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1. Gravitational effects on Faraday instability in a viscoelastic liquid

   https://doi.org/10.1017/jfm.2025.328  

   Ignatius, IB; Dinesh, B; Dietze, GF; Narayanan, R (May 2025, Journal of Fluid Mechanics)

   The influence of parametric forcing on a viscoelastic fluid layer, in both gravitationally stable and unstable configurations, is investigated via linear stability analysis. When such a layer is vertically oscillated beyond a threshold amplitude, large interface deflections are caused by Faraday instability. Viscosity and elasticity affect the damping rate of momentary disturbances with arbitrary wavelength, thereby altering the threshold and temporal response of this instability. In gravitationally stable configurations, calculations show that increased elasticity can either stabilize or destabilize the viscoelastic system. In weakly elastic liquids, higher elasticity increases damping, raising the threshold for Faraday instability, whereas the opposite is observed in strongly elastic liquids. While oscillatory instability occurs in Newtonian fluids for all gravity levels, we find that parametric forcing below a critical frequency will cause a monotonic instability for viscoelastic systems at microgravity. Importantly, in gravitationally unstable configurations, parametric forcing above this frequency stabilizes viscoelastic fluids, until the occurrence of a second critical frequency. This result contrasts with the case of Newtonian liquids, where under the same conditions, forcing stabilizes a system for all frequencies below a single critical frequency. Analytical expressions are obtained under the assumption of long wavelength disturbances predicting the damping rate of momentary disturbances as well as the range of parameters that lead to a monotonic response under parametric forcing. 

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2. IMAGING OF FOCUSED ULTRASOUND-INDUCED SHEAR WAVES TO PROBE MECHANICAL ANISOTROPY OF TISSUE

   https://doi.org/10.1115/DMD2021-1030  

   C.A. Guertler, R.J. Okamoto (April 2021, Proceedings of the 2021 Design of Medical Devices Conference)

   null (Ed.)

   It is important to understand mechanical anisotropy in fibrous soft tissues because of the relationship of anisotropy to tissue function, and because anisotropy may change due to injury and disease. We have developed a method to noninvasively investigate anisotropy, based on MR imaging of harmonic ultrasound-induced motion (MR-HUM), using focused ultrasound (FUS) and magnetic resonance elastography (MRE). MR-HUM produces symmetric, radial waves inside a tissue, which enables a simple assessment of anisotropy using features of the resulting shear wave fields. This method was applied to characterize ex vivo muscle tissue, which is known to exhibit mechanical anisotropy. Finite element (FE) simulations of the experiment were performed to illustrate and validate the approach. Anisotropy was characterized by ratios of apparent shear moduli and strain components in different directions. 

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3. Lubricated steady sliding of a rigid sphere on a soft elastic substrate: hydrodynamic friction in the Hertz limit

   https://doi.org/10.1039/C9SM02447F  

   Wu, Haibin; Moyle, Nichole; Jagota, Anand; Hui, Chung-Yuen (March 2020, Soft Matter)

   Lubricated sliding on soft elastic substrates occurs in a variety of natural and technological settings. It very often occurs in the iso-viscous elasto-hydrodynamic lubrication (EHL) regime ( e.g. , soft solid, low pressure). In this regime, for sliding of a smooth sphere on a soft solid, a “Hertz-like” effective contact region forms. Much of the fluid is squeezed out of the contact region although enough is retained to keep the solid surfaces fully separated. This is accompanied by complex deformation of the soft solid. The behavior of such soft lubricated contacts is controlled by a single dimensionless parameter 1/ β that can be interpreted as a normalized sliding velocity. Solving this fundamental soft-lubrication problem poses significant computational difficulty for large β , which is the limit relevant for soft solids. As a consequence, little is known about the structure of the flow field under soft lubrication in the intake and outlet regions. Here we present a new solution of this soft lubrication problem focusing on the “Hertz” limit. We develop a formulation in polar coordinates that handles difficult computational issues much better than previous methods. We study how hydrodynamic pressure, film thickness and hydrodynamic friction vary with β . Scaling laws for these relationships are given in closed form for a range of β not previously accessible theoretically but that is typical in applications. The computational method presented here can be used to study other soft lubrication problems. 

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4. The many behaviors of deformable active droplets

   https://doi.org/https://doi.org/10.3934/mbe.2021145  

   Young, Y; Shelley, M; Stein, D (June 2021, Mathematical biosciences and engineering)

   null (Ed.)

   Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motions over scales far larger than their microscopic constituents. In some cases, the mechanisms that give rise to this phenomenon have been well characterized, and can explain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well understood. In this work, we examine the behavior of droplets of an active nematic fluid. We study their linear stability about the isotropic equilibrium over a wide range of parameters, identifying regions in which different modes of instability dominate. Simulations of their full dynamics are used to identify their nonlinear behavior within each region. When a single mode dominates, the droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zigzaggers, washing machines, wanderers, and pulsators. 

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5. Recent Progress on Moving Boundary Problems

   Canic, Suncica (January 2020, American Mathematical Society Current Events Bulletin)

   We give a brief survey of the recent progress in the area of mathematical well-posedness for moving boundary problems describing fluid-structure interaction between incompressible, viscous fluids and elastic, viscoelastic, and rigid solids. 

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