Figure 1

Typical picture from the optical microscope of toner particles clustered in a nonaqueous liquid suspension that reminds one of a diffusion-limited aggregate. For this toner $12.7\mu \mathrm{m}$ particle size and 10% SAC) the fractal dimension obtained from settling experiments in gas fluidization [9] is $D\simeq 2.53$.Reuse & Permissions

Figure 2

Particle volume fraction as a function of the consolidation stress. Data obtained by consolidating the powder allowing it to settle under upward directed gas flows (solid symbols) are jointly plotted with data obtained by consolidating the powder by means of a downward directed gas flow (open symbols). Data correspond to commercial toner Canon CLC700 (100% SAC) and to an experimental toner with reduced surface additive coverage (32% SAC) and similar particle size. The lines correspond to the power law ${\sigma }_c\propto (\varphi -{\varphi }_J{)}^{\beta }$ that fits to the data in a range ${\sigma }_c\lesssim {\sigma }_{c0}=10\mathrm{P}\mathrm{a}$ and to a logarithmic fit $\varphi -{\varphi }_J\simeq \nu \log ({\sigma }_c/{\sigma }_{c0})$ that fits to the data in the range ${\sigma }_c\gtrsim {\sigma }_{c0}$. Inset: data in the logarithmic region for toners with the same SAC (32%) but different particle size (indicated).Reuse & Permissions

Figure 3

Compression index versus the granular Bond number for toners with the same surface additive coverage (32% SAC) and varying particle size (indicated). The continuous line is a power law fit to the data ($\lambda \simeq 0.1{\mathrm{B}\mathrm{o}}_g^{0.21}$). Inset: inverse of particle volume fraction versus the consolidation stress, where lines are logarithmic fits to the data (${\sigma }_{c0}=10\mathrm{P}\mathrm{a}$).Reuse & Permissions

Figure 4

Compression index versus granular Bond number for toners with different particle size and % SAC (indicated). In the main graph ${\mathrm{B}\mathrm{o}}_g$ is calculated assuming that the interparticle attractive force in fluidization is the van der Waals force for $\mathrm{S}\mathrm{A}\mathrm{C}>30\%$, while contact memory (see text) is considered for toners with $\mathrm{S}\mathrm{A}\mathrm{C}<30\%$. In the inset the van der Waals force is used for all the toners. For toners with 20% and 100% SAC, the effect of increasing the size of silica nanoparticle additives from 8 to 50 nm has been tested. Additionally, four different amounts of cross-linking agent in the parent polymer (from 0% to 45%) have been used in these toners. The continuous lines are power law fits to the data, only for toners with $\mathrm{S}\mathrm{A}\mathrm{C}>30\%$ in the inset ($\lambda \propto {\mathrm{B}\mathrm{o}}_g^{0.24}$) and for the whole set of toners in the main graph ($\lambda \propto {\mathrm{B}\mathrm{o}}_g^{0.25}$).Reuse & Permissions