The Einstein formula in problem 6 only applies when the volume fraction of particles is very small. Often, we deal with very concentrated suspensions such as in a fermentation of yeast cells. An alternative expression for the viscosity of such a suspension is:

\[\mu_{r}=\frac{1-0.5 \kappa \phi}{(1-\kappa \phi)^{2}(1-\phi)} \quad \kappa \sim 1+0.6 \phi[41]\]

a. Plot both the original Einstein relation and the expression given here and discuss the difference as \(\phi\) gets large, say beyond \(10 \%\).

b. The data below shows the reduced viscosity for 5 micron particles in water. How does the viscosity stack up to the model? If you fit for \(\kappa\), what value do you get?

Problem 6

Using the results of Free Volume theory for calculating the viscosity of liquids, determine \(\Delta G^{\dagger}\) for the following liquids \(\left(20^{\circ} \mathrm{C})\) : water, ethylene glycol, refrigerant \(134 \mathrm{a}\), and engine oil. Is there any relationship between their molecular structure and interactions and \(\Delta G^{\dagger}\) ?

Transcribed Image Text:

Volume Fraction Particles 0 0.05 0.1 Reduced Viscosity , 1 1.07 1.2 0.15 1.3 0.2 1.6 0.3 1.8 0.4 2.9 0.5 4.6