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1. Effect of interfacial viscosities on droplet migration at low surfactant concentrations

   https://doi.org/10.1017/jfm.2020.551  

   Dandekar, Rajat; Ardekani, Arezoo M. (November 2020, Journal of Fluid Mechanics)

   null (Ed.)

   In this paper, we theoretically investigate the migration of a surfactant covered droplet in a Poiseuille flow by including the surface viscosities of the droplet. We employ a regular perturbation expansion for low surface Péclet numbers and solve the problem up to a second-order approximation. We represent the drop surface as a two-dimensional homogeneous fluid using the Bousinessq–Scriven law and employ Lamb's general solution to represent the velocity fields inside and outside the droplet. We obtain an expression for the cross-stream migration velocity of the droplet, where the surface viscosities are captured by the Bousinessq numbers for surface shear and surface dilatation. We elucidate the influence of the surface viscosities on the migration characteristics of the droplet and the surfactant redistribution on the droplet surface. Our study sheds light on the importance of including the droplet surface viscosities to accurately predict the migration characteristics of the droplet. 

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2. Pressure-driven flow across a hyperelastic porous membrane

   https://doi.org/10.1017/jfm.2019.298  

   Song, Ryungeun; Stone, Howard A.; Jensen, Kaare H.; Lee, Jinkee (July 2019, Journal of Fluid Mechanics)

   We report an experimental investigation of pressure-driven flow of a viscous liquid across thin polydimethylsiloxane (PDMS) membranes. Our experiments revealed a nonlinear relation between the flow rate $$Q$$ and the applied pressure drop $$\unicode[STIX]{x0394}p$$ , in apparent disagreement with Darcy’s law, which dictates a linear relationship between flow rate, or average velocity, and pressure drop. These observations suggest that the effective permeability of the membrane decreases with pressure due to deformation of the nanochannels in the PDMS polymeric network. We propose a model that incorporates the effects of pressure-induced deformation of the hyperelastic porous membrane at three distinct scales: the membrane surface area, which increases with pressure, the membrane thickness, which decreases with pressure, and the structure of the porous material, which is deformed at the nanoscale. With this model, we are able to rationalize the deviation between Darcy’s law and the data. Our result represents a novel case in which macroscopic deformations can impact the microstructure and transport properties of soft materials. 

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3. Inference of the Timescale‐Dependent Apparent Viscosity Structure in the Upper Mantle Beneath Greenland

   https://doi.org/10.1029/2022AV000751  

   Paxman, Guy J. G.; Lau, Harriet C. P.; Austermann, Jacqueline; Holtzman, Benjamin K.; Havlin, C. (February 2023, AGU Advances)

   Abstract Contemporary crustal uplift and relative sea level (RSL) change in Greenland is caused by the response of the solid Earth to ongoing and historical ice mass change. Glacial isostatic adjustment (GIA) models, which seek to match patterns of land surface displacement and RSL change, typically employ a linear Maxwell viscoelastic model for the Earth's mantle. In Greenland, however, upper mantle viscosities inferred from ice load changes and other geophysical phenomena occurring over a range of timescales vary by up to two orders of magnitude. Here, we use full‐spectrum rheological models to examine the influence of transient deformation within the Greenland upper mantle, which may account for these differing viscosity estimates. We use observations of shear wave velocity combined with constitutive rheological models to self‐consistently calculate mechanical properties including the apparent upper mantle viscosity and lithosphere thickness across a broad spectrum of frequencies. We find that the contribution of transient behavior is most significant over loading timescales of 10²–10³ years, which corresponds to the timeframe of ice mass loss over recent centuries. Predicted apparent lithosphere thicknesses are also in good agreement with inferences made across seismic, GIA, and flexural timescales. Our results indicate that full‐spectrum constitutive models that more fully capture broadband mantle relaxation provide a means of reconciling seemingly contradictory estimates of Greenland's upper mantle viscosity and lithosphere thickness made from observations spanning a range of timescales. 

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4. Hydrodynamic Bulge Testing: Materials Characterization Without Measuring Deformation

   https://doi.org/10.1115/1.4046297  

   Anand, Vishal; Muchandimath, Sanjan C.; Christov, Ivan C. (May 2020, Journal of Applied Mechanics)

   Abstract Characterizing the elastic properties of soft materials through bulge testing relies on accurate measurement of deformation, which is experimentally challenging. To avoid measuring deformation, we propose a hydrodynamic bulge test for characterizing the material properties of thick, pre-stressed elastic sheets via their fluid–structure interaction with a steady viscous fluid flow. Specifically, the hydrodynamic bulge test relies on a pressure drop measurement across a rectangular microchannel with a deformable top wall. We develop a mathematical model using first-order shear deformation theory of plates with stretching and the lubrication approximation for the Newtonian fluid flow. Specifically, a relationship is derived between the imposed flowrate and the total pressure drop. Then, this relationship is inverted numerically to yield estimates of the Young’s modulus (given the Poisson ratio) if the pressure drop is measured (given the steady flowrate). Direct numerical simulations of two-way-coupled fluid–structure interaction are carried out in ansys to determine the cross-sectional membrane deformation and the hydrodynamic pressure distribution. Taking the simulations as “ground truth,” a hydrodynamic bulge test is performed using the simulation data to ascertain the accuracy and the validity of the proposed methodology for estimating material properties. An error propagation analysis is performed via Monte Carlo simulation to characterize the susceptibility of the hydrodynamic bulge test estimates to noise. We find that, while a hydrodynamic bulge test is less accurate in characterizing material properties, it is less susceptible to noise, in the input (measured) variable, than a hydrostatic bulge test. 

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5. Viscoplastic modeling of elastic and creep deformation of fractured Berea sandstone.

   Talukdar, M.; Sone, H.; Griffith, W. A. (June 2021, 55th US Rock Mechanics/Geomechanics Symposium)

   null (Ed.)

   We observed and modeled the elastic, inelastic and time-dependent viscous properties of damaged Berea Sandstone samples to investigate the impact of damage on the rheological properties of rocks. Cylindrical Berea Sandstone plugs were prepared both parallel and perpendicular to bedding. We impacted the samples with Split Hopkinson Pressure Bar to pervasively fracture the specimens at different strain rates. Longitudinal mode-I fractures are dominant in specimens impacted at relatively low strain rates (about 130 /s), whereas shear fractures also form in specimens deformed at high strain rates (up to 250 /s). The damaged rocks were subjected to multiple steps of differential stress loading and hold stages under 15 MPa confining pressure. A key observation is that higher damaged specimens showed greater axial and volumetric creep strain deformation during loading and hold stages. Poisson ratio also increase with increasing damage. We modeled the volumetric strain of the sandstone specimens using a Perzyna viscoplasticity law that employs the Modified Cam Clay model as the yield criterion (Haghighat et al. 2020). We deduced that fractured rocks undergo substantial bulk time-dependent deformation due to volumetric compaction and fracture closure. Damage increase results in decrease of the effective viscosity of the material. 

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