Time Scale Of Deformation Research Articles

Effect of surfactants and interfacial rheology on equilibrium drop size in turbulent liquid-liquid dispersions

Surfactants are often required to stabilize liquid-liquid dispersions produced by high shear mixers. Due to the high power input, drops are deformed rapidly in the dispersion zone so the dynamic interfacial properties governed by the surfactant adsorption rate can have a significant impact on the resulting drop size. The objective of this work is to develop a fundamental link between surfactant adsorption dynamics, interfacial properties, and turbulent emulsification processes. To ensure constant bulk surfactant concentration during dispersion, equilibrium drop size for dilute dispersions produced by a batch rotor-stator mixer were studied. Silicone oils of various viscosity were dispersed in aqueous nonionic surfactant solutions. Drop size distributions (DSD) were measured via a video microscopy/automated image analysis technique. Equilibrium interfacial tension was measured via a pendant drop technique, as a function of surfactant concentration. The dynamic surface tension was similarly measured. The data were fit to the Langmuir adsorption isotherm and the long-times approximation to the Ward – Tordai equation and the adsorption parameters and surfactant diffusivities so obtained were employed, with an estimate of the drop deformation timescale, to estimate the surface dilational modulus (Esd) or Marangoni stress acting on the drop’ surface due to interfacial tension gradients. Trends observed in the measured equilibrium mean drop size and DSD are explained in terms of the interfacial and rheological properties. Below the CMC, Esd peaks and the drop size increases with bulk surfactant concentration, despite a decrease in equilibrium interfacial tension. Above the CMC, Marangoni stresses are small but the presence of the surfactant still modifies the rheology of the interface, increasing the effective viscosity of the drops. A comprehensive set of mechanistic models for drop size in turbulent flows, based on Kolmogorov-Hinze theory, was developed and modified to partially account for the effect of surfactants via an appropriately defined effective viscosity. The approach allows integration of surfactant phenomena into widely accepted correlations for drop size in surfactant free systems.

Measured changes in the bridge mobility and radiativity of violins due to material creep following tensioning of strings

Violins have been observed to undergo a small, but measurable, deformation of the corpus after being brought into tune following a prolonged period without string tension. This behavior, which is analagous to the flexing of a bow, can be attributed to the viscoelastic properties of wood. Because of the relatively long time scale of deformation, the process is sometimes referred to as material “creep.” To assess the impact of creep on the sound of a violin, we measured the vibrational and acoustic response of multiple violins during this period of deformation. The measurement process involves tapping the bridge with a small modal impact hammer and recording the velocity response of the top plate using a laser Doppler vibrometer, as well as the far-field acoustic response in an anechoic chamber. Results show modest changes in the amplitude of the main body modes, most notably the CBR and B1- modes, and a consistent shift in the peak frequency of higher modes, over a two-day period after the strings were tuned.

Edge fracture of thixotropic elastoviscoplastic liquid bridges.

It has recently been shown that torsion can break liquid bridges of viscoelastic fluids, with potential application to their clean and rapid dispensing. However, many commonplace fluids (paints, adhesives, pastes, and foodstuffs like chocolate) have more complex thixotropic elastoviscoplastic (TEVP) properties that depend on the imposed stress and the timescale of deformation. Using a commercial thermal paste, we show that liquid bridges of TEVP fluids can also be broken by torsion, demonstrating the applicability of the technique for improved dispensing of real industrial fluids. The liquid bridge breaking mechanism is an elastic instability known as "edge fracture." Dimensional analysis predicts that the effects of thixotropy and plasticity can be neglected during edge fracture. Simulation using a nonlinear, phenomenological TEVP constitutive model confirms such a prediction. Our work yields new insight into the free-surface flows of TEVP fluids, which may be important to processes such as electronic packaging, additive manufacturing, and food engineering.

Three-dimensional finite element modelling on strain localization around the Mabian earthquake swarm, Sichuan Province

SUMMARYThe Mabian fault zone, distanced ∼200 km to the east of the Xianshuihe–Xiaojiang fault system, is located in the western vicinity of the relatively stable South China Block. Since 1917, about 54 M > 4.7 earthquakes, including the 1974 Ms = 7.1 Mabian event have occurred around this fault zone, suggesting that significant strain is localized within the Mabian fault zone. Here, we built a 3-D finite element model to investigate the main parameters that possibly control strain localization around the Mabian fault zone averaged over the active deformation timescale. In the model, the Xianshuihe–Xiaojiang fault system is specified as a discontinuous contact interface for its motion governed by a Coulomb-friction law, and the crustal rheology is simplified as a frictional upper crust underlain by a viscoelastic lower crust. In addition, global positioning system (GPS) data are used to mimic the horizontal tectonic loading, and the model base is supported by a hydrostatic pressure. Numerical results show that with the weak fault strength and the low viscosity contrast between the Tibetan plateau and the South China Block, strain rates from motion of the southeastern Tibetan plateau could be propagated across the Xianshuihe–Xiaojiang fault system more widely within the Mabian fault zone. Constrained by the estimates on slip rates of the faults and on rheological structures of the crust, our optimal model predicts the effective friction coefficient of the Xianshuihe–Xiaojiang fault of 0.05–0.1. Under this condition, relative motion across the Xianshuihe–Xiaojiang fault system is largely partitioned by the geometric bend near the central portion of the fault system, resulting in a relatively high strain rate of 2.1–3×10–8 yr–1 accumulating around the Mabian fault zone. Keeping the weak strength of the fault, numerical results also show that if the central portion of the Xianshuihe–Xiaojiang fault system follows the Daliangshan fault, strain accumulation around the Mabian fault zone could be significantly reduced. It thus can be concluded that the strain partitioning from the weak strength and the special geometry of the Xianshuihe–Xiaojiang fault system must play a crucial role in active deformation around the Mabian area out of the Tibetan plateau deformation domain. This in turn means that in the Xianshuihe–Xiaojiang fault system, the Anninghe–Zemuhe fault is still the main boundary between the southeastern Tibetan plateau and the South China Block.

Vesicle dynamics in large amplitude oscillatory extensional flow

Although the behaviour of fluid-filled vesicles in steady flows has been extensively studied, far less is understood regarding the shape dynamics of vesicles in time-dependent oscillatory flows. Here, we investigate the nonlinear dynamics of vesicles in large amplitude oscillatory extensional (LAOE) flows using both experiments and boundary integral (BI) simulations. Our results characterize the transient membrane deformations, dynamical regimes and stress response of vesicles in LAOE in terms of reduced volume (vesicle asphericity), capillary number ( ${Ca}$ , dimensionless flow strength) and Deborah number ( ${De}$ , dimensionless flow frequency). Results from single vesicle experiments are found to be in good agreement with BI simulations across a wide range of parameters. Our results reveal three distinct dynamical regimes based on vesicle deformation: pulsating, reorienting and symmetrical regimes. We construct phase diagrams characterizing the transition of vesicle shapes between pulsating, reorienting and symmetrical regimes within the two-dimensional Pipkin space defined by ${De}$ and ${Ca}$ . Contrary to observations on clean Newtonian droplets, vesicles do not reach a maximum length twice per strain rate cycle in the reorienting and pulsating regimes. The distinct dynamics observed in each regime result from a competition between the flow frequency, flow time scale and membrane deformation time scale. By calculating the particle stresslet, we quantify the nonlinear relationship between average vesicle stress and strain rate. Additionally, we present results on tubular vesicles that undergo shape transformation over several strain cycles. Broadly, our work provides new information regarding the transient dynamics of vesicles in time-dependent flows that directly informs bulk suspension rheology.

Frequency Dependent Mantle Viscoelasticity via the Complex Viscosity: Cases From Antarctica

AbstractStudies of glacial isostatic adjustment (GIA) often use paleoshorelines and present‐day deformation to constrain the viscosity of the mantle and the thickness of the elastic lithosphere. However, several studies focused on similar locations have resulted in different estimates of these physical properties. We argue that these different estimates infer apparent viscosities and apparent lithospheric elastic thicknesses, dependent on the timescale of deformation. We use recently derived relationships between these frequency dependent apparent quantities and the underlying thermodynamic conditions to produce predictions of viscoelastic properties and lithospheric thickness across a broad spectrum of geophysical timescales for two Antarctic locations (Amundsen Sea Embayment and the Antarctic Peninsula). Our predictions are constrained by input from seismic tomography, require the self‐consistent consideration of elastic, viscous, and transient rheological behavior and also include non‐linear steady state viscosity, which have been determined by several laboratories. We demonstrate that when the full spectrum of viscoelasticity is considered, lithospheric thickness displays a significant range across frequency and that transient creep may play an important role across the timescales relevant for the GIA studies we explore. We suggest that observational studies could move toward a framework of determining the frequency dependence of viscoelastic quantities—rather than single, frequency independent values of viscosity. There remains much work to accomplish this both theoretically and observationally, but the eventual result would provide deeper insight into the rheological behavior of Earth.

Statistical thermodynamics of dislocations in solids

The thermodynamic dislocation theory (TDT) is based on two fundamental but unconventional assumptions: first, that the dislocations in a persistently deforming crystalline solid must obey the second law of thermodynamics and thus be described by an effective temperature; and second, that the controlling time scale for deformation of these systems is the inverse of the thermally activated rate at which entangled dislocation lines become unpinned from each other. By use of these first-principles concepts and comparisons with experimental data, I show that this theory achieves new, usefully predictive understandings of strain hardening, yield stresses, shear banding, and brittle and ductile fracture. I argue that it opens new directions for research.

Impact Versus Frictional Earthquake Models for High‐Frequency Radiation in Complex Fault Zones

AbstractEarthquakes occur within complex fault zones containing numerous intersecting fault strands. This complexity poses a computational challenge for rupture models, which typically simplify fault structure to a small number of rough fault surfaces, with all other deformation assumed to be off‐fault viscoplastic deformation. In such models, high‐frequency ground motions originate solely from frictionally mediated, heterogeneous slip on a small number of potentially rough fault surfaces or from off‐fault viscoplastic deformation. Alternative explanations for high‐frequency ground motion generation that can account for a larger number of fault surfaces remain difficult to assess. Here, we evaluate the efficacy of a recently proposed stochastic impact model in which high‐frequency ground motion is caused by elastic impacts of structures within a complex fault zone. Impacts are envisioned to occur in response to fault motion in the presence of geometrical incompatibilities, which promotes transfer of slip onto different fault strands on timescales mediated by elasticity. We investigate the role of a complex fault zone for high‐frequency ground motion by comparing the underlying assumptions and resulting predictions of impact and rough fault frictional models. Relative to rough fault frictional models, impact models are characterized by deformation timescales and corner frequencies that are set by elasticity rather than viscoplasticity, relatively angular rather than smoothly varying fault roughness geometries, high‐frequency radiation patterns that are more isotropic, and higher P/S radiated energies. We outline ways to discriminate whether impact or rough fault frictional models are more likely to explain observations of high‐frequency ground motions.

The relation between short- and long-term deformation in actively deforming plate boundary zones.

Satellite-based measuring systems are making it possible to monitor deformation of the Earth's surface at a high spatial resolution over periods of several decades and a significant fraction of the seismic cycle. It is widely assumed that this short-term deformation directly reflects the long-term pattern of crustal deformation, although modified in detail by local elastic effects related to locking on individual faults. This way, short-term deformation is often jointly inverted with long-term estimates of fault slip rates, or even stress, over periods of 10 s to 100 s kyrs. Here, I examine the relation between these two timescales of deformation for subduction, continental shortening and rifting tectonic settings, with examples from the active New Zealand and Central Andean plate boundary zone. I show that the relation is inherently non-unique, and simple models of locking on a deep-seated megathrust or decollement, or mantle flow, provide excellent fits to the short-term observations without requiring any information about the geometry and rate of surface faulting. The short-term deformation, in these settings at least, cannot be used to determine the behaviour of individual faults, but instead places constraints on the forces that drive deformation. Thus, there is a fundamental difference between the stress loading and stress relief parts of the earthquake cycle, with failure determined by dynamical rather than kinematic constraints; the same stress loading can give rise to widely different modes of long-term deformation, depending on the strength and rheology of the deforming zone, and the role of gravitational stresses. The process of slip on networks of active faults may have an intermediate timescale of kyrs to 10 s kyrs, where individual faults fail piecemeal without any characteristic behaviour. Physics-based dynamical models of short-term deformation may be the best way to make full use of the increasing quality of this type of data in the future. This article is part of a discussion meeting issue 'Understanding earthquakes using the geological record'.

Analysis of linear viscoelasticity of aging soft glasses

Aging soft glassy materials do not follow time-translational invariance and violate the principles of linear viscoelasticity, such as the relation between the dynamic moduli in the frequency domain and the stress relaxation modulus in the time domain. Using an aqueous suspension of hectorite clay, a model aging soft glassy material, we account for time-dependent behavior by transforming the experimentally obtained stress relaxation and dynamic moduli from the real-time domain to the effective-time domain by normalizing the real-time by a time-dependent relaxation time. We find that the two sets of experiments probe different aging and deformation timescales, and simultaneous analysis provides insights into material behavior over a wide range of timescales. Careful analysis of the dynamic moduli reveals contamination of (slow) aging α modes by (fast) nonaging β modes, which is not clearly evident in the stress relaxation modulus. On the other hand, the stress relaxation measurements probe timescales long enough to characterize the terminal relaxation of the suspension. A toy Maxwell model is used to elucidate the interaction of the slow aging and fast nonaging modes, and their effect of measurements. The synergistic relationship between the two sets of experiments offers guidelines for characterizing time-dependent materials by generalizing the principles of linear viscoelasticity.

Hardness and Yield Strength of CO Ice Under Martian Temperature Conditions

AbstractAlthough ice fracturing and deformation is key to understanding some of the landforms encountered in the high‐latitude regions on Mars and on other icy bodies in the solar system, little is known about the mechanical characteristics of CO ice. We have measured the hardness of solid CO ice directly in the laboratory with a Leeb hardness tester and calculated the corresponding yield strength. We have also measured the hardness of water ice by the same method, confirming previous work. Our results indicate that CO ice is slightly weaker, ranging between Leeb 200 and 400 ( 10 and 30 MPa yield strength, assuming only plastic deformation and no strain hardening during the experiment), for typical Martian temperatures. Our results can be used for models of CO ice rupture (depending on the deformation timescales) explaining surface processes on Mars and solar system icy bodies.

Cell Mechanical and Physiological Behavior in the Regime of Rapid Mechanical Compressions that Lead to Cell Volume Change.

Cells respond to mechanical forces by deforming in accordance with viscoelastic solid behavior. Studies of microscale cell deformation observed by high speed video microscopy have elucidated a new cell behavior in which sufficiently rapid mechanical compression of cells can lead to transient cell volume loss and then recovery. This work has discovered that the resulting volume exchange between the cell interior and the surrounding fluid can be utilized for efficient, convective delivery of large macromolecules (2000 kDa) to the cell interior. However, many fundamental questions remain about this cell behavior, including the range of deformation time scales that result in cell volume loss and the physiological effects experienced by the cell. In this study, a relationship is established between cell viscoelastic properties and the inertial forces imposed on the cell that serves as a predictor of cell volume loss across human cell types. It is determined that cells maintain nuclear envelope integrity and demonstrate low protein loss after the volume exchange process. These results define a highly controlled cell volume exchange mechanism for intracellular delivery of large macromolecules that maintains cell viability and function for invaluable downstream research and clinical applications.

Timing of magmatism and ultrahigh- to high-grade metamorphism in the Kannak Complex, Kon Tum Massif, Vietnam: Magmatic activity and its tectonic implications

Detailed geochronological and petrological investigations of metamorphic and igneous rocks can significantly improve our understanding of the tectonic processes that occur in orogenic belts. The Kon Tum Massif, central Vietnam, includes various types of magmatic and metamorphic rocks, the latter including ultrahigh- to high-temperature units. The Late Permian–Early Triassic metamorphic rocks in the massif correspond to the metamorphic characteristics of a collision between the Indochina and South China blocks in terms of their metamorphic evolution and timescales of deformation. U–Pb geochronological analyses of zircon obtained from two samples of garnet granite in the massif yielded magmatic ages of 239.6 ± 3.9 Ma and 243.5 ± 3.4 Ma. This permitted the reevaluation of previous Th–U–Pb electron microprobe analyses of monazite from the garnet granite and garnet-orthopyroxene gneiss and previously published U–Pb dating. These data reveal the metamorphic and magmatic history of the western part of the massif. The metamorphic rocks show a thermal evolution from 260 Ma to 240 Ma. Magmatic activity started at 260 Ma and ceased at 240 Ma. Considering this in terms of the regional-scale igneous activities in the Kon Tum Massif, the base of the massif, already thickened by the collision, was situated above underplating plume-related magma. Such magmatic activity resulted in high- to ultrahigh-temperature metamorphism and crustal melting during the Late Permian to Early Triassic, between 260 and 240 Ma.

Effect of surfactant chemistry on drilling mud performance

Drilling muds used in deepwater operations experience large variations in temperature, as well as pressure, when flowing through the different geometric conduits that are; the drill string, openhole (casing) - riser annuli present when drilling offshore. They behave as viscoelastic mixtures due to the suspension- and emulsion-dispersions used in their preparation. As a consequence, they display liquid-like and solid-like flow properties depending on the time scale of deformation they are subjected to. In addition to rate of deformation, environmental conditions such as temperature, and to a lesser extent pressure, are known to affect their rheological behavior.Nonionic surfactants are commonly used upstream in the stabilization of emulsions in drilling fluids, and in some instances as wetting agents. Inversion of pure emulsions systems stabilized by nonionic surfactants, from one type to another, as a result of temperature changes has been investigated and finds great application in the food and chemical industries.In this study, assessment of phase inversion occurrence in drilling muds, as well as resulting changes in their rheology was experimentally investigated at temperatures ranging from 0 to 90. Water- (WBM) and oil-based muds (OBM) samples were prepared using nonionic and ionic surfactants. Effect of surfactant nature and dispersed phase volume fraction on fluid loss properties of the different mud samples was equally carried at room temperature.Phase inversion of WBM samples stabilized by nonionic polyoxyethylene oleyl ether surfactants was observed for the range of conditions covered in the experimental investigation. Differences in flow behavior and apparent viscosity of the sample, as a result of inversion from one mud type to another, was equally noted.On one hand, the results underscored the importance of assessing potential application of nonionic surfactants to induce phase inversion in drilling fluids used for offshore operations. On the other hand, setbacks observed in the use of complex fluids for offshore drilling could possibly be accounted by the unknown occurrence of this phenomenon.

Corrigendum: Spatial and temporal characterisation of sea-ice deformation

Correcting a sign error results in no changes to the key conclusions of Hutchings and others (2011). However, there is an improved agreement with previous work. Mean total sea-ice deformation scales log linearly with distance and the scaling exponent was found to be dependent on time. We find a linear relationship between the temporal scale and spatial scaling exponent, for timescales of an hour to a day. Extrapolating to the timescales of deformation resolved by RADARSAT, we find total deformation and distance scale with an exponent of between −0.16 and −0.19.

Liquid behavior of cross-linked actin bundles

The actin cytoskeleton is a critical regulator of cytoplasmic architecture and mechanics, essential in a myriad of physiological processes. Here we demonstrate a liquid phase of actin filaments in the presence of the physiological cross-linker, filamin. Filamin condenses short actin filaments into spindle-shaped droplets, or tactoids, with shape dynamics consistent with a continuum model of anisotropic liquids. We find that cross-linker density controls the droplet shape and deformation timescales, consistent with a variable interfacial tension and viscosity. Near the liquid-solid transition, cross-linked actin bundles show behaviors reminiscent of fluid threads, including capillary instabilities and contraction. These data reveal a liquid droplet phase of actin, demixed from the surrounding solution and dominated by interfacial tension. These results suggest a mechanism to control organization, morphology, and dynamics of the actin cytoskeleton.

The Physical Origins of Cell Transit through Microfluidic Constrictions

Altered cell mechanical properties are implemented in a range of physiological processes, such as stem cell differentiation and cancer. Methods to measure the mechanical properties of single cells are integral to advancing our understanding of these processes. One such technique tracks the deformation and speed of cells as they flow through micron-scale constrictions of a microfluidic device; however, the physical origins of the timescale for cells to deform through narrow pores remain poorly understood. By fabricating soft microparticles with distinct mechanical properties, we show that deformation times strongly depend on elastic modulus and viscosity, and weakly depend on surface tension and size. Higher resolution tracking of gel particle and oil droplet deformations reveals power-law behavior; we also observe this behavior in the deformation of HL-60 cells. While various physical models have been used to interpret results from similar microfluidic assays, our results indicate that the viscous and elastic properties of materials modulate deformation timescales through micron-scale constrictions, and that power law rheology may provide valuable insight into cell deformability studies using this technique.

The physical origins of transit time measurements for rapid, single cell mechanotyping.

The mechanical phenotype or 'mechanotype' of cells is emerging as a potential biomarker for cell types ranging from pluripotent stem cells to cancer cells. Using a microfluidic device, cell mechanotype can be rapidly analyzed by measuring the time required for cells to deform as they flow through constricted channels. While cells typically exhibit deformation timescales, or transit times, on the order of milliseconds to tens of seconds, transit times can span several orders of magnitude and vary from day to day within a population of single cells; this makes it challenging to characterize different cell samples based on transit time data. Here we investigate how variability in transit time measurements depends on both experimental factors and heterogeneity in physical properties across a population of single cells. We find that simultaneous transit events that occur across neighboring constrictions can alter transit time, but only significantly when more than 65% of channels in the parallel array are occluded. Variability in transit time measurements is also affected by the age of the device following plasma treatment, which could be attributed to changes in channel surface properties. We additionally investigate the role of variability in cell physical properties. Transit time depends on cell size; by binning transit time data for cells of similar diameters, we reduce measurement variability by 20%. To gain further insight into the effects of cell-to-cell differences in physical properties, we fabricate a panel of gel particles and oil droplets with tunable mechanical properties. We demonstrate that particles with homogeneous composition exhibit a marked reduction in transit time variability, suggesting that the width of transit time distributions reflects the degree of heterogeneity in subcellular structure and mechanical properties within a cell population. Our results also provide fundamental insight into the physical underpinnings of transit measurements: transit time depends strongly on particle elastic modulus, and weakly on viscosity and surface tension. Based on our findings, we present a comprehensive methodology for designing, analyzing, and reducing variability in transit time measurements; this should facilitate broader implementation of transit experiments for rapid mechanical phenotyping in basic research and clinical settings.

Ground motions induced by a producing hydrocarbon reservoir that is overlain by a viscoelastic rocksalt layer: a numerical model

Hydrocarbon reservoir pressure depletion leads to stress changes inside the reservoir and ground deformation which is registered at the surface as subsidence. As reservoirs are often overlain by layers of rocksalt (or other evaporites), which are materials that flow so as to relax stresses inside them, there is the potential for time-varying surface subsidence. This work focuses on understanding the macroscopic mechanisms that lead to rocksalt flow-induced ground displacements. A Finite Element Model is used for this purpose in which the rocksalt layer is represented by a viscoelastic Maxwell material. Two distinct mechanisms that lead to displacement are observed. These are active during different stages of the deformation and have different timescales associated with them. An important observation is that the timescale for deformation that is measured at the ground surface is not equal to the timescale for deformation of a viscoelastic material element, but can be many times larger than that. The sensitivity of the response to the thickness and location of the rocksalt layer is also presented. Conclusions are drawn which allow for the relative importance of the presence of the rocksalt layer to be assessed and for a framework for understanding time-dependent subsidence above producing hydrocarbon reservoirs to be developed. Finally the changes in stress distribution around a producing reservoir are also briefly discussed.

Radial alignment of elliptical galaxies by the tidal force of a cluster of galaxies

Unlike the random radial orientation distribution of field elliptical galaxies, galaxies in a cluster are expected to point preferentially towards the center of the cluster, as a result of the cluster's tidal force on its member galaxies. In this work an analytic model is formulated to simulate this effect. The deformation time scale of a galaxy in a cluster is usually much shorter than the time scale of change of the tidal force; the dynamical process of the tidal interaction within the galaxy can thus be ignored. An equilibrium shape of a galaxy is then assumed to be the surface of equipotential, which is the sum of the self-gravitational potential of the galaxy and the tidal potential of the cluster at this location. We use a Monte-Carlo method to calculate the radial orientation distribution of these galaxies, by assuming the NFW mass profile of the cluster and the initial ellipticity of field galaxies. The radial angles show a single peak distribution centered at zero. The Monte-Carlo simulations also show that a shift of the reference center from the real cluster center weakens the anisotropy of the radial angle distribution. Therefore, the expected radial alignment cannot be revealed if the distribution of spatial position angle is used instead of that of radial angle. The observed radial orientations of elliptical galaxies in cluster Abell~2744 are consistent with the simulated distribution.