Sousa # What is the appropriate shear rate for viscosity calculation?

Hello Dear MS users,

I am trying to calculate viscosity of a polymer solution. Accordingly, after model construction and doing main simulation I applied Forcite->Shear task. But i did not know what the best way to choice SHEAR RATE is!!! In order to solve this problem i calculate Rotational time correlation function from Forcite analysis to find relaxation time. In order to that I calculate Rotational time correlation function for polymer chain in the solution due to its more complexity compared to solvent molecule. Then i tried to fit stretched exponential Kohlrausch−Williams−Watts (KWW) [y=A exp(-(t/t0)^B)] on the second Legendre polynomial (M2).

I tried a lot for fitting on all data but i could not. But according to reference

**"THE JOURNAL OF CHEMICAL PHYSICS 128, 184905 2008"**

*I found that only part of the data could fit on stretched exponential curve. Accordingly, i calculated B=0.89 and finally t*_{0}=7.6*10^{5 }ps. I calculated shear rate of a mixture according to Question Title “**How to calculate the viscosity**” (shear rate=1/t_{0}). The calculated shear rate is 1.3*10^{-5}. This shear rate is too short. I really do not know the correctness of my applied method. Generally how the appropriate shear rate can be obtained? I will be thankful if guide me.

Best Regards

Sousa

I am trying to calculate viscosity of a polymer solution. Accordingly, after model construction and doing main simulation I applied Forcite->Shear task. But i did not know what the best way to choice SHEAR RATE is!!! In order to solve this problem i calculate Rotational time correlation function from Forcite analysis to find relaxation time. In order to that I calculate Rotational time correlation function for polymer chain in the solution due to its more complexity compared to solvent molecule. Then i tried to fit stretched exponential Kohlrausch−Williams−Watts (KWW) [y=A exp(-(t/t0)^B)] on the second Legendre polynomial (M2).

I tried a lot for fitting on all data but i could not. But according to reference

Best Regards

Sousa

reinierHi Sousa,

My understanding is that at increased shear rate molecules will orient or align with the shear flow. This ordered state has a lower viscosity, hence has the effect of shear thinning. A deeper understanding may be found in mode-coupling theory.

In [1] the shear rate at which shear thinning starts was correlated with the rotational relaxation time. This paper uses similar simulation times, so it seems reasonable from that point of view.

Good luck,

Reinier

[1] S. T. Cui, S. A. Gupta, and P. T. Cummings, H. D. Cochran,

Molecular dynamics simulations of the rheology of normal decane, hexadecane, and tetracosane, J. Chem. Phys.105, 1214 (1996).## All Answers

reinierHi Sousa,

Have a look at the topic questions about the viscosity of n-alkanes. Typically the viscosity is calculated over a range of shear rates, and then extrapolated to zero shear rate, for example by fitting to a Carreau model.

The inverse rotational correlation time is roughly the point where shear thinning sets in, but you need slower rates than that to sample the Newtonian regime.

Best,

Reinier

SousaHi Reinier,

Thank you for your reply. About my system I should mentioned that I try to model a

polymer dilutesolution, which its behavior is close to Newtonian fluid. The I expect that its density is independent of shear rate, but it was not happened. Another strange point that I faced with was calculation of puretoluene. We know that toluene is aNewtonian fluid...but after performing the mentioned method for calculation of viscosity, viscosity was dependent to shear rate. The obtained results at different shear rate was attached to the post. I am completely confusing!!! Is the calculation method wrong? or if it is right how I can explain this shear rate dependency? would you please guide my what is wrong in my calculation?reinierHi Sousa,

I think that most liquids will show shear thinning under the extreme shear rates used in simulations, even if they are Newtonian under experimental conditions. So your result for toluene seems plausible, though it is curious to see the inflection at around 0.4/ps. The shape is similar to this paper by Lee, though your viscosities are almost 10 times larger (assuming unit cP). Are the simulations long enough?

Regards,

Reinier

Sousa

Dear Reinier,

I really thank you for your reply and guidance. According to your comment, shear thinning is observed for most of Newtonian fluid in molecular simulation. Is can be related to the inability of the fluids to relax and adopt with shearing, at high shear rate? Generally what is its reason?

About the shearing time, I tried with 100, 200 and 500 ps separately and obtained the same results. Do you think that my results may have problem? Or were these devoted time enough?

Best Regards

Sousa

reinierHi Sousa,

My understanding is that at increased shear rate molecules will orient or align with the shear flow. This ordered state has a lower viscosity, hence has the effect of shear thinning. A deeper understanding may be found in mode-coupling theory.

In [1] the shear rate at which shear thinning starts was correlated with the rotational relaxation time. This paper uses similar simulation times, so it seems reasonable from that point of view.

Good luck,

Reinier

[1] S. T. Cui, S. A. Gupta, and P. T. Cummings, H. D. Cochran,

Molecular dynamics simulations of the rheology of normal decane, hexadecane, and tetracosane, J. Chem. Phys.105, 1214 (1996).SousaHi Reinier,

I really thank you for your helpful guide.

Best Regards

Sousa