THERMODYNAMIC SCALING OF VISCOSITY APPLIED TO MIXTURES: MODEL AND REAL FLUIDS

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THERMODYNAMIC SCALING OF VISCOSITY APPLIED TO MIXTURES: MODEL AND REAL

FLUIDS

Guillaume Galliero, Stephanie Delage Santacreu, Jean-Patrick Bazile, J.

Fernandez, Christian Boned

To cite this version:

Guillaume Galliero, Stephanie Delage Santacreu, Jean-Patrick Bazile, J. Fernandez, Chris- tian Boned. THERMODYNAMIC SCALING OF VISCOSITY APPLIED TO MIXTURES:

MODEL AND REAL FLUIDS. ECTP 2014 - European Conference on Thermophysical Properties (http://ectp2014.fc.up.pt/), Aug 2014, porto, Portugal. pp.00, 2014. �hal-00996307�

Mie 36-6 mole fraction

0.0 0.2 0.4 0.6 0.8 1.0



4 6 8 10 12

14 MD results

One fluid approx.

Mixing rule

n

10 15 20 25 30 35



4 6 8 10 12

14 MD results

Linear Fit Bohling et al.

 *

 T*

0.0 0.2 0.4 0.6 0.8 1.0 1.2



0 5 10 15

20 Mie 8-6

Mie 12-6 Mie 18-6 Mie 24-6 Mie 36-6 Fit

^/T^*

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

r res

0 5 10 15

20 x_8-6=0.875

x_8-6=0.5 x_8-6=0.125

THERMODYNAMIC SCALING OF VISCOSITY APPLIED TO MIXTURES: MIE FLUIDS AND REAL FLUIDS

THEORY

In this work, we have tested the ability of the so-called “thermodynamic scaling” to deal with the shear viscosity of mixtures. For this purpose we have performed extensive Non-Equilibrium Molecular Dynamics simulations on the Mie n-6 fluids to define a general scheme to tackle the problem. Interestingly, the viscosity scaling has been found to be well respected in such model fluids (pure and mixtures) as well as in real mixtures using a simple mixing rule.

Guillaume GALLIÉRO

, Stéphanie DELAGE-SANTACREU

, Jean-Patrick BAZILE

, Hai HOANG

, Josefa FERNANDEZ

and Christian BONED

1

Laboratoire des Fluides Complexes et leurs Réservoirs (UMR-5150 CNRS/UPPA/TOTAL), Pau University, FRANCE

2

Laboratoire de Mathématiques et leurs Applications (UMR-5142 CNRS/UPPA), Pau University, FRANCE

3

Laboratorio de Propiedades Termofisicas, Santiago de Compostela University, SPAIN

THE MIE FLUID MODEL THERMODYNAMIC SCALING

We gratefully acknowledge the PCSTD (UPPA) and the MCIA (Bordeaux) for the provided computing facilities

RESULTS

MIE PURE FLUIDS MODEL AND REAL MIXTURES

Spheres interacting through :

Three parameters : n, e, s

Reduced residual viscosity scales as:

f is an unknown function and  is a parameter

The semi-empirical relation allows to correlate well the NEMD results. For a given dimensionless state,  increases with n

As expected,  increases with n (linearly)

Work in progress :

1. Application of the mixing rules to other real mixtures, with a special focus on  asymmetric ones

2. Extend the scheme to be used in a predictive manner, i.e. define a strategy to estimate the b_i parameters

MOLECULAR DYNAMICS VISCOSITY MODELING

8 ≤ n ≤ 36, Lennard-Jones: n=12

where

𝜼

= 𝒃

[ ^𝒆

^{+ 𝒃}

^𝑿

^{− 𝟏} ]

Semi-empirical relation :

where

and b_i : fitting parameters

Momentum Exchange

Non-Equilibrium Molecular Dynamics scheme :

Shear viscosity is directly accessible

1500 particles, 1.5 10⁷ time-steps  

Dimensionless units :

It allows to determine unambiguously 

The zero-density viscosity, ₀, is computed by Chapman-Enskog relation

Exchange frequency : 500

Gas, liquid and supercritical states are covered

In soft sphere fluids = n/3 but in Mie fluids :

 n/2.78

_r^/T_r

0 500 1000 1500 2000 2500 3000 3500

r res

0 5 10 15 20

25 x_C1=0.31

x_C1=0.49 x_C1=0.6

The application of the thermodynamic scaling is adequate to deal with Mie fluids mixtures (deviations < 10 %)

The most efficient mixing rule is : Mie n-6 fluids viscosity scaling

Scaling param. vs repulsion expo.

Mie mixtures viscosity scaling Scaling param. vs concentration Binary mixtures of Mie 8-6 and Mie 36-6 fluids

The Mie fluid allows to test very asymmetric mixtures !

Scaling of C1-nC10 mixtures

293-373 K, 20-140 MPa

Canet et al. Data

The proposed scheme seems efficient for real mixtures !

Thermodynamic scaling of viscosity in mixtures is applicable with a simple

mixing rule

Tested on a alcohol-alkane as well

Müller-Plathe Scheme

Ashurst and Hoover approach

The scheme yields deviations below 10 %

Bohling et al. relation yields a reasonable estimate

r / s

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

U Mie /e

-1 0 1 2

3 Mie 8-6

Lennard-Jones Mie 36-6