# Sorting out viscosity methods

It is possible to calculate the viscosity using the SLLOD equations of motion together with the Nosé-Hoover thermostat. Then the viscosity is obtained as the ratio of the shear stress and the velocity gradient. Note, however, that you get the viscosity in the non-Newtronian regime. You have to go down to very low shear rates to get the viscosity in the Newtonian regime that should be the same one as the one that you obtain by using the Green-Kubo relations.

When you apply the Lees-Edwards boundary conditions you simulate homogeneous system and there are no wall effects. If you want to know more about the SLLOD equations you can read the book Statistical Mechanics of Nonequilibrium Liquids, Academic Press, London, 1990, by D. J. Evans and G. P. Morriss.

However, if you want to simulate shear banding you must realise that this is a nonequilibrium system. If you use the SLLOD equations the results will depend on the implementation of the thermostat.It is not possible to use Green-Kubo relations because they only work close to equilibrium. There are more appropriate thermostats but they cannot be used in Lammps. I can send you the references if you want. If you have other questions on shear flow simulations, feel free to ask.

Best Regards,

Sten Sarman

Den Thu, 8 Oct 2015 16:11:27 -0400, Salomon Turgman Cohen <sturgman@…29…> skrev:

Method 1: Involves SLLOD with Langevin thermostat. This is currently not possible in Lammps since
nvt/sllod uses Nose-Hoover. Correct?

You can do the following. Use fix deform and fix nve.

Also use fix langevin and assign a temperature compute

to it (like compute temp/deform), that subtracts a bias

before Langevin terms are applied to the thermal velocities.

This is close to fix deform with fix nvt/sllod. I think

all it is missing is the SLLOD correction in the transverse

direction to the shear. My recollection is that is typically

small. You might be able to derive a LangevinSLLOD class

from Fix Langevin that added that term. I think it is just

a few lines of code if I remember.

Method 2: Maybe this is possible using fix_deform + pair_style dpd/tstat. Then the shear will only be applied >by fix_deform and not by the equations of motion. It sounds like this would accomplish what they describe in >the paper but I should be careful to subtract the streaming velocity from the thermostating. Am I >understanding the LAMMPS commands correctly?

I think you could also use fix deform with fix nve, and add

pair dpd/tstat as a thermostat. Dpd/tstat thermostats

pairs of particles based on their relative velocity, so I think

it inherently accounts for streaming. I.e. no need to subtract

it. Again, DPD/tstat knows nothing about SLLOD, so thats

a separate issue.

Basically both these approaches will deform the liquid and

should apply proper thermostatting, though I’ve never tried

dpd/tstat in that setting.

Steve

Thank you Steve. I will run a few simulations to see if I get similar results to their paper. I suspect that method 2 might be exactly the same but method 1 might show slight deviations. Thanks again for your response.

-s-