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Experimental Analysis Of Flow Birefringence In Jeffery-Hamel Flow

Miu Kobayashi, William Kai Alexander Worby, Yuto Yokoyama, Misa Kawaguchi, Yoshiyuki Tagawa

Tokyo University of Agriculture and Technology, Tokyo, Japan


The photoelastic method, a stress field measurement method in solid mechanics, is being considered for application to fluids. In previous studies, simple shear flow and uniaxial extensional flow experiments have shown a relationship between the measured phase retardation and the velocity field. However, no clear relationship has been shown for extensional and shear combined flow fields. The objective of the present study is to clarify the relationship between the velocity field and the measured phase retardation in an extensional-shear combined flow. For this objective, photoelastic measurements were conducted in a steady flow field using the Jeffery-Hamel flow, which is an extensional-shear combined flow with an analytical solution for the velocity field. Comparison with the analytical velocity field showed that birefringence was proportional to the 0.88 and 0.92 power of the deformation in the shear or extensional-dominated region, respectively. The results show that the birefringence Δ_n followed the power law of extensional rate ε^{0.95} where it is dominant. Whereas shear is dominant, Δ_n proportional to a power-law of γ^{0.88} holds. These results are consistent with previous studies using shear flow and uniaxial extensional flow. Furthermore, it is shown that in the extensional-shear combined flow, the sum-of-squares root of two equations suggests that the theory developed mainly for solids could also be applied to fluids.

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