Jones–Dole equation

The Jones–Dole equation, or Jones–Dole expression, is an empirical expression that describes the relationship between the viscosity of a solution and the concentration of solute within the solution (at a fixed temperature and pressure).[1] The Jones–Dole equation is written as[2] $${\displaystyle {\frac {\eta }{\eta _{0}}}=1+AC^{\frac {1}{2}}+BC,}$$ where

η is the viscosity of the solution (at a fixed temperature and pressure),

η₀ is the viscosity of the solvent at the same temperature and pressure,

A is a coefficient that describes the impact of charge–charge interactions on the viscosity of a solution (it is usually positive) and can be calculated from Debye–Hückel theory,

B is a coefficient that characterises the solute–solvent interactions at a defined temperature and pressure,

C is the solute concentration.

The Jones–Dole B coefficient[3] is often used to classify ions as either structure-makers (kosmotropes) or structure-breakers (chaotropes) according to their supposed strengthening or weakening of the hydrogen-bond network of water.[4][5] The Jones–Dole expression works well up to about 1 M, but at higher concentrations breaks down, as the viscosity of all solutions increase rapidly at high concentrations.

The large increase in viscosity as a function of solute concentration seen in all solutions above about 1 M is the effect of a jamming transition at a high concentration. As a result, the viscosity increases exponentially as a function of concentration and then diverges at a critical concentration. This has been referred to as the "Mayonnaise effect",[6] as the viscosity of mayonnaise (essentially a solution of oil in water) is extremely high because of the jamming of micrometer-scale droplets.

References

1. http://www.le.ac.uk/chemistry/thermodynamics/pdfs/3000/Topic2930.pdf ^[bare URL PDF]
2. Jones, Grinnell; Dole, Malcolm (1929-10-01). "The Viscosity of Aqueous Solutions of Strong Electrolytes with Special Reference to Barium Chloride". Journal of the American Chemical Society. 51 (10): 2950–2964. doi:10.1021/ja01385a012. ISSN 0002-7863.
3. Jenkins, H. Donald B.; Marcus, Yizhak (1995-12-01). "Viscosity B-Coefficients of Ions in Solution". Chemical Reviews. 95 (8): 2695–2724. doi:10.1021/cr00040a004. ISSN 0009-2665.
4. Marcus, Yizhak (2009-03-11). "Effect of Ions on the Structure of Water: Structure Making and Breaking". Chemical Reviews. 109 (3): 1346–1370. doi:10.1021/cr8003828. ISSN 0009-2665. PMID 19236019.
5. Ball, Philip; Hallsworth, John E. (2015-03-23). "Water structure and chaotropicity: their uses, abuses and biological implications". Physical Chemistry Chemical Physics. 17 (13): 8297–8305. Bibcode:2015PCCP...17.8297B. doi:10.1039/c4cp04564e. ISSN 1463-9084. PMID 25628033.
6. Wynne, Klaas (2017-12-08). "The Mayonnaise Effect" (PDF). The Journal of Physical Chemistry Letters. 8 (24): 6189–6192. doi:10.1021/acs.jpclett.7b03207. ISSN 1948-7185. PMID 29220573.