Table 6.

Some models commonly used to estimate the viscosity of micro-dispersions as a function of the solid particles volume fraction. The intrinsic viscosity $\left[\eta \right]$ has a typical value of 2.5 for spherical particles, ${\varphi }_m$ is the maximum particle packing fraction (which has been chosen here as an adjustment parameter) and usually $5.2\le \alpha \le 7.6$.

Models	Einstein	Brinkman	Batchelor	Krieger–Dougherty
$\eta /{\eta }_{\mathbf{bf}}=$	$1+2.5\varphi$	$1/{(1-\varphi )}^{2.5}$	$1+2.5\varphi +\alpha {\varphi }^2$	${\left(1-\frac{\varphi }{{\varphi }_m}\right)}^{-\left[\eta \right]{\varphi }_m}$