# Viscosity at CMC

What happens to viscosity at critical micelle concentration? Does it increase or decrease abruptly, and if so, what's the reason behind it?

I'm aware of changes in other properties such as conductivity, concentration etc, but not viscosity.

• Do you mean as the concentration of the monomer increases (at constant T)? Mar 23 at 12:28
• No, I mean at the critical micelle concentration, when the individual ions of the soap molecules cluster together Mar 23 at 12:37
• Yes, sorry, never mind my comment. It turns out the viscosity often increases. Mar 23 at 13:42
• whats the reason behind it? i tried making a comparison with gases, where the viscosity increases with the radius of the gas, and also with density... here, the "radius" is increasing, due to micelle formation and the "density" (which i think is analogous here to concentration) is decreasing... how do we decide which factor dominates? Mar 23 at 15:06

$$\frac{\eta}{\eta_0} = 1 +2.5\phi \tag{1}$$
where $$\eta_0$$ is the viscosity of the pure solvent, $$\phi$$ is the volume fraction of solute (here: aggregating detergent) Note we are ignoring higher order terms that describe the dependence on micelle-micelle interactions (e.g. on the second virial coefficient).