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.
Influence of surface viscosities on the electrodeformation of a prolate viscous drop
Contaminants and other agents are often present at the interface between two fluids, giving rise to rheological properties such as surface shear and dilatational viscosities. The dynamics of viscous drops with interfacial viscosities has attracted greater interest in recent years, due to the influence of surface rheology on deformation and the surrounding flows. We investigate the effects of shear and dilatational viscosities on the electro-deformation of a viscous drop using the Taylor–Melcher leaky dielectric model. We use a large deformation analysis to derive an ordinary differential equation for the drop shape. Our model elucidates the contributions of each force to the overall deformation of the drop and reveals a rich range of dynamic behaviors that show the effects of surface viscosities and their dependence on rheological and electrical properties of the system. We also examine the physical mechanisms underlying the observed behaviors by analyzing the surface dilatation and surface deformation.
more »
« less
- NSF-PAR ID:
- 10412911
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 19
- Issue:
- 4
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 776 to 789
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
Abstract -
more » « less
Abstract We use Sentinel‐1 and ALOS‐2 Interferometric Synthetic Aperture Radar (InSAR), and Global Navigation Satellite System (GNSS) data to investigate the mechanisms of coseismic and postseismic deformation due to the 2021 M7.4 Maduo (China) earthquake. We present a refined coseismic slip model constrained by the rupture trace and precisely located aftershocks. The InSAR time series corrected for the atmospheric and decorrelation noise reveal postseismic line of sight displacements up to ∼0.1 m. The displacements are discontinuous along the fault trace, indicating shallow afterslip and velocity‐strengthening friction in the top 2–3 km of the upper crust. The magnitude of shallow afterslip is however insufficient to compensate for the coseismic slip deficit, implying substantial off‐fault yielding. The observed surface deformation does not exhibit obvious features that could be attributed to poroelastic effects. We developed a fully coupled model that accounts for both stress‐driven creep on a deep localized shear zone and viscoelastic relaxation in the bulk of the lower crust. The mid‐ to near‐field data can be reasonably well explained by deep afterslip and/or non‐Maxwellian visco‐elasticity. Our results suggest a power‐law stress exponent of ∼4–4.5 assuming a power‐law rheology, and transient and steady‐state viscosities of 1018and 1019 Pa s, respectively, assuming a bi‐viscous (Burgers) rheology. However, a good fit to the GNSS data cannot be achieved assuming the bulk viscoelastic relaxation alone, and requires a contribution of deep afterlip and/or a localized shear zone extending through much of the lower crust.
-
Abstract. Accurate glacial isostatic adjustment (GIA) modelling in the cryosphere is required for interpreting satellite, geophysical and geological recordsand for assessing the feedbacks of Earth deformation and sea-level change on marine ice-sheet grounding lines. GIA modelling in areas of active ice lossin West Antarctica is particularly challenging because the ice is underlain by laterally varying mantle viscosities that are up to several orders ofmagnitude lower than the global average, leading to a faster and more localised response of the solid Earth to ongoing and future ice-sheet retreatand necessitating GIA models that incorporate 3-D viscoelastic Earth structure. Improvements to GIA models allow for computation of the viscoelasticresponse of the Earth to surface ice loading at sub-kilometre resolution, and ice-sheet models and observational products now provide the inputs toGIA models at comparably unprecedented detail. However, the resolution required to accurately capture GIA in models remains poorly understood, andhigh-resolution calculations come at heavy computational expense. We adopt a 3-D GIA model with a range of Earth structure models based on recentseismic tomography and geodetic data to perform a comprehensive analysis of the influence of grid resolution on predictions of GIA in the AmundsenSea Embayment (ASE) in West Antarctica. Through idealised sensitivity testing down to sub-kilometre resolution with spatially isolated ice loadingchanges, we find that a grid resolution of ∼ 13 of the radius of the load or higher is required to accurately capture the elasticresponse of the Earth. However, when we consider more realistic, spatially coherent ice loss scenarios based on modern observational records andfuture ice-sheet model projections and adopt a viscoelastic Earth, we find that predicted deformation and sea-level change along the grounding lineconverge to within 5 % with grid resolutions of 7.5 km or higher, and to within 2 % for grid resolutions of 3.75 km andhigher, even when the input ice model is on a 1 km grid. Furthermore, we show that low mantle viscosities beneath the ASE lead to viscousdeformation that contributes to the instrumental record on decadal timescales and equals or dominates over elastic effects by the end of the 21stcentury. Our findings suggest that for the range of resolutions of 1.9–15 km that we considered, the error due to adopting a coarser gridin this region is negligible compared to the effect of neglecting viscous effects and the uncertainty in the adopted mantle viscosity structure.more » « less
-
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.more » « less
-
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.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/D2SM01307J
