Blockwise friction heterogeneity redistributes stretching in a 2D Gaussian polymer under Batchelor-Kraichnan random flow
Abstract
We study a two-dimensional Gaussian Rouse chain divided into two contiguous blocks with different local friction coefficients but identical Hookean elasticity. In quiescent conditions, friction heterogeneity leaves the continuous-time equilibrium Gaussian conformation unchanged while producing distinct block mobilities and a modified generalized relaxation spectrum. The exact friction-weighted translational diffusion coefficient retains the scaling Dγ∝ N−1, with a friction-dependent prefactor; the corresponding diffusion law and generalized-mode formulation extend beyond the diblock to more general local friction profiles. We then place the chain in an incompressible Batchelor-Kraichnan random flow. Under a common external flow, the high-friction block becomes more extended than the low-friction block. The deformation asymmetry strengthens with friction contrast and develops across the weak- to moderate-flow regime, remaining clearly visible at the strongest finite-time conditions. It also persists when the chain-specific longest-mode Weissenberg number is matched across friction ratios, showing that, within the same finite-time protocol, the effect is not accounted for solely by a shift of the global relaxation timescale. In generalized-mode coordinates, the smooth random strain does not directly mix mode indices and preferentially amplifies the slowest mode. At larger flow strengths, extension distributions broaden markedly and exhibit pronounced temporal drift over the simulated time window. Since all simulated chain-specific longest-mode Weissenberg numbers remain below unity, this drift is interpreted as slow convergence toward the broad, power-law-tailed stationary Hookean regime near the coil-stretch threshold. Overall, friction heterogeneity alone is sufficient to redistribute deformation along an otherwise mechanically uniform polymer.
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BibTeX
@misc{dey2026blockwise,
title = {{Blockwise friction heterogeneity redistributes stretching in a 2D Gaussian polymer under Batchelor-Kraichnan random flow}},
author = {Arpan Dey},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31707},
eprint = {2609.31707},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05785264v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Blockwise friction heterogeneity redistributes stretching in a 2D Gaussian polymer under Batchelor-Kraichnan random flow
AU - Arpan Dey
PY - 2026
DA - 2026/09/20
PB - HAL
DO - 10.48550/arxiv.2609.31707
UR - https://hal.science/hal-05785264v1
AB - We study a two-dimensional Gaussian Rouse chain divided into two contiguous blocks with different local friction coefficients but identical Hookean elasticity. In quiescent conditions, friction heterogeneity leaves the continuous-time equilibrium Gaussian conformation unchanged while producing distinct block mobilities and a modified generalized relaxation spectrum. The exact friction-weighted translational diffusion coefficient retains the scaling D_γ∝ N^−1, with a friction-dependent prefactor; the corresponding diffusion law and generalized-mode formulation extend beyond the diblock to more general local friction profiles. We then place the chain in an incompressible Batchelor-Kraichnan random flow. Under a common external flow, the high-friction block becomes more extended than the low-friction block. The deformation asymmetry strengthens with friction contrast and develops across the weak- to moderate-flow regime, remaining clearly visible at the strongest finite-time conditions. It also persists when the chain-specific longest-mode Weissenberg number is matched across friction ratios, showing that, within the same finite-time protocol, the effect is not accounted for solely by a shift of the global relaxation timescale. In generalized-mode coordinates, the smooth random strain does not directly mix mode indices and preferentially amplifies the slowest mode. At larger flow strengths, extension distributions broaden markedly and exhibit pronounced temporal drift over the simulated time window. Since all simulated chain-specific longest-mode Weissenberg numbers remain below unity, this drift is interpreted as slow convergence toward the broad, power-law-tailed stationary Hookean regime near the coil-stretch threshold. Overall, friction heterogeneity alone is sufficient to redistribute deformation along an otherwise mechanically uniform polymer.
ER -