In simulating nanofluid viscosities, say using modified Krieger Dougherty model, literature says the maximum particle packing fraction in dispersion is dependent on shear and provides a rough estimate of 0.605 for high shear and 0.5 for low shear.
But how do we differentiate high shear and low shear?
Whilst you could generalise to orders of magnitude of shear, the behaviour of a material in relation to shear rate is definitely sample specific.
Defining what is 'high' or 'low' shear could be based on observations of different types of flow, especially for fluids that shear thicken or shear thin, whereby the shear rate at which a change in viscosity is observed could be used to differentiate between low and high shear.
A more appropriate parameter might be the Weissenberg number, which takes into account the elasticity of your fluid, allowing more convenient comparison of different sample types at different shear rates
Binu, as you say, it will depend on the sample, but I would suggest, as a rough guide, that 0.1s-1 is "low", 10s-1 is "medium" and 1000s-1 is "high". To discuss.
Alexander, could you give an example of how using the Weissenberg number is more convenient than the shear reate? Its measurement requires more effort and extra calculation, so it is not obvious to me that it is more convenient.
Dear Colleague,
Both non-linear and linear behaviors of complex fluids depend on the scale of observation. This is no more the case at large scales where the asymptotic behavior is reached. But as soon as the sub-millimeter scale, different authors using different techniques highlight specifies related to the dimensions probed.
Yours,
LN
B.V. Derjaguin, U.B. Bazaron, K.T. Zandanova and O.R. Budaev, Polymer 30, 97 (1989)
D. Collin and P. Martinoty, Physica A 320, 235 (2003)
Noirez L, Mendil-Jakani H and Baroni P 2009 Polym. Int. 58 962
Kahl P., Baroni P., Noirez L., PloS One 2016, e0147914 doi: 10.1371/journal.pone0147914.
@Alan,
I realise that determining the Weissenberg number requires additional measurement, so isn't practically more convenient, however I meant that referring to Weissenberg number might make comparisons between different samples more straight forward and "convenient", given that fluids with different visco-elastic properties may display very different behaviour at a certain shear rate, but similar behaviour at the same Weissenberg number.
Nanofluids are two-phase systems that have fine solids (nanoparticles) dispersed in traditional working liquids (water, oil or ethylene glycol). Mere addition of solids without applying shear results in systems having agglomerates of the fine solids. When agglomerates are present the maximum packing fraction is lower. Application of shear aids in breaking the agglomerates and hence the greater the shear the more is the breakdown of agglomerates and better is the dispersion resulting in a higher value of maximum packing fraction. There is no precise value of shear that can demark when the agglomerates can be broken down and when the dispersion can be improved, as it is greatly dependent on the strength of solid-solid and solid-liquid physico-chemical interactions which is system specific. The maximum packing fraction cannot be given a precise value for high shear or low shear as these are only very rough estimates based on the limited system sets that are analyzed. It needs to be realized that among other things the maximum packing fraction is dependent on the shape of the solid particles and on the particle size & size distribution as well. The method and conditions used during the preparation of the nanofluids will control the value of the maximum packing fraction that can be achieved. There is an entire chapter (Chapter 5) dedicated to the Preparation of filled polymer systems in the following book: Aroon V. Shenoy, Rheology of Filled Polymer Systems, Kluwer Academic Publishers, Netherlands (1999). The ideas discussed may be useful to get a clearer picture. In section 5.4, there is a detailed discussion on the compounding /mixing variables that affect the quality of the mix. Some variables are more sensitive to changes than others. It is important to study and identify these variables and understand their sensitivity so that the compounding /mixing can be carried out under optimum conditions. Variables affecting compounding operations could be machine variables (mixer type, rotor geometry) or operating variables (mixing time, rotor speed, ram pressure, chamber loading, mixing temperature, order of ingredient addition).
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