# Viscosity of Muddy Water

How do I calculate the viscosity of muddy water at 25 deg C and knowing the weight of undissolved solids either SiO2 or Al2SiO5 in H2O, grain size < 150 microns? Do I have enough information to get an approximation with a precision of +/- 10%?

• Please use MathJax to write the mathematical part. Also express your opinions regarding your question. This is not a homework help service. Commented Oct 27, 2015 at 6:03

The quantity you are asking about is the viscosity of a dispersion, and Googling will find you many articles describing how to calculate this. For dilute suspensions of spheres the equation for the viscosity was derived by Albert Einstein (yes, the Albert Einstein!):

$$\mu \approx \mu_0 (1 + 2.5\phi)$$

where $\mu_0$ is the viscosity of water and $\phi$ is the volume fraction of the suspended spheres. This applies to very dilute suspensions, but there is an extension due to Guth and Simha that applies to more concentrated suspensions:

$$\mu \approx \mu_0 (1 + 2.5\phi - 14.1\phi^2)$$

You can get an idea of well these equations apply to your system by calculating the viscosity using both equations. If they give the same result to within 10% they're likely to be a good approximation.

From (bitter!) experience the trouble with this approach is calculating the effective volume fraction of the suspended matter. The fraction you get by dividing the mass of the suspended particles by the density will be an underestimate because the particles aren't spheres and they're surrounded by an electric double layer that increases their effective volume. If you plan to use this approach in your research I strongly suggest to do some calibrations to check it i.e. measure the viscosities for know concentrations of suspended particles.

• Thank you for your great response to my question, especially the "bitter experience" part. Most useful! Commented Oct 27, 2015 at 21:11