Rheometry (from Greek ῥέος (rheos) 'stream') generically refers to the experimental techniques used to determine the rheological properties of materials,[1] that is the qualitative and quantitative relationships between stresses and strains and their derivatives. The techniques used are experimental.[1] Rheometry investigates materials in relatively simple flows like steady shear flow, small amplitude oscillatory shear, and extensional flow.[2]

The choice of the adequate experimental technique depends on the rheological property which has to be determined. This can be the steady shear viscosity, the linear viscoelastic properties (complex viscosity respectively elastic modulus), the elongational properties, etc.

For all real materials, the measured property will be a function of the flow conditions during which it is being measured (shear rate, frequency, etc.) even if for some materials this dependence is vanishingly low under given conditions (see Newtonian fluids).

Rheometry is a specific concern for smart fluids such as electrorheological fluids and magnetorheological fluids, as it is the primary method to quantify the useful properties of these materials[citation needed].

Rheometry is considered useful in the fields of quality control, process control, and industrial process modelling, among others.[2] For some, the techniques, particularly the qualitative rheological trends, can yield the classification of materials based on the main interactions between different possible elementary components and how they qualitatively affect the rheological behavior of the materials.[3] Novel applications of these concepts include measuring cell mechanics in thin layers, especially in drug screening contexts.[4]

## Of non-Newtonian fluids

The viscosity of a non-Newtonian fluid is defined by a power law:[5]

${\displaystyle \eta =\eta _{0}{\dot {\gamma ))^{n-1))$

where η is the viscosity after shear is applied, η0 is the initial viscosity, γ is the shear rate, and if

• ${\displaystyle n<1}$, the fluid is shear thinning,
• ${\displaystyle n>1}$, the fluid is shear thickening,
• ${\displaystyle n=1}$, the fluid is Newtonian.

In rheometry, shear forces are applied to non-Newtonian fluids in order to investigate their properties.

### Shear thinning fluids

Due to the shear thinning properties of blood, computational fluid dynamics (CFD) is used to assess the risk of aneurysms. Using High-Resolution solution strategies, the results when using non-Newtonian rheology were found to be negligible.[6]

### Shear thickening fluids

A method for testing the behavior of shear thickening fluids is stochastic rotation dynamics-molecular dynamics (SRD-MD).[7] The colloidal particles of a shear thickening fluid are simulated, and shear is applied. These particles create hydroclusters which exert a drag force resisting flow.[7]

## References

1. ^ a b Malkin, Aleksandr I︠A︡kovlevich; Malkin, Alexander; Isayev, Avraam (2006). Rheology: Concepts, Methods and Applications. Toronto: ChemTec Publishing. p. 241. ISBN 9781895198331.
2. ^ a b Gallegos, Crispulo (2010). Rheology - Volume I. London: EOLSS Publications/UNESCO. pp. 7–8. ISBN 9781848267695.
3. ^ Coussot, Philippe (2005). Rheometry of Pastes, Suspensions, and Granular Materials: Applications in Industry and Environment. Hoboken, NJ: Wiley-Interscience. pp. 2. ISBN 9780471653691.
4. ^ Bashir, Khawaja Muhammad Imran; Lee, Suhyang; Jung, Dong Hee; Basu, Santanu Kumar; Cho, Man-Gi; Wierschem, Andreas (2022-06-23). "Narrow-Gap Rheometry: A Novel Method for Measuring Cell Mechanics". Cells. 11 (13): 2010. doi:10.3390/cells11132010. ISSN 2073-4409. PMC 9265971. PMID 35805094.
5. ^ Antonsik, A.; Gluszek, M.; Zurowski, R.; Szafran, M. (June 2017). "Influence of carrier fluid on the electrokinetic and rheological properties of shear thickening fluids". Ceramics International. 43 (15): 12293–12301. doi:10.1016/j.ceramint.2017.06.092.
6. ^ Khan, M.; Steinman, D.; Valen-Sendstad, K. (September 2016). "Non-Newtonian versus numerical rheology: Practical impact of shear-thinning on the prediction of stable and unstable flows in intracranial aneurysms". International Journal for Numerical Methods in Biomedical Engineering. 33 (7): e2836. doi:10.1002/cnm.2836. PMID 27696717. S2CID 4554875.
7. ^ a b Chen, Kaihui; Wang, Yu; Xuan, Shouhu; Gong, Xinglong (March 2017). "A hybrid molecular dynamics study on the non-Newtonian rheological behaviors of shear thickening fluid". Journal of Colloid and Interface Science. 497: 378–384. Bibcode:2017JCIS..497..378C. doi:10.1016/j.jcis.2017.03.038. PMID 28314143.