2020 年 48 巻 5 号 p. 259-269
Normalized extensional and shear viscosities, ηE/ηE0 and η/η0 with the subscript “0” standing for quantities in the linear viscoelastic (LVE) regime, are theoretically analyzed for the FENE-dumbbell in the presence of isotropic friction-reduction under flow. The basic parameters in the analysis are the friction reduction factor rζ = ζsf/ζeq, FENE factor rκ = κsf/κeq, and the Brownian force intensity factor rB = Bsf/Beq, with ζ and κ being the bead friction coefficient and spring strength of the dumbbell, B denoting the intensity of the Brownian force acting on the bead, and the subscripts “sf” and “eq” standing for the quantities under steady flow and at equilibrium, respectively: Beq = 2ζeqkBT with kBT being the thermal energy, according to the fluctuation-dissipation theorem valid at equilibrium. The normalized viscosities were found to be analytically expressed as ηE/ηE0 = (rB/rκ){1−2(rζ/rκ)Wi}−1{1+(rζ/rκ)Wi}−1 and η/η0 = (rB/rκ), with Wi being the Weissenberg number defined with respect to the LVE relaxation time. Both ηE/ηE0 and η/η0 are proportional to the rB factor, so that comparison of these quantities allows us to characterize the intensity of the Brownian force Bsf under flow. For example, for a test case of power-law decay of rζ with Wi, the above expressions of ηE/ηE0 and η/η0 suggested a relationship 2ζsfkBT < Bsf < 2ζeqkBT
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