Rheological Analysis of Elongational Flows - Kolitawong, Chanyut (Burapha Science Journal, 2026)
The objective of this paper is to analyze the fluid element under the elongational deformation and to explain the origin of the rheology functions of shear free flows. The analysis’s shown that flow kinematics of the uniaxial and biaxial elongations are rotational, while those of the planar elongation are irrotational. From force balances of the free body diagram of a fluid element in an uniaxial elongational flow experiment, the stretching force is related to the elongational viscosity and the Young’s elastic modulus. Moreover, the force balances of the fluid element give the biaxial elongational viscosity and the Young’s elastic modulus in biaxial flow. Last, the rheology functions of planar elongational flow are examined. The first and second planar elongational viscosities, and, and the first and second planar elongational moduli, and, are exploded. Moreover, the relationships between shear viscosity and extensional parameters are determined. These elongational rheology functions are standardized by the American the Society of Rheology to be commonly used worldwide.