More Like this

1. Collective vibrations of a hydrodynamic active lattice

   https://doi.org/10.1098/rspa.2020.0155  

   Thomson, S. J.; Durey, M.; Rosales, R. R. (July 2020, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   null (Ed.)

   Recent experiments show that quasi-one-dimensional lattices of self-propelled droplets exhibit collective instabilities in the form of out-of-phase oscillations and solitary-like waves. This hydrodynamic lattice is driven by the external forcing of a vertically vibrating fluid bath, which invokes a field of subcritical Faraday waves on the bath surface, mediating the spatio-temporal droplet coupling. By modelling the droplet lattice as a memory-endowed system with spatially non-local coupling, we herein rationalize the form and onset of instability in this new class of dynamical oscillator. We identify the memory-driven instability of the lattice as a function of the number of droplets, and determine equispaced lattice configurations precluded by geometrical constraints. Each memory-driven instability is then classified as either a super- or subcritical Hopf bifurcation via a systematic weakly nonlinear analysis, rationalizing experimental observations. We further discover a previously unreported symmetry-breaking instability, manifest as an oscillatory–rotary motion of the lattice. Numerical simulations support our findings and prompt further investigations of this nonlinear dynamical system. 

   more » « less
2. Oscillatory and tip-splitting instabilities in 2D dynamic fracture: The roles of intrinsic material length and time scales

   https://doi.org/104372  

   Vasudevan, A; Lubmirsky, L; Chen, C-H; Bouchbinder, A; Karma, A (January 2021, Journal of the mechanics and physics of solids)

   null (Ed.)

   Recent theoretical and computational progress has led to unprecedented understanding of symmetry-breaking instabilities in 2D dynamic fracture. At the heart of this progress resides the identification of two intrinsic, near crack tip length scales — a nonlinear elastic length scale ℓ and a dissipation length scale ξ — that do not exist in Linear Elastic Fracture Mechanics (LEFM), the classical theory of cracks. In particular, it has been shown that at a propagation velocity v of about 90% of the shear wave-speed, cracks in 2D brittle materials undergo an oscillatory instability whose wavelength varies linearly with ℓ, and at larger loading levels (corresponding to yet higher propagation velocities), a tip-splitting instability emerges, both in agreements with experiments. In this paper, using phase-field models of brittle fracture, we demonstrate the following properties of the oscillatory instability: (i) It exists also in the absence of near-tip elastic nonlinearity, i.e. in the limit ℓ→0, with a wavelength determined by the dissipation length scale ξ. This result shows that the instability crucially depends on the existence of an intrinsic length scale associated with the breakdown of linear elasticity near crack tips, independently of whether the latter is related to nonlinear elasticity or to dissipation. (ii) It is a supercritical Hopf bifurcation, featuring a vanishing oscillations amplitude at onset. (iii) It is largely independent of the phenomenological forms of the degradation functions assumed in the phase-field framework to describe the cohesive zone, and of the velocity-dependence of the fracture energy Γ(v) that is controlled by the dissipation time scale in the Ginzburg-Landau-type evolution equation for the phase-field. These results substantiate the universal nature of the oscillatory instability in 2D. In addition, we provide evidence indicating that the tip-splitting instability is controlled by the limiting rate of elastic energy transport inside the crack tip region. The latter is sensitive to the wave-speed inside the dissipation zone, which can be systematically varied within the phase-field approach. Finally, we describe in detail the numerical implementation scheme of the employed phase-field fracture approach, allowing its application in a broad range of materials failure problems. 

   more » « less
3. Oscillatory thermocapillary instability of a film heated by a thick substrate

   https://doi.org/10.1017/jfm.2019.417  

   Batson, W.; Cummings, L. J.; Shirokoff, D.; Kondic, L. (August 2019, Journal of Fluid Mechanics)

   In this work we consider a new class of oscillatory instabilities that pertain to thermocapillary destabilization of a liquid film heated by a solid substrate. We assume the substrate thickness and substrate–film thermal conductivity ratio are large so that the effect of substrate thermal diffusion is retained at leading order in the long-wave approximation. As a result, the system dynamics is described by a nonlinear partial differential equation for the film thickness that is non-locally coupled to the full substrate heat equation. Perturbing about a steady quiescent state, we find that its stability is described by a non-self-adjoint eigenvalue problem. We show that, under appropriate model parameters, the linearized eigenvalue problem admits complex eigenvalues that physically correspond to oscillatory (in time) instabilities of the thin-film height. As the principal results of our work, we provide a complete picture of the susceptibility to oscillatory instabilities for different model parameters. Using this description, we conclude that oscillatory instabilities are more relevant experimentally for films heated by insulating substrates. Furthermore, we show that oscillatory instability where the fastest-growing (most unstable) wavenumber is complex, arises only for systems with sufficiently large substrate thicknesses. Finally, we discuss adaptation of our model to a practical setting and make predictions of conditions at which the reported instabilities can be observed. 

   more » « less
4. Emerging Design Tools for Functional Architectures in Monofilament Fibers

   https://doi.org/10.1002/adem.202400919  

   Gumennik, Alexander; Faccini_de_Lima, Camila (September 2024, Advanced Engineering Materials)

   The structural control of the monofilament fiber cross‐sectional architecture is a well‐established method for imparting its active functionality. Resulting from a thermal draw, the fiber device, until recently, is expected to be a cross‐sectionally scaled‐down and axially scaled‐up replica of its preform. However, thermal draw is a melt‐shaping process in which the preform is heated to a viscous liquid to be scaled into a fiber. Thus, it is prone to capillary instabilities on the interfaces between preform cladding and materials it encapsulates, distorting the fiber‐embedded architecture and complicating preform‐to‐fiber geometry translation. Traditionally, capillary instabilities are suppressed by performing the draw at a high‐viscosity, large‐feature‐size regime, such that the scaling of the preform into the fiber happens faster than a pronounced instability can develop. It is discovered recently that highly nonlinear, at times even chaotic capillary instabilities, in some fluid dynamic regimes, become predictable and thus engineerable. Driven by ever‐growing demand for enhancing the fiber‐device functionality, piggybacking on a capillary instability, instead of suppressing it, establishes itself as a new material processing strategy to achieve fiber‐embedded systems with user‐engineered architecture in all 3D, including the axial. Considering this development, the notable emerging methodologies are cross‐compared for designing 3D fiber‐embedded architectures. 

   more » « less
5. Seagrass deformation affects fluid instability and tracer exchange in canopy flow

   https://doi.org/10.1038/s41598-023-30401-9  

   Vieira, Guilherme S.; Allshouse, Michael R.; Mahadevan, Amala (December 2023, Scientific Reports)

   Abstract Monami is the synchronous waving of a submerged seagrass bed in response to unidirectional fluid flow. Here we develop a multiphase model for the dynamical instabilities and flow-driven collective motions of buoyant, deformable seagrass. We show that the impedance to flow due to the seagrass results in an unstable velocity shear layer at the canopy interface, leading to a periodic array of vortices that propagate downstream. Our simplified model, configured for unidirectional flow in a channel, provides a better understanding of the interaction between these vortices and the seagrass bed. Each passing vortex locally weakens the along-stream velocity at the canopy top, reducing the drag and allowing the deformed grass to straighten up just beneath it. This causes the grass to oscillate periodically even in the absence of water waves. Crucially, the maximal grass deflection is out of phase with the vortices. A phase diagram for the onset of instability shows its dependence on the fluid Reynolds number and an effective buoyancy parameter. Less buoyant grass is more easily deformed by the flow and forms a weaker shear layer, with smaller vortices and less material exchange across the canopy top. While higher Reynolds number leads to stronger vortices and larger waving amplitudes of the seagrass, waving amplitude is maximized at intermediate grass buoyancy. All together, our theory and computations develop an updated schematic of the instability mechanism consistent with experimental observations. 

   more » « less