Universal scaling for polymer chain scission in turbulence

Abstract

We report that previous polymer chain scission experiments in strong flows, long analyzed according to accepted laminar flow scission theories, were in fact affected by turbulence. We reconcile existing anomalies between theory and experiment with the hypothesis that the local stress at the Kolmogorov scale generates the molecular tension leading to polymer covalent bond breakage. The hypothesis yields a universal scaling for polymer scission in turbulent flows. This surprising reassessment of over 40 years of experimental data simplifies the theoretical picture of polymer dynamics leading to scission and allows control of scission in commercial polymers and genomic DNA.bond breakage ͉ drag reduction ͉ polymer dynamics ͉ Kolmogorov cascade ͉ DNA rupture L ong-chain polymers undergo scission in strong flows because of the coupling of continuum-scale mechanical and atomicscale chemical processes (1, 2). The interactions that connect these disparate scales are poorly understood. Yet, practically, polymer chain scission is a principal determinant of the performance of operations in many fields, including turbulent drag reduction for pipelines and ships (3), microfluidic handling of polymeric fluids (4), and gene therapy using plasmid DNA (5). Alternatively, chain scission underlies technologies such as the shotgun sequencing of DNA (6) and the generation of monodisperse polymer standards (7). The design and control of polymer scission in each of these flows is driven by the scaling relationship between the strength of the flow, as quantified by the fluid strain rate, and the scission product distribution, as quantified by the molar mass of ruptured polymer chains. Since Frenkel (8) published the first treatise on polymer chain scission more than 60 years ago, this fundamental issue has remained unresolved.Scission theories for laminar flow hypothesize that the drag force, F d , experienced by the chain induces a tension that breaks the molecule if it is greater than the critical strength of a polymer covalent bond. In a purely extensional flow, for example, the maximum tension is at the midpoint (9). If the extended chain is modeled as a slender rod, then the tension induced by the drag is F d ϳ VR ϳ R 2 (10). Here is the solvent viscosity, V is the relative velocity of the solvent flowing past the rod at its half-length R and is the macroscopic fluid strain rate (ϳV͞R). Two laminar theories identify different regimes depending on the ratio of polymer relaxation time to flow residence time, the Deborah number (De). For the De Ͻ Ͻ 1 regime, such as in stagnation point flow of a cross-slot, chains are fully stretched such that R ϳ O(L), where L is the contour length of the chain (10). For the De Ͼ Ͼ 1 regime, such as in transient extensional flows generated in contraction-expansion geometries, chains adopt only a partially stretched conformation and R ϳ O(R g ), where R g is the radius of gyration (11). These viscous flow models yield distinct scaling relationships: c ϳ L Ϫ2 for De Ͻ Ͻ 1 and c ϳ L Ϫ1 for De Ͼ Ͼ 1, whe...

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