Smoluchowski equation

Input(s)

$\boldsymbol{\mu}_{\boldsymbol{o}}$: Viscosity of the Suspension (cP)

$\emptyset$: Volume Fraction of Spheres (dimensionless)

D: Dielectric Constant $\left(\mathrm{A}^{2} \mathrm{~s}^{2} / \mathrm{cm}^{3}\right)$

R: Particle Radius $(\mathrm{cm})$

$\zeta$: Electro kinetic Potential of the Particles $(\mathrm{J})$

$\boldsymbol{k}_{\boldsymbol{e}}$: Specific Electrical Conductivity of the Suspension $(\mathrm{ohm} / \mathrm{cm})$

Output(s)

$\boldsymbol{\mu}_{\text {eff }}$: Effective Viscosity (cP)

Formula(s)

$$ \mu_{\mathrm{eff}}=\mu_{\mathrm{o}} *\left(1+2.5 * \varnothing\left(1+\frac{\left(\frac{\mathrm{D} * \zeta}{2 * \pi * \mathrm{R}}\right)^{2}}{\mu_{\mathrm{o}} * \mathrm{k}_{\mathrm{e}}}\right)\right) $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 1, Page: 34.