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.