scholarly journals Faraday waves in soft elastic solids

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200129
Author(s):  
Giulia Bevilacqua ◽  
Xingchen Shao ◽  
John R. Saylor ◽  
Joshua B. Bostwick ◽  
Pasquale Ciarletta
Keyword(s):  
Soft Matter ◽  
Theoretical Explanation ◽  
Subharmonic Resonance ◽  
Viscous Fluids ◽  
Faraday Waves ◽  
Elastic Solids ◽  
Soft Solids ◽  
Elastic Bodies ◽  
Faraday Instability ◽  
Elastic Slab

Recent experiments have observed the emergence of standing waves at the free surface of elastic bodies attached to a rigid oscillating substrate and subjected to critical values of forcing frequency and amplitude. This phenomenon, known as Faraday instability, is now well understood for viscous fluids but surprisingly eluded any theoretical explanation for soft solids. Here, we characterize Faraday waves in soft incompressible slabs using the Floquet theory to study the onset of harmonic and subharmonic resonance eigenmodes. We consider a ground state corresponding to a finite homogeneous deformation of the elastic slab. We transform the incremental boundary value problem into an algebraic eigenvalue problem characterized by the three dimensionless parameters, that characterize the interplay of gravity, capillary and elastic waves. Remarkably, we found that Faraday instability in soft solids is characterized by a harmonic resonance in the physical range of the material parameters. This seminal result is in contrast to the subharmonic resonance that is known to characterize viscous fluids, and opens the path for using Faraday waves for a precise and robust experimental method that is able to distinguish solid-like from fluid-like responses of soft matter at different scales.

scholarly journals Moulding hydrodynamic 2D-crystals upon parametric Faraday waves in shear-functionalized water surfaces

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mikheil Kharbedia ◽  
Niccolò Caselli ◽  
Diego Herráez-Aguilar ◽  
Horacio López-Menéndez ◽  
Eduardo Enciso ◽  
...  
Keyword(s):  
Soft Matter ◽  
Shear Stiffness ◽  
External Control ◽  
Faraday Waves ◽  
Plane Shear ◽  
Unit Cell Size ◽  
Ordering Transitions ◽  
Water Surfaces ◽  
Ordering Transition ◽  
Surface Rigidity

AbstractFaraday waves, or surface waves oscillating at half of the natural frequency when a liquid is vertically vibrated, are archetypes of ordering transitions on liquid surfaces. Although unbounded Faraday waves patterns sustained upon bulk frictional stresses have been reported in highly viscous fluids, the role of surface rigidity has not been investigated so far. Here, we demonstrate that dynamically frozen Faraday waves—that we call 2D-hydrodynamic crystals—do appear as ordered patterns of nonlinear gravity-capillary modes in water surfaces functionalized with soluble (bio)surfactants endowing in-plane shear stiffness. The phase coherence in conjunction with the increased surface rigidity bears the Faraday waves ordering transition, upon which the hydrodynamic crystals were reversibly molded under parametric control of their degree of order, unit cell size and symmetry. The hydrodynamic crystals here discovered could be exploited in touchless strategies of soft matter and biological scaffolding ameliorated under external control of Faraday waves coherence.

scholarly journals Contact lines on stretched soft solids: modelling anisotropic surface stresses

2021 ◽  
Vol 477 (2245) ◽  
pp. 20200673
Author(s):  
Stefanie Heyden ◽  
Nicolas Bain ◽  
Qin Xu ◽  
Robert W. Style ◽  
Eric R. Dufresne
Keyword(s):  
Soft Matter ◽  
Liquid Droplet ◽  
Substrate Surface ◽  
Contact Lines ◽  
Soft Substrate ◽  
Soft Solids ◽  
Anisotropic Surface ◽  
Surface Profiles ◽  
Free Parameters ◽  
Lamé Coefficients

We present fully analytical solutions for the deformation of a stretched soft substrate due to the static wetting of a large liquid droplet, and compare our solutions to recently published experiments (Xu et al. 2018 Soft Matter 14, 916–920 (doi:10.1039/C7SM02431B)). Following a Green’s function approach, we extend the surface-stress regularized Flamant–Cerruti problem to account for uniaxial pre-strains of the substrate. Surface profiles, including the heights and opening angles of wetting ridges, are provided for linearized and finite kinematics. We fit experimental wetting ridge shapes as a function of applied strain using two free parameters, the surface Lamé coefficients. In comparison with experiments, we find that observed opening angles are more accurately captured using finite kinematics, especially with increasing levels of applied pre-strain. These fits qualitatively agree with the results of Xu et al ., but revise values of the surface elastic constants.

scholarly journals How surface stress transforms surface profiles and adhesion of rough elastic bodies

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200477
Author(s):  
Chung-Yuen Hui ◽  
Zezhou Liu ◽  
Nicolas Bain ◽  
Anand Jagota ◽  
Eric R. Dufresne ◽  
...  
Keyword(s):  
Surface Stress ◽  
Periodic Structures ◽  
Surface Profile ◽  
Initial Surface ◽  
One Dimensional ◽  
Patterned Substrate ◽  
Soft Solids ◽  
Elastic Bodies ◽  
Surface Profiles ◽  
Qualitative Changes

The surface of soft solids carries a surface stress that tends to flatten surface profiles. For example, surface features on a soft solid, fabricated by moulding against a stiff-patterned substrate, tend to flatten upon removal from the mould. In this work, we derive a transfer function in an explicit form that, given any initial surface profile, shows how to compute the shape of the corresponding flattened profile. We provide analytical results for several applications including flattening of one-dimensional and two-dimensional periodic structures, qualitative changes to the surface roughness spectrum, and how that strongly influences adhesion.

scholarly journals Secondary Instabilities of Surface Waves on Viscous Fluids in the Faraday Instability

1995 ◽  
Vol 32 (4) ◽  
pp. 313-318 ◽  
Author(s):  
L Daudet ◽  
V Ego ◽  
S Manneville ◽  
J Bechhoefer
Keyword(s):  
Surface Waves ◽  
Viscous Fluids ◽  
Faraday Instability ◽  
Secondary Instabilities

scholarly journals Extreme cavity expansion in soft solids: Damage without fracture

2020 ◽  
Vol 6 (13) ◽  
pp. eaaz0418 ◽  
Author(s):  
Jin Young Kim ◽  
Zezhou Liu ◽  
Byung Mook Weon ◽  
Tal Cohen ◽  
Chung-Yuen Hui ◽  
...  
Keyword(s):  
Phase Separation ◽  
Brittle Materials ◽  
Damage Mechanism ◽  
Cavity Expansion ◽  
Small Scale ◽  
Elastic Solids ◽  
Ductile Metals ◽  
Scale Free ◽  
Soft Solids ◽  
Bond Breakage

Cavitation is a common damage mechanism in soft solids. Here, we study this using a phase separation technique in stretched, elastic solids to controllably nucleate and grow small cavities by several orders of magnitude. The ability to make stable cavities of different sizes, as well as the huge range of accessible strains, allows us to systematically study the early stages of cavity expansion. Cavities grow in a scale-free manner, accompanied by irreversible bond breakage that is distributed around the growing cavity rather than being localized to a crack tip. Furthermore, cavities appear to grow at constant driving pressure. This has strong analogies with the plasticity that occurs surrounding a growing void in ductile metals. In particular, we find that, although elastomers are normally considered as brittle materials, small-scale cavity expansion is more like a ductile process. Our results have broad implications for understanding and controlling failure in soft solids.

An evaluation of acrylic complete-dentures using the discrimination of elastic bodies or viscous fluids

1999 ◽  
Vol 26 (7) ◽  
pp. 608-612 ◽  
Author(s):  
K. Inoue ◽  
K. Fujii ◽  
T. Kanie ◽  
A. Kadokawa ◽  
G. Tsukada
Keyword(s):  
Viscous Fluids ◽  
Complete Dentures ◽  
Elastic Bodies

Faraday instability threshold in large-aspect-ratio containers

2002 ◽  
Vol 467 ◽  
pp. 307-330 ◽  
Author(s):  
FRANCISCO J. MANCEBO ◽  
JOSÉ M. VEGA
Keyword(s):  
Aspect Ratio ◽  
Numerical Solution ◽  
Closed Form ◽  
Ad Hoc ◽  
Linear Problem ◽  
Experimental Results ◽  
Large Aspect Ratio ◽  
Faraday Waves ◽  
Closed Form Solutions ◽  
Faraday Instability

We consider the Floquet linear problem giving the threshold acceleration for the appearance of Faraday waves in large-aspect-ratio containers, without further restrictions on the values of the parameters. We classify all distinguished limits for varying values of the various parameters and simplify the exact problem in each limit. The resulting simplified problems either admit closed-form solutions or are solved numerically by the well-known method introduced by Kumar & Tuckerman (1994). Some comparisons are made with (a) the numerical solution of the original exact problem, (b) some ad hoc approximations in the literature, and (c) some experimental results.

scholarly journals The Bakerian Lecture: On the viscosity or internal friction of air and other gases

1867 ◽  
Vol 15 ◽  
pp. 14-17 ◽  
Keyword(s):  
Internal Friction ◽  
The Other ◽  
Elastic Solids ◽  
Soft Solids

All bodies which are capable of having their form indefinitely altered, and which resist the change of form with a force depending on the rate of deformation, may be called Viscous Bodies. Taking tar or treacle as an instance in which both the change of form and the resistance opposed to it are easily observed, we may pass in one direction through the series of soft solids up to the materials commonly supposed to be most unyielding, such as glass and steel, and in the other direction through the series of liquids of various degrees of mobility id the gases, of which oxygen is the most viscous, and hydrogen the least. The viscosity of elastic solids has been investigated by M. F. Kohlrausch and Professor W. Thomson; that of gases by Professor Stokes, M. O. E. Meyer, and Mr. Graham.

scholarly journals Waves in elastic bodies with discrete and continuous dynamic microstructure

2019 ◽  
Vol 378 (2162) ◽  
pp. 20190313 ◽  
Author(s):  
Gennady S. Mishuris ◽  
Alexander B. Movchan ◽  
Leonid I. Slepyan
Keyword(s):  
Comparative Analysis ◽  
Energy Distribution ◽  
Unified Approach ◽  
Elastic Solids ◽  
Theme Issue ◽  
Elastic Bodies ◽  
Structured Media ◽  
Continuous Dynamic ◽  
Dynamic Phenomena ◽  
Non Locality

This paper presents a unified approach to the modelling of elastic solids with embedded dynamic microstructures. General dependences are derived based on Green's kernel formulations. Specifically, we consider systems consisting of a master structure and continuously or discretely distributed oscillators. Several classes of connections between oscillators are studied. We examine how the microstructure affects the dispersion relations and determine the energy distribution between the master structure and microstructures, including the vibration shield phenomenon. Special attention is given to the comparative analysis of discrete and continuous distributions of the oscillators, and to the effects of non-locality and trapped vibrations. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.

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