Extracting the surface tension of soft gels from elastocapillary wave behavior

Shao, Xingchen; Saylor, J. R.; Bostwick, Joshua

doi:10.1039/c8sm01027g

Cited by 23 publications

(13 citation statements)

References 53 publications

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“…For a Newtonian fluid, the resonance frequency has been given by 4 and the spectral width by 24 , 25 with ν the kinematic viscosity. Shao et al 35 have taken a similar approach for gel drops but included the added effect of elasticity.…”

Section: Resultsmentioning

confidence: 99%

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Oscillations of a soft viscoelastic drop

Tamim

Bostwick

2021

npj Microgravity

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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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Section: Resultsmentioning

confidence: 99%

“…Previous studies on surface waves in viscoelastic materials have predicted complex eigenfrequencies with the real part corresponding to the oscillation frequency and imaginary part the decay rate of oscillation 33 – 35 . Naturally, the purely elastic limit has no decay rate.…”

Section: Introductionmentioning

confidence: 99%

Oscillations of a soft viscoelastic drop

Tamim

Bostwick

2021

npj Microgravity

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“…As expected the presence of a surface tension has a regularized effect on the onset of a Faraday instability, since it penalizes any morphological transition creating a non-flat free surface [14,15]. The physical range of interest for the dimensionless parameter αγ for soft solids with shear modulus in the range μ ∈ [10, 100] Pa made by hydrogels with γ ∈ [0, 0.05] N m −1 [23] is about αγ∈false[0,0.2false]. In figure 4 e , f , we plot the marginal stability threshold a~cr and the corresponding critical wavenumber k~cr versus αω fixing λ x = 1, α g = 0.001 and varying αγ∈false[0,0.2false] step 0.05.…”

Section: Marginal Stability Analysismentioning

confidence: 99%

Faraday waves in soft elastic solids

et al. 2020

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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.

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“…Due to their nearly incompressible nature, soft materials indeed present interesting dynamical properties embodied by the propagation of elastic waves: The velocity of the transversely polarized waves is several orders of magnitude smaller than its longitudinal counterpart. This aspect has been at the center of interesting developments in various contexts from evidencing the role of surface tension in soft solids (22,23) to model experiments for fracture dynamics (24) or transient elastography (25,26).…”

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confidence: 99%

Dirac cones and chiral selection of elastic waves in a soft strip

Lanoy

Lemoult

Eddi

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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We study the propagation of in-plane elastic waves in a soft thin strip, a specific geometrical and mechanical hybrid framework which we expect to exhibit a Dirac-like cone. We separate the low frequencies guided modes (typically 100 Hz for a 1-cm-wide strip) and obtain experimentally the full dispersion diagram. Dirac cones are evidenced together with other remarkable wave phenomena such as negative wave velocity or pseudo-zero group velocity (ZGV). Our measurements are convincingly supported by a model (and numerical simulation) for both Neumann and Dirichlet boundary conditions. Finally, we perform one-way chiral selection by carefully setting the source position and polarization. Therefore, we show that soft materials support atypical wave-based phenomena, which is all of the more interesting as they make most of the biological tissues.

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Extracting the surface tension of soft gels from elastocapillary wave behavior

Cited by 23 publications

References 53 publications

Oscillations of a soft viscoelastic drop

Oscillations of a soft viscoelastic drop

Faraday waves in soft elastic solids

Dirac cones and chiral selection of elastic waves in a soft strip

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