What is Viscosity Blending Index and Why It Matters
Viscosity is a fluid's resistance to flow -- essentially a measure of how "thick" a liquid is. It plays a crucial role in various industries, including lubricants, pharmaceuticals, and food production. If you have ever poured honey or tried to get ketchup out of a bottle, you have experienced viscosity firsthand.
What if you have two or more liquids and want to predict the viscosity of their blend? That is where the Viscosity Blending Index (VBI) comes in. The VBI, calculated through the Refutas equation, lets you predict how a mixture of liquids will behave. Whether you are blending oils or formulating a new product, understanding VBI can save significant trial and error.
The Refutas Equation
The Refutas equation converts a liquid's kinematic viscosity (in cSt) into a Viscosity Blending Index using the following formula:
[\text{VBI} = 14.534 \cdot \ln(\ln(\nu + 0.8)) + 10.975]
Where:
- VBI is the Viscosity Blending Index (dimensionless).
- v is the kinematic viscosity of the liquid in centistokes (cSt).
To find the blend viscosity for two or more components:
- Calculate the VBI for each component.
- Compute the weighted average: [\text{VBI}{\text{blend}} = x{1} \times \text{VBI}{1} + x{2} \times \text{VBI}_{2} + \ldots] where each x represents the volume fraction of component i.
- Invert the formula to recover the blend viscosity: [\nu_{\text{blend}} = \exp!\left(\exp!\left(\frac{\text{VBI}_{\text{blend}} - 10.975}{14.534}\right)\right) - 0.8]
Quick Tip
Always double-check your numbers with a calculator to ensure accuracy. The Refutas equation works best for liquids that mix well and have similar chemical properties. It may not be accurate for liquids that chemically react or do not mix well.
Calculation Example
Suppose you have two liquids with the following kinematic viscosities:
- Liquid 1: 5.0 cSt (60% by volume)
- Liquid 2: 20.0 cSt (40% by volume)
Step-by-Step Calculation
-
Calculate VBI for Liquid 1:
- Add 0.8: 5.0 + 0.8 = 5.8
- First natural log: ln(5.8) = 1.7579
- Second natural log: ln(1.7579) = 0.5643
- Multiply and add: 14.534 x 0.5643 + 10.975 = 19.1718
-
Calculate VBI for Liquid 2:
- Add 0.8: 20.0 + 0.8 = 20.8
- First natural log: ln(20.8) = 3.0350
- Second natural log: ln(3.0350) = 1.1101
- Multiply and add: 14.534 x 1.1101 + 10.975 = 27.1102
-
Calculate the blend VBI:
- VBI_blend = 0.60 x 19.1718 + 0.40 x 27.1102 = 11.5031 + 10.8441 = 22.3472
-
Convert back to viscosity:
- Subtract and divide: (22.3472 - 10.975) / 14.534 = 0.7824
- Double exponential: exp(exp(0.7824)) = exp(2.1867) = 8.9066
- Subtract 0.8: 8.9066 - 0.8 = 8.1066 cSt
The predicted blend viscosity is approximately 8.11 cSt.
Why the Refutas Equation Works
Viscosity does not blend linearly. A 50/50 mix of a 5 cSt oil and a 20 cSt oil does not produce a 12.5 cSt blend. The relationship between viscosity and composition is logarithmic, which is why the Refutas equation applies a double-logarithmic transformation. This transformation linearizes the blending behavior, making a simple weighted average accurate.
The approach was originally developed for petroleum products and is widely used in the oil and lubricant industries. ASTM D341 and related standards reference this type of viscosity-temperature-composition relationship. The constants 14.534 and 10.975 were empirically determined to provide accurate predictions across a broad range of hydrocarbon viscosities.
Practical Applications
- Lubricant formulation: Blending base oils to achieve a target viscosity grade.
- Fuel blending: Combining different fuel stocks while meeting viscosity specifications for combustion or pipeline transport.
- Process engineering: Predicting fluid behavior in mixing operations where viscosity affects heat transfer and flow rates.
- Quality control: Verifying that a blend meets specification before committing to large-scale production.
Understanding the Viscosity Blending Index can save considerable time, especially if you work in industries that require precise fluid behavior. Knowing how to calculate the VBI and predict blend viscosity is an invaluable skill for anyone working with fluid mixtures.