An Experimental Study of Constitutive Equations for Viscoelastic Fluids

Four viscoelastic constitutive equations are examined for their ability to correlate linear dynamic data with non-linear viscosity and first normal stress data. The theories examined are due to Oldroyd; Pao; Bogue; and Bernstein, Kearsley, and Zapas. The concepts and viscometric predictions of each theory are reviewed with more emphasis on the Pao theory due to a lack of discussion in the literature. A summary of classical linear theory is also presented.

Experimental data were obtained on a Weissenberg Rheogoniometer for two materials: solutions of 10 per cent polyisobutylene in Decalin and 12 per cent polystryene in Aroclor. A limited amount of data were also obtained for a 3 per cent napalm solution. Where possible, viscometric data covered a shear rate range of five decades and dynamic data covered a frequency range of four decades. In some cases instrument or material limitations restricted the range. All data were taken at 25°C.

It was found that Oldroyd's three-constant theory and Pao's theory do not agree quantitatively with viscometric data. Bogue's theory and the Bernstein-Kearsley-Zapas theory do agree quantitatively with certain restrictions: (1) in the forms examined, these theories do not predict limiting viscosoties at high shear rates; (2) an adjustable material parameter is used (although it is possible that this parameter is constant for classes of materials); and (3) there are no data for the second normal stress difference.

Simplifications of some of the theories are presented and take the form of series truncations of discrete relaxation functions or of empirical representations of continuous relaxation functions. Also discussed is the problem of the minimum data required to represent a viscoelastic fluid, with suggestions concerning the range of data needed. Finally, dimensionless groups are extracted from a combination of a constitutive theory with a momentum balance and applications to complex problems are discussed.