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<p>This study reexamines the constraint for volume conservation of the Rouse chain proposed recently (Kwon 2024). We provide conceivable reasoning for the constraint written in terms of the normal mode amplitude. Formulating the necessary number of constraints is verified to require vanishing correlation between distinct linear combinations of segmental vectors. Considering these observations, we prove that the normal mode amplitude is the only choice appropriate for the constraint. The constitutive equation derived expresses shear thinning with the exponent in the range between <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:-0.4\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:-0.6\)</EquationSource> </InlineEquation>, and therefore approximately matches the experiments. Second, we investigate the anisotropic friction. The anisotropy is modeled by substituting the friction tensor. We decompose the inverse of the friction tensor into reduced, isotropic and accreted friction terms. This implementation enables modeling finite value of <i>N</i><sub>2</sub> as well as friction reduction. Probable correlation between <i>N</i><sub>2</sub> and the extensional friction reduction has been also demonstrated.</p>

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The modified Rouse model incorporating supplementary effects: I. Nonlinear modification for chain volume conservation and anisotropic friction

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  • 发表日期：

    2026年2月17日

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  • Youngdon Kwon

摘要

This study reexamines the constraint for volume conservation of the Rouse chain proposed recently (Kwon 2024). We provide conceivable reasoning for the constraint written in terms of the normal mode amplitude. Formulating the necessary number of constraints is verified to require vanishing correlation between distinct linear combinations of segmental vectors. Considering these observations, we prove that the normal mode amplitude is the only choice appropriate for the constraint. The constitutive equation derived expresses shear thinning with the exponent in the range between \(\:-0.4\) and \(\:-0.6\) , and therefore approximately matches the experiments. Second, we investigate the anisotropic friction. The anisotropy is modeled by substituting the friction tensor. We decompose the inverse of the friction tensor into reduced, isotropic and accreted friction terms. This implementation enables modeling finite value of N2 as well as friction reduction. Probable correlation between N2 and the extensional friction reduction has been also demonstrated.