mathematics

Jones–Dole equation

Jones–Dole equation is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Jones–Dole equation rather than just read about it. In short: 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). The Jones–Dole equation is written as η η 0 = 1 + A C 1 2 + B C , {\displaystyle {\frac {\eta }{\eta _{0}}}=1+AC^{\frac {1}{2}}+BC,} where η is the viscosity of the solution (at a fi…

Key takeaways

Jones–Dole equation belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Jones–Dole equation to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Jones–Dole equation from memory before moving on to harder problems.

Reference excerpt

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). The Jones–Dole equation is written as

η η 0 = 1 + A C 1 2 + B C , {\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 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. 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", as the viscosity of mayonnaise (essentially a solution of oil in water) is extremely high because of the jamming of micrometer-scale droplets.

References

Worked examples

Example 1 — a first encounter with Jones–Dole equation

Start with the simplest possible case. Write down what Jones–Dole equation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Jones–Dole equation before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Jones–Dole equation ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Jones–Dole equation

In research: Jones–Dole equation appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Jones–Dole equation in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Jones–Dole equation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Equations, Physical chemistry stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Jones–Dole equation outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Jones–Dole equation in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Jones–Dole equation means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Jones–Dole equation out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Jones–Dole equation in simple terms?

Why does Jones–Dole equation matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Jones–Dole equation?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Jones–Dole equation.