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Which one of the following measures of viscosity is dimensionless?

  • A.Inherent viscosity
  • B.Reduced viscosity
  • C.Zero-shear viscosity
  • D.Specific viscosity

Answer: D

The dimensionless measure is specific viscosity.

Specific viscosity is the fractional increase in viscosity that the dissolved polymer causes, \(\eta_{sp} = (\eta - \eta_{s})/\eta_{s}\), a ratio of two viscosities, so its units cancel.

The others carry units. Reduced viscosity is \(\eta_{sp}/c\) and inherent viscosity is \(\ln(\eta_{rel})/c\); dividing by the concentration c gives both units of volume per mass, such as dL/g. Zero-shear viscosity is an actual viscosity, the limiting value at vanishing shear rate, measured in Pa s.

Relative viscosity \(\eta/\eta_{s}\) is the other dimensionless member of the family, but it is not among the options.

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