting in increased viscosity of suspensions over val￾ues predicted by the Einstein model. This deviation is expressed in terms of the primary electroviscous function, expressed as16–19: CV = 2.5(1 + p) (4) where p is the primary electroviscous function depending on the ionic strength and composition of the electrolyte. In the case where the diffusion coefficients of ions forming the electrolyte do not differ too much, one can derive an analytical