Abstract
We employ a matrix-based solver for the linear rheology of fluid-immersed disordered spring networks to reveal four distinct dynamic response regimes. One regime - completely absent in the known vacuum response - exhibits coupled fluid flow and network deformation, with both components responding nonaffinely. This regime contains an additional plateau (peak) in the frequency-dependent storage (loss) modulus - features that vanish without full hydrodynamic interactions. The mechanical response of immersed networks such as biopolymers and hydrogels is thus richer than previously established and offers additional modalities for design and control through fluid interactions.
| Original language | English |
|---|---|
| Article number | 238005 |
| Number of pages | 5 |
| Journal | Physical Review Letters |
| Volume | 123 |
| Issue number | 23 |
| DOIs | |
| Publication status | Published - 3 Dec 2019 |
Funding
For nonzero damping coefficient ζ and solvent viscosity η , we have shown that any finite driving frequency ω > 0 rigidifies floppy networks with p < p c (Supplemental Material Fig. S3 [27] ). Since most fibrous materials are immersed in a liquid, and ω ≡ 0 as stated is impossible to achieve in reality, we can argue that fiber networks should generically be regarded as rigid, albeit possibly very soft. This extends known means to rigidify subisostatic networks that include thermal fluctuations [32] , fibers that resist bending [33] , and an embedding elastic medium [34] . It is not yet clear if known results for G ⋆ ( ω ) near p c [16,18] can be expanded into a critical-like “phase” diagram in ( ω , ζ , η ) space, similar to these other works. Similarly, it is not known how fluid might affect the strain-induced rigidity transition under continuous (rather than oscillatory) flow [35,36] . Investigations into these questions, and improved numerical methodology for immersed fiber networks, would be welcome. Coupling only at network nodes [16,18] is numerically convenient, and based on the conceptually similar bead-spring formalism of the Rouse and Zimm models [4] and rod-based coupling of Huisman et al. [15] , which exhibits the same high-frequency limit, we expect equivalent results up to scaling for all coupling schemes. Nonetheless, it is desirable to extend more rigorous frameworks [37] to elastic networks to confirm this expectation, in addition to extending this formalism to include semiflexibility and entanglements. The authors would like to thank Thomas Ranner, Holger Stark, and Matthew Dennison for discussions. This work was partly funded by the ECR Internationalisation Activity Fund, University of Leeds, UK. C. 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