"Can you explain how to calculate the viscosity of a viscosity index improver? I can't do this on my viscometer. If I make a blend of 10 percent polymer in SN 150 base oil, how can I calculate this mathematically?"

Viscosity index improvers (VII) vary greatly based on their specific chemistry and molecular structure, so unfortunately there is no simple calculation that can be made. The additive supplier should be able to provide a blending chart with the information you are looking for along with a few other variables. This chart should identify the blended viscosity and viscosity index based on a given treat rate.

Remember, viscosity is a fluid's measure of resistance to flow and shear. The viscosity index is a measure of a fluid's change in viscosity relative to its change in temperature. Viscosity index improvers resist the thinning that occurs in a lubricant as the temperature is increased. These additives are polymeric molecules that are sensitive to temperature. As the temperature increases, these molecules tend to stretch out. As the molecules stretch out, the fluid's internal friction will increase, causing the fluid to flow at a slower rate. Therefore, it will have a higher viscosity.

Among the materials that are generally used for viscosity index improvers include polymethacrylates (PMA), polyisobutylene (PIB), radial polyisoprene and olefin co-polymers (OCP). As you can see, there are several different types, and each will have its own reaction curve.  

Viscosity index improvers are commonly used in multigrade engine oils, gear oils, automatic transmission fluids, power-steering fluids, greases and some hydraulic fluids. They allow the fluid to flow more freely at a lower temperature so it can reach the bearings quicker. At a higher operating temperature, the fluid will have a higher viscosity and will provide the required film thickness to protect the bearings and moving parts within your equipment.

One of the major issues with the viscosity index improver additives is that they are very susceptible to mechanical shearing. For example, imagine a piece of spaghetti moving with the oil throughout an engine or in a gearbox. There are areas in the engine or gearbox that have very tight clearances and will act much like a pair of scissors cutting the spaghetti noodle (viscosity index improver molecule) into smaller pieces. Over time this greatly reduces the ability of these molecules to add to the viscosity of the fluid.