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Frumkin V, Gokhale S. Coupled instabilities drive quasiperiodic order-disorder transitions in Faraday waves. Phys Rev E 2023; 108:L012601. [PMID: 37583202 DOI: 10.1103/physreve.108.l012601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2022] [Accepted: 05/31/2023] [Indexed: 08/17/2023]
Abstract
We present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. We show that the transition is driven initially by a long-wave amplitude modulation instability, which excites the oscillatory transition phase instability, leading to the formation of dislocations in the Faraday lattice. The appearance of dislocations dampens amplitude modulations, which prevents further defects from being created and allows the system to relax back to its ordered state. The process then repeats itself in a quasiperiodic manner. Our experiments reveal an unexpected mechanism for temporal quasiperiodicity that results from a coupling between two distinct instabilities on the route to chaos.
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Affiliation(s)
- Valeri Frumkin
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Shreyas Gokhale
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Pickard D, Martynowych D, Lem J, Koshakji A, Lin S, Zhao X, Nelson K, Giovanardi B, Radovitzky R. Converging-diverging shock-driven instabilities along soft hydrogel surfaces. Phys Rev E 2023; 107:L022601. [PMID: 36932538 DOI: 10.1103/physreve.107.l022601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Accepted: 01/06/2023] [Indexed: 06/18/2023]
Abstract
Intense surface eruptions are observed along the curved surface of a confined cylindrical film of hydrogel subject to laser-induced converging-diverging shock loading. Detailed numerical simulations are used to identify the dominant mechanisms causing mechanical instability. The mechanisms that produce surface instability are found to be fundamentally different from both acoustic parametric instability and shock-driven Richtmyer-Meshkov instability. The time scale of observed and simulated eruption formation is much larger than that of a single shock reflection, in stark contrast to previously studied shock-driven instabilities. Moreover, surface undulations are only found along external, as opposed to internal, soft solid boundaries. Specifically, classic bubble surface instability mechanisms do not occur in our experiments and here we comment only on the new surface undulations found along the outer boundary of solid hydrogel cylinders. Our findings indicate a new class of impulsively excited surface instability that is driven by cycles of internal shock reflections.
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Affiliation(s)
- Daniel Pickard
- Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Dmitro Martynowych
- Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jet Lem
- Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Anwar Koshakji
- Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Shaoting Lin
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Xuanhe Zhao
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Keith Nelson
- Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Bianca Giovanardi
- Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Faculty of Aerospace Engineering, Delft University of Technology, 2628 CD Delft, Netherlands
| | - Raul Radovitzky
- Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Liu J, Song W, Ma G, Li K. Faraday Instability in Viscous Fluids Covered with Elastic Polymer Films. Polymers (Basel) 2022; 14:polym14122334. [PMID: 35745910 PMCID: PMC9231276 DOI: 10.3390/polym14122334] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2022] [Revised: 06/06/2022] [Accepted: 06/07/2022] [Indexed: 02/05/2023] Open
Abstract
Faraday instability has great application value in the fields of controlling polymer processing, micromolding colloidal lattices on structured suspensions, organizing particle layers, and conducting cell culture. To regulate Faraday instability, in this article, we attempt to introduce an elastic polymer film covering the surface of a viscous fluid layer and theoretically study the behaviors of the Faraday instability phenomenon and the effect of the elastic polymer film. Based on hydrodynamic theory, the Floquet theory is utilized to formulate its stability criterion, and the critical acceleration amplitude and critical wave number are calculated numerically. The results show that the critical acceleration amplitude for Faraday instability increases with three increasing bending stiffness of the elastic polymer film, and the critical wave number decreases with increasing bending stiffness. In addition, surface tension and viscosity also have important effects on the critical acceleration amplitude and critical wave number. The strategy of controlling Faraday instability by covering an elastic polymer film proposed in this paper has great application potential in new photonic devices, metamaterials, alternative energy, biology, and other fields.
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Affiliation(s)
- Junxiu Liu
- Anhui Province Key Laboratory of Building Structure and Underground Engineering, Anhui Jianzhu University, Hefei 230601, China;
- College of Civil Engineering, Anhui Jianzhu University, Hefei 230601, China; (W.S.); (G.M.)
| | - Wenqiang Song
- College of Civil Engineering, Anhui Jianzhu University, Hefei 230601, China; (W.S.); (G.M.)
| | - Gan Ma
- College of Civil Engineering, Anhui Jianzhu University, Hefei 230601, China; (W.S.); (G.M.)
| | - Kai Li
- Anhui Province Key Laboratory of Building Structure and Underground Engineering, Anhui Jianzhu University, Hefei 230601, China;
- College of Civil Engineering, Anhui Jianzhu University, Hefei 230601, China; (W.S.); (G.M.)
- Correspondence:
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Tamim SI, Bostwick JB. Oscillations of a soft viscoelastic drop. NPJ Microgravity 2021; 7:42. [PMID: 34728641 PMCID: PMC8563899 DOI: 10.1038/s41526-021-00169-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2021] [Accepted: 10/01/2021] [Indexed: 12/31/2022] Open
Abstract
A soft viscoelastic drop has dynamics governed by the balance between surface tension, viscosity, and elasticity, with the material rheology often being frequency dependent, which are utilized in bioprinting technologies for tissue engineering and drop-deposition processes for splash suppression. We study the free and forced oscillations of a soft viscoelastic drop deriving (1) the dispersion relationship for free oscillations, and (2) the frequency response for forced oscillations, of a soft material with arbitrary rheology. We then restrict our analysis to the classical cases of a Kelvin-Voigt and Maxwell model, which are relevant to soft gels and polymer fluids, respectively. We compute the complex frequencies, which are characterized by an oscillation frequency and decay rate, as they depend upon the dimensionless elastocapillary and Deborah numbers and map the boundary between regions of underdamped and overdamped motions. We conclude by illustrating how our theoretical predictions for the frequency-response diagram could be used in conjunction with drop-oscillation experiments as a "drop vibration rheometer", suggesting future experiments using either ultrasonic levitation or a microgravity environment.
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Affiliation(s)
- Saiful I Tamim
- Department of Mechanical Engineering, Clemson University, Clemson, SC, 29634, USA
| | - Joshua B Bostwick
- Department of Mechanical Engineering, Clemson University, Clemson, SC, 29634, USA.
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