Hi,

as you know, k is the consistency factor. For n = 1, the consistency factor reduces to the Newtonian viscosity μ; in general, the units of K depend on the value of n.

You can take a look at these links for more detailed inormation:

https://www.sciencedirect.com/topics/engineering/power-law-model

https://www.sciencedirect.com/topics/engineering/consistency-factor

This is not so easy to answer. Especially for n \ne 1. As it stands. sigma, k and \dot\gamma all have units which makes it impossible to qualify them as large or small because we have nothing to compare them to. sigma has the units of energy density so using k_BT/d^3 with a characteristic size of your particles d (diameter, radius of gyration, etc.) seems a good start to make the stress dimensionless. In this way you have the stress roughly as k_BT per particle (up to volume fraction). Next the shear rate should be compared to some meaningful time scale. Maybe the Stokes friction coefficient of the particles, their collision frequency, or something. One sigma and \dot\gamma are dimensionless, you will have defined a dimensionless k. For n = 1 the Newtonian viscosity will then be of the order 1 for a dilute gas and one expects it to rise with concentration. For n < 1 I am not sure what to expect but I would still associate small values of the dimensionless k with a dilute gas/suspension where collective effects are negligible and bigger values of k with a growing importance of correlations between the particles.

Dear Dr. Kranz,

Thank you so much for your help and attention. I greatly appreciate it.

Could you please introduce an article to me to briefly understand what is happening in the molecular scale during shear rate implementation to a polymeric solution (for example when it is being stirred or cast as a thin film) which follows power law model as a non-Newton fluid?

Kind Regards

Foroogh