Calculate the following for suspensions of spherical particles

$($a$)$ What is the intrinsic viscosity $$ of suspensions of spherical particles? Provide your

assumptions$/$reasoning $($be concise$).$

$($b$)$ Estimate the zero$-$shear viscosity of a suspension of hard spheres $250nm$ in

diameter at a volume fraction of $=0\mathrm{.}43$ in a solvent of viscosity $1cP.$

$($c$)$ What will be the zero$-$shear viscosity of the suspension under the same condition

except that particles are charged and the effective diameter of charged particle is $280$

nm$?$

$($d$)$ Explain what caused the differences in the zero$-$shear viscosity of the hard and

charged particle suspensions $($be concise$)?$

$($e$)$ Critical shear rate for shear thickening ${}_c^{}$ for spherical particle suspensions is shown

below. Do you expect the same value of ${}_c^{}$ for hard and charged particle suspensions at

the same volume fraction? If not, what would be the difference and explain why $($be

concise$).$