Two-Component Viscosity Blend Calculator

Free online viscosity blending calculator: kinematic viscosity of a two-component lubricant blend over the whole mixing range, using the Lederer–Roegiers equation.

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Two-Component Viscosity Blend Calculator on Tribology Universe: blend viscosity versus volume fraction with Lederer–Roegiers reference bands — The Two-Component Viscosity Blend Calculator on Tribology Universe

What the app does

Lubricants are rarely made from a single base oil. Formulators blend base oils from different API groups to reach a target viscosity grade and performance: mineral oils (Groups I–III), polyalphaolefins (PAO, Group IV) and the wide Group V family, which includes synthetic esters, polyalkylene glycols (PAG), naphthenic oils and vegetable oils such as rapeseed (canola) or sunflower oil. Typical examples are a light and a heavy mineral oil blended to an ISO VG grade, a PAO combined with a polyol ester in a compressor or gear oil, or a mineral oil with a vegetable oil in a biodegradable product.

The viscosity of such a blend is rarely the arithmetic mean of the two components, and the deviation grows as the molecular structures of the two oils differ. This app estimates the kinematic viscosity of a two-component blend over the whole mixing range with the Lederer–Roegiers equation, an empirical one-parameter model built on the mass fractions and viscosities of both components and an interaction parameter α that describes the intermolecular cohesion between the two fluids.

The model

With x₁ and x₂ the fractions of the two components, the blend viscosity is ν_blend = ν₁^x₁′ · ν₂^x₂′, where the effective fractions are x₁′ = x₁ / (x₁ + α x₂) and x₂′ = 1 − x₁′.

α = 1: the equation reduces to the classical logarithmic (Arrhenius) mixing rule — a good approximation for chemically similar oils, e.g. two mineral oils of the same group.
α > 1: the blend is less viscous than the logarithmic rule predicts — typical when a light hydrocarbon is blended with a polar ester.
α < 1: the blend is more viscous than the logarithmic rule predicts — typical when a light oil is blended with a heavy naphthenic or highly viscous component.

Inputs

Temperature at which the viscosity data apply.
For each component: kinematic viscosity and density at 15.6 °C (the densities convert volume to mass fractions).
Intermolecular cohesion parameter α (0.3 to 1.7).

Output

A curve of blend viscosity against the volume fraction of component 1, plotted against reference bands for typical base-oil pairs.

Typical values of α:

Blend type	Typical α
Similar base oils (e.g. two mineral oils)	1.0
Light naphthenic oil / polyol ester	1.3–1.7
Light paraffinic oil / polyol ester	1.0–1.4
Light hydrocarbon / heavy paraffinic oil	0.5–0.9
Light hydrocarbon / heavy naphthenic oil	0.3–0.4

Example

At 40 °C, blending a 112 mm²/s oil (878 kg/m³) with a 13 mm²/s oil (812 kg/m³): read off the fraction of the heavy component needed to reach a target ISO VG grade, and see how much that fraction changes if the pair behaves like two similar mineral oils or like a hydrocarbon/ester blend.

For an exact α, measure the viscosity of one blend and fit α to it; the equation then predicts the rest of the mixing range for the same two oils.

Limits

Both components must be fully miscible. Conventional (water-soluble) PAGs, for example, do not mix with mineral oils or PAO.
The equation describes base oils and Newtonian fluids. Polymer-thickened oils and viscosity-index improvers behave differently.
Both viscosities must be given at the same temperature.

How to access the app

The Two-Component Viscosity Blend Calculator runs in your web browser on Tribology Universe, the app platform of i-TRIBOMAT: The European Tribology Centre. Use is free; you only need a Tribology Universe account, which takes a minute to create.

Launch the Viscosity Blend app →

Need more than the free app?

Our Modelling & Simulation team builds custom models for your geometry, materials and lubricants, and can validate them against tests on more than 130 tribometers across our partner laboratories. Contact us or write to office@i-tribomat.eu.

References

E. L. Lederer, Zur Theorie der Viskosität von Flüssigkeiten, Kolloid-Beihefte 34 (1932) 270–338
L. Grunberg, A. H. Nissan, Mixture law for viscosity, Nature 164 (1949) 799–800
M. Roegiers, B. Zhmud, Property blending relationships for binary mixtures of mineral oil and elektrionised vegetable oil: viscosity, solvent power, and seal compatibility index, Lubrication Science 23 (2011) 263–278
B. Zhmud, Viscosity blending equations, Lube-Tech No. 93
API 1509, Engine Oil Licensing and Certification System, Appendix E: Base oil interchangeability guidelines (API base oil Groups I–V)