Jones–Dole equation¶
An empirical dilute-solution relation separating a square-root and a linear concentration contribution to relative viscosity.
Core Idea¶
The Jones–Dole equation describes a solution's viscosity relative to a matched solvent as solute concentration changes: \(\eta/\eta_0=1+A\sqrt c+Bc\). Here \(c\) is concentration; \(A\) and \(B\) belong to the system and conditions.[ref-4376ac0150e3][ref-722b456edfc2] The equation is empirical and applies only where its simple form fits; it does not promise an exact prediction for every measured solution. It is a kind of Mathematical Relation: typed concentration and viscosity quantities satisfy an equation with parameters and scope. Its particular viscosity ratio and two concentration terms distinguish it from other relations.
Scope of Application¶
In solution-viscosity work, specify solvent reference, concentration convention, temperature, and pressure. Habitats include:
- Aqueous alkali chlorides: Reported \(A\) and \(B\) values differ by salt; one study found systematic limiting-law departures except, apparently, for LiCl.[^ref-f11516dcd4a2]
- Alcohol–water chloride solutions: Several salts followed the simple form up to 30% propan-1-ol; LiCl needed an added \(Dc^2\) term.[^ref-4376ac0150e3]
- Higher-alcohol mixtures: The same study required an ion-association correction, marking a boundary of the simple equation.[^ref-4376ac0150e3]
- Pressure and temperature studies: A KCl study used an extended equation and tracked changes in \(B\) across conditions.[^ref-722b456edfc2]
- Saccharide coefficient work: A study uses the name for \(B\) values; its accessible abstract does not establish the full two-term fit.[^ref-f08aa72704c7]
Clarity¶
The ratio \(\eta/\eta_0\) identifies the matched solvent baseline.[^ref-722b456edfc2] The \(A\sqrt c\) and \(Bc\) terms separate lower-power and linear contributions.[^ref-722b456edfc2] A reported \(B\) alone is not the whole relation. In electrolyte work \(A\) is associated with interionic effects.[^ref-722b456edfc2] But \(B\) does not prove one microscopic account of water structure.[^ref-9a1edb969f05] A generic viscosity regression lacks this equation's named variables, terms, and tested range.
Manages Complexity¶
Within a supported range, two coefficients summarize a series of concentration-dependent viscosity measurements.[^ref-4376ac0150e3] The compression helps compare systems when the reference, units, and conditions accompany the coefficients. It can hide a real departure: an added \(Dc^2\) term produces an extended relation rather than another reading of \(B\). Both mixed-solvent LiCl and pressure-dependent KCl analyses illustrate this boundary.[ref-4376ac0150e3][ref-722b456edfc2]
Abstract Reasoning¶
First specify the solute, matched solvent, conditions, and concentration series. Then test whether the two-term form describes the measurements. The mixed-solvent authors reported a LiCl quadratic term and a higher-alcohol association correction.[^ref-4376ac0150e3] A KCl analysis also used an extended form.[^ref-722b456edfc2] Compare coefficients only within the supported scope; if residuals require a correction, record the simple form's limit. In that extended KCl analysis, \((\eta_r-1-A\sqrt c)/c=B+Dc\): the zero-concentration intercept identifies \(B\), while a nonzero slope reveals the added quadratic contribution.[^ref-722b456edfc2]
Knowledge Transfer¶
The relation carries literally between solution systems when new solutes, solvents, and coefficients fill the same roles and the fit is tested again. Aqueous and alcohol–water chloride studies are distinct instances.[ref-f11516dcd4a2][ref-4376ac0150e3] Coefficients must be refitted under the new solution conditions; copying them untested erases the empirical boundary. A similar curve for unrelated quantities is only an analogy. The broader lesson of declaring inputs, parameters, and scope belongs to Mathematical Relation; the Jones–Dole identity stays within solution viscosity.
Relationships to Other Abstractions¶
Current abstraction Jones–Dole equation Domain-specific
Parents (1) — more general patterns this builds on
-
Jones–Dole equation is a kind of Mathematical Relation Domain-specific
The Jones–Dole equation is a bounded empirical mathematical relation with typed concentration and relative-viscosity quantities, a stated satisfaction equation, and system-specific coefficients.
Hierarchy path (1) — routes to 1 parentless root
- Jones–Dole equation → Mathematical Relation
Neighborhood in Abstraction Space¶
Jones–Dole equation sits in a sparse region of the domain-specific corpus (94th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Molecular Structure & Chemical Bonding (35 abstractions)
Nearest neighbors
- Davies equation — 0.81
- Solvent model — 0.79
- Colligative Properties — 0.79
- Freezing-point depression — 0.77
- Solubility — 0.77
Computed from structural-signature embeddings · 2026-10-17
References¶
[^ref-4376ac0150e3]: Joseph Crudden, Gerard M. Delaney, David Feakins, Philip J. O'Reilly, W. Earle Waghorne, and Kenneth G. Lawrence, “The viscosity and structure of solutions. Part 2.—Measurement of the B coefficient of viscosity for alkali-metal chlorides in propan-1-ol–water mixtures at 25 and 35 °C,” Journal of the Chemical Society, Faraday Transactions 1 82 (1986): 2195–2206, DOI: 10.1039/F19868202195. Publisher abstract consulted for formula, systems, and reported fit limits; full article not inspected.
[^ref-f11516dcd4a2]: Robert Dordick, Lawrence Korson, and W. Drost-Hansen, “High-precision viscosity measurements: I. Aqueous solutions of alkali chlorides,” Journal of Colloid and Interface Science 72 (1979): 206–214, DOI: 10.1016/0021-9797(79)90102-4. Publisher-indexed abstract consulted for tested salts, coefficients, and qualified deviations; direct page access was blocked and full article was not inspected.
[^ref-722b456edfc2]: Takehiro Nakai, Seiji Sawamura, Yoshihiro Taniguchi, and Takashi Kuboyama, “Effects of Pressure and Temperature on the Viscosity B Coefficient for Potassium Chloride in Water,” Materials Science Research International 3 (1997): 204–209, publisher PDF, PDF pp. 1–4, especially Eq. 1, §3.3 Eqs. 7–8 and Fig. 3. Full six-page original consulted; the text extraction damages Greek glyphs, so equation meaning was checked against the page context.
[^ref-9a1edb969f05]: David Feakins, W. Earle Waghorne, and Kenneth G. Lawrence, “The viscosity and structure of solutions. Part 1.—A new theory of the Jones–Dole B-coefficient and the related activation parameters: application to aqueous solutions,” Journal of the Chemical Society, Faraday Transactions 1 82 (1986): 563–568, DOI: 10.1039/F19868200563. Publisher abstract consulted for the alternative account of \(B\) trends; full article not inspected.
[^ref-f08aa72704c7]: Kuldeep Kumar, Baljeet Singh Patial, and Suvarcha Chauhan, “Interactions of Saccharides in Aqueous Glycine and Leucine Solutions at Different Temperatures of (293.15 to 313.15) K: A Viscometric Study,” Journal of Chemical & Engineering Data 60 (2015): 47–56, DOI: 10.1021/je500647a. Publisher-indexed abstract consulted for saccharide \(B\)-coefficient use; direct page access was blocked and full \(A\)-term treatment and fit window were not inspected.