Viscoelastic Rheology Research Articles

A bi-component model to assess the rheology of soft cellular aggregates probed using the micropipette aspiration technique

The micro-pipette aspiration technique is a classical experiment used to characterize the physical properties of inert fluids and biological soft materials such as cellular aggregates. The physical parameters of the fluid, as viscosity and interfacial tension, are obtained by studying how the fluid enters the pipette when the suction pressure is increased and how it relaxes when the suction pressure is put to zero. A mathematical model representative of the experiment is needed to extrapolate the physical parameters of the fluid-like matter; however, for biological materials as cells or cell aggregates mathematical models are always based on strong starting hypotheses that impact the significance of the identified parameters. In this article, starting from the bi-constituent nature of the cell aggregate, we derive a general mathematical model based of a Cahn–Hilliard–Navier–Stokes set of equations. The model is applied to describe quantitatively the aspiration-retraction dynamics of a cell-aggregate into and out of a pipette. We demonstrate the predictive capability of the model and highlight the impact of the assumptions made on the identified parameters by studying two cases: one with a non-wetting condition between the cells and the wall of the pipette (classical assumption in the literature) and the second one, which is more realistic, with a partial wetting condition (contact angle θs = 150°). Furthermore, our results provide a purely physical explanation to the asymmetry between the aspiration and retraction responses which is alternative to the proposed hypothesis of an mechano-responsive alteration of the surface tension of the cell aggregate. Statement of significanceOur study introduces a general mathematical model, based on the Cahn-Hilliard-Navier-Stokes equations, tailored to model micro-pipette aspiration of cell aggregates. The model accounts for the multi-component structure of the cell aggregate and its intrinsic viscoelastic rheology. By challenging prevailing assumptions, particularly regarding perfect non-wetting conditions and the mechano-responsive alteration of cell surface tension, we demonstrate the reliability of the mathematical model and elucidate the mechanisms at play, offering a purely physical explanation for observed asymmetries between the aspiration and retraction stages of the experiment.

Microstructure, Viscoelasticity, and Extensional Rheology of Ethylene–Propylene Copolymer Vitrimers

Microstructure, Viscoelasticity, and Extensional Rheology of Ethylene–Propylene Copolymer Vitrimers

Effects of Andrade and Burgers rheologies on glacial isostatic adjustment modeling in Antarctica

Variations in ice mass deform the Earth and modify its gravity field, a process known as Glacial Isostatic Adjustment (GIA). GIA in Antarctica remains poorly constrained due to the cumulative effect of past and present ice-mass changes, the unknown history of the past ice-mass change, and the uncertainties on the mechanical properties of the Earth. This paper investigates the effect of using Andrade and Burgers viscoelastic rheologies, rather than the commonly used Maxwell rheology, to model GIA-induced deformation in Antarctica. The Love number and Green's function formalism are used to compute the radial surface displacements and the gravity changes induced by the past and present ice-mass changes. We consider an Earth model whose elastic properties and radial structure are averaged from the Preliminary Reference Earth Model and two viscosity profiles to account for the recently published results on the present ice-mass changes. Using the three rheological laws affects the temporal response of the Earth differently, leading to smaller discrepancies than those induced by the two viscosity structures. The differences are the largest between Maxwell and Burgers rheologies during the 100–1000 years following the beginning of the surface-mass change. Results show that using the Andrade and Burgers rheologies allows the Earth to respond on decennial to centennial time scales, up to 10 m more than Maxwell. Considering only the recent ice-mass changes, the deformation rates derived from Burgers and Andrade rheologies are several times larger than those estimated by Maxwell rheology.

Semi-analytical solutions of Newtonian fluid-FENE-P fluid core annular flow

Water-lubricated transportation of viscous oil is an important application of core annular flow (CAF), which significantly reduces friction pressure drop and saves pump power. However, the core oil floats up due to the density difference of oil and water, causing instability and even destruction of CAF, which restricts the application and development of the drag reduction technology. The viscoelastic fluid in the annular can inhibit the tendency of the core oil to float up and enhance the stability of the CAF. Nevertheless, theoretical studies related to the viscoelastic fluid CAF are currently missing. To make up for the lack of theoretical research, the solutions of laminar concentric viscous oil-viscoelastic fluid CAF in horizontal and inclined pipes are obtained in this work, and the annular fluid is regarded as viscoelastic fluid conforming to the FENE-P model. Based on the Navier–Stokes equation and FENE-P model, a non-dimensional CAF model is established, and the Newton–Raphson method is used to solve the model. The rheological behavior of annular fluid and the effects of viscoelastic fluid rheology and viscosity ratio on various CAF flow characteristics, including holdup, pressure gradient, slip ratio, and Ledinegg instability, are investigated. The results indicate that the shear-thinning effect of viscoelastic fluid has a significant effect on water holdup and expands the multi-solution region. Different from Newtonian fluid, when the annulus fluid is viscoelastic, the slip ratio can be less than 2. The most significant property is that the shear-thinning effect can transform the hydraulic characteristic curve in the multi-valued region into a single-valued curve, which helps to eliminate Ledinegg instability.

Water content of rocky exoplanets in the habitable zone

In this study we investigated the interiors of rocky exoplanets in order to identify those that may have large quantities of water. We modelled the interiors of 28 rocky exoplanets, assuming four different layers – an iron core, a rock mantle, a high-pressure ice layer, and a surface ice/water layer. Due to observational bias, our study is limited to habitable zone exoplanets. We determined a range of possible water mass fractions for each planet consistent with the modelled planetary structures. We calculated the tidal heating experienced by these exoplanets through gravitational interactions with their host stars, assuming a temperature- and composition-dependent Maxwell viscoelastic rheology. Assuming radioactive elemental abundances observed in Solar System meteorites, we also calculated the radiogenic heat flux inside the planets. We estimated the probability of the presence of a thick ocean layer in these planets, taking into account the effect of both tidal and radiogenic heating. Our results showed that Proxima Centauri b, Ross 128 b, Teegarden’s b and c, GJ 1061 c and d, and TRAPPIST-1 e may have an extended liquid water reservoir. Furthermore, extremely high H2O-content of the exoplanets Kepler-62 f, Kepler-1652 b, Kepler-452 b, and Kepler-442 b suggests that these planets may maintain a water vapour atmosphere and may in fact be examples of larger ocean worlds. Upon the discovery of new rocky exoplanets beyond the habitable zone, our study can be extended to icy worlds.

Contribution of rational design and fractional rheology on magnetic nanoparticle-based drug targeting in a microvessel with Saffman force

Magnetic nanoparticles based drug targeting is one of the prominent drug targeting methods due to non-invasive treatments, and recovery efficiency. The aim of the present problem is to analyze the trajectories of drug carrier particles and the total volume fraction of magnetic nanoparticles required for capturing purposes close to the tumor region. Due to the complex nature of blood, the viscoelastic Maxwell fluid relation is used to describe blood, and the flow of nanoparticles is investigated using momentum equations with the time-variant Caputo-Fabrizio fractional order expression to capture memory effects. The rational design of the nanoparticles such as size and shape with different aspect ratio along particle-particle interaction, Saffman force and external magnetic force are incorporated in the governing equation. The velocity profile of the fluid is represented in the form of the inverse of Laplace and Hankel transform. The velocity profile is solved by numerical integration and trajectories of the drug carrier particles analyzed by using the fourth order Runge-Kutta method by developing an algorithm. The conclusion drawn from the study shows that drug carriers lead towards the tumor region with long term memory effects, and it is easily captured at the tumor region. Viscoelastic rheology capture possibly opposes the drugs carrying magnetic nanoparticles to capture at tumor regions following a similar phenomenon by Saffman force. Spherical shaped drugs carrying magnetic nanoparticles are more prominent to be targeted to the tumor region than other shaped drugs carrying magnetic nanoparticles. The present study will help biomedical engineers and nanomedicine researchers develop magnetic devices and the next generation of drug carrier particles to treat cancerous tumors.

Identifying applicability viscoelastic systems in the context of improving well casing processe

The object of research in this study is viscoelastic systems used as spacer systems in well casing during drilling. Polymer network-metal ion systems display distinctive properties, facilitating effective well coverage through their normal stresses. The primary problem addressed in this research was optimizing viscoelastic system composition for well casing. Researchers sought the ideal sodium dichromate concentration to maximize viscosity in polyacrylamide-based spacer fluids. This optimization is crucial for enhancing casing cementing quality, especially in challenging geological conditions. Utilizing a precise HAAKE MARS III rheometer, various tests, including shear, oscillatory, frequency, creep, and recovery tests, were performed to assess viscoelastic system rheology. Obtained results of optimal deformation interval for a solution with sodium bichromate is 40 Pa and aluminum sulfate, the yield strength was equal to 110 Pa. This research optimized cross-linker concentration, increasing spacer system viscosity. This enhancement improves well cementing efficiency and allows for operation in challenging geological conditions. The precise rheometer unveiled previously unexplored rheological characteristics. The optimized viscoelastic spacer fluid is invaluable in well casing, especially in challenging geological settings. This research guides the design of process fluids, enhancing casing cementing quality, and improving drilling efficiency and safety. Engineers and researchers can leverage the rheological data for informed decisions and better field performance

Geodetic slip rate partitioning in the central Anninghe and Daliangshan faults: Effects of fault geometry, elastic heterogeneity, and viscoelastic rheology

Geodetic measurements can be employed to estimate the secular slip rates and locking depths of crustal faults, two key parameters which influence assessment of long-term seismic hazard presented by a fault. However, this process requires making assumptions about the rheological properties of the Earth's crust and lithosphere, as well as the fault geometry at depth. Previous geodetic studies have inferred widely varying slip rates and locking depths for the central Xianshuihe-Xiaojiang Fault System, located along the southeastern margin of the Tibetan plateau. In this study, we use updated GNSS measurements, including 13 new velocities, to explore the effects of assumed rheology and fault geometry on the inferred slip rates and locking depths of the subparallel Anninghe (ANH) and Daliangshan (DLS) faults in this region. We demonstrate that only models taking into account the viscoelastic relaxation of the lower crust can resolve the apparent discrepancies. Models assuming a fully elastic rheology suggest very deep locking depths (∼35 km) and a lower slip rate on the ANH fault (∼5 mm/yr) than the DLS fault (∼7 mm/yr). Neither the relative slip rates nor the locking depths agree with seismic or geologic observations. We also consider models assuming a heterogeneous elastic rheology, but find they are indistinguishable from the homogeneous models. Modifying the fault geometry can impact the relative slip rates of the two faults but does not produce a reasonable locking depth either. In contrast, viscoelastic models accounting for seismic cycle effects indicate a faster ANH slip rate (∼5–7 mm/yr), a slower DLS rate (∼4–5 mm/yr), and a shallower locking depth for both faults (∼18 km), all of which are more consistent with independent seismic and geological observations. Our study suggests that steady long-term motion on these faults is modulated by long-lasting viscoelastic effects over a relatively broad region.

Viscoelastic rheology of polymer solution probed by resonant thermal capillary fluctuation

We present a measurement of viscoelastic properties of polymer solutions using resonant thermal capillary fluctuations of the surface of a polymer solution droplet. The instantaneous deflection of a cantilever in contact with the drop surface allows for measuring the nanoscale thermal fluctuations of the interface. From the power spectral density of measured fluctuations, we determine the two components of the rheological (dynamic and elastic viscosity) response of the fluid. Our experimental results were compared with rheological measurements using a classical commercial rheometer. We find a good agreement between the two measurements. Our experiments allow to extend the range for dynamical measurements of rheological properties of the solutions up to 20 000 s−1. Furthermore, our method requires only a small volume of liquid (10 μl) to measure the viscosity and is thus suitable for measurements on precious liquids.

Thermomechanics of ferri-antiferromagnetic phase transition in finitely-strained rocks towards paleomagnetism

The thermodynamic model of visco-elastic deformable magnetic materials at finite strains is formulated in a fully Eulerian way in rates with the aim to describe thermoremanent paleomagnetism in crustal rocks. The Landau theory applied to a ferro-to-para-magnetic phase transition, the gradient theory for magnetization (leading to exchange energy) with general mechanically dependent coefficient, hysteresis in magnetization evolution by Gilbert equation involving objective corotational time derivative of magnetization, and demagnetizing field are considered in the model. The Jeffreys viscoelastic rheology is used with temperature-dependent creep to model solidification or melting transition. The model complies with energy conservation and the Clausius-Duhem entropy inequality.

Engineering alginate/carboxymethylcellulose scaffolds to establish liver cancer spheroids: Evaluation of molecular variances between 2D and 3D models

Natural polymeric hydrogels represent an optimal framework for 3D culture development. This study demonstrates a freeze-thaw-based ionic crosslinking technique for fabricating alginate/carboxymethylcellulose scaffold for culturing human hepatocellular carcinoma, Huh-7 cells to generate 3D spheroids. Consolidating morphological and biomechanical characterization of Alg/CMC scaffolds shows the formation of uniform hydrogels with significant crosslinking (ATR-FTIR), multiscale pores (FE-SEM), swelling/water absorbance, softer texture, viscoelasticity (rheology), spreading nature (contact angle), and degradation rate optimal for 3D culture establishment. The influence of cell seeding density and time with spheroid formation reveals a maximal size of 250–300 μm on day 7. Calcein AM and Propidium iodide staining confirm that a culmination of viable and dead cells generates spheroidal heterogeneity. RT-qPCR in 3D culture against RPL-13 and 2D culture controls indicate an upregulation of E-cadherin, N-cadherin, fibronectin, and integrin α9/β6. Further, western blotting and immunofluorescence confirm the collective display of cellular interactions in 3D spheroids. Thus, the expression profile signifies the role of key genes during the assembly and formation of 3D spheroids in 1%Alg/1%CMC scaffolds with a profound epithelial characteristic. In the future, this study will bring a 3D spheroid model in a platter for elucidating epithelial to mesenchymal transition of cells during in vitro disease modeling.

Viscoelastic Slider Blocks as a Model for a Seismogenic Fault.

In this work, a model is proposed to examine the role of viscoelasticity in the generation of simulated earthquake-like events. This model serves to investigate how nonlinear processes in the Earth's crust affect the triggering and decay patterns of earthquake sequences. These synthetic earthquake events are numerically simulated using a slider-block model containing viscoelastic standard linear solid (SLS) elements to reproduce the dynamics of an earthquake fault. The simulated system exhibits elements of self-organized criticality, and results in the generation of avalanches that behave similarly to naturally occurring seismic events. The model behavior is analyzed using the Epidemic-Type Aftershock Sequence (ETAS) model, which suitably represents the observed triggering and decay patterns; however, parameter estimates deviate from those resulting from natural aftershock sequences. Simulated aftershock sequences from this model are characterized by slightly larger p-values, indicating a faster-than-normal decay of aftershock rates within the system. The ETAS fit, along with realistic simulated frequency-size distributions, supports the inclusion of viscoelastic rheology to model the seismogenic fault dynamics.

Experimental studies and mathematical modeling of the viscoelastic rheology of tracheobronchial mucus from respiratory healthy patients.

Tracheobronchial mucus plays a crucial role in pulmonary function by providing protection against inhaled pathogens. Due to its composition of water, mucins, and other biomolecules, it has a complex viscoelastic rheological behavior. This interplay of both viscous and elastic properties has not been fully described yet. In this study, we characterize the rheology of human mucus using oscillatory and transient tests. Based on the transient tests, we describe the material behavior of mucus under stress and strain loading by mathematical models. Mucus samples were collected from clinically used endotracheal tubes. For rheological characterization, oscillatory amplitude-sweep and frequency-sweep tests, and transient creep-recovery and stress-relaxation tests were performed. The results of the transient test were approximated using the Burgers model, the Weibull distribution, and the six-element Maxwell model. The three-dimensional microstructure of the tracheobronchial mucus was visualized using scanning electron microscope imaging. Amplitude-sweep tests showed storage moduli ranging from 0.1 Pa to 10,000 Pa and a median critical strain of 4%. In frequency-sweep tests, storage and loss moduli increased with frequency, with the median of the storage modulus ranging from 10 Pa to 30 Pa, and the median of the loss modulus from 5 Pa to 14 Pa. The Burgers model approximates the viscoelastic behavior of tracheobronchial mucus during a constant load of stress appropriately (R2 of 0.99), and the Weibull distribution is suitable to predict the recovery of the sample after the removal of this stress (R2 of 0.99). The approximation of the stress-relaxation test data by a six-element Maxwell model shows a larger fit error (R2 of 0.91). This study provides a detailed description of all process steps of characterizing the rheology of tracheobronchial mucus, including sample collection, microstructure visualization, and rheological investigation. Based on this characterization, we provide mathematical models of the rheological behavior of tracheobronchial mucus. These can now be used to simulate mucus flow in the respiratory system through numerical approaches.

Beyond the Stokes approximation: shallow visco-elastic ice-sheet models

Abstract The hypothesis that ice-sheet evolution is only controlled by the long-term non-Newtonian viscous behavior of ice has been challenged by observations indicating that effects like brittle failure, stick-slip sliding, tides and wave action may affect ice-sheet evolution on sub-daily timescales. Over these timescales, the quasi-static-creep approximation is no longer appropriate and elastic effects become important. Simulating elastic effects in ice-sheet models over relevant timescales, however, remains challenging. Here, we show that by including a visco-elastic rheology and reintroducing the oft neglected acceleration term back into the ice-sheet stress balance, we can create a visco-elastic system where the velocity is locally determined and information propagates at the elastic wave speed. Crucially, the elastic wave speed can be treated like an adjustable parameter and set to any value to reproduce a range of phenomena, provided the wave speed is large compared to the viscous velocity. We illustrate the system using three examples. The first two examples demonstrate that the system converges to the steady-state viscous and elastic limits. The third example examines ice-shelf rifting and iceberg calving. This final example hints at the utility of the visco-elastic formulation in treating both long-term evolution and short-term environmental effects.

Evaluating bubble chain phenomena as a mechanism for open system degassing in basaltic systems

Passive degassing – i.e., the open-system degassing of a magmatic gas phase that is decoupled from the melt phase – is common at many basaltic volcanic systems and consistently makes a greater contribution to total volcanic gas emissions than eruptive degassing. However, the mechanism for passive degassing is not fully understood. We investigate the feasibility of permeable gas flow through connected bubbles or pathways using experiments with aqueous solutions of hydroxyethyl cellulose (HEC), a non-Newtonian analogue material for magma. Stable chains of connected bubbles have previously been reported in similar non-Newtonian polymer solutions. We observe a range of bubble chain phenomena and identified five regimes, numbering in order of increasing gas flow rate: 1) small individual bubbles; 2) chains of rounded bubbles; 3) chains of elongate bubbles; 4) pipe-like ‘winding flue’; 5) large individual bubbles. The bubble chain phenomena (regimes 2–4) are observed over a restricted interval of gas flow rates. We determine the rheology of the solutions and conclude that the HEC solutions that produced bubble chain phenomena in our experiments are well scaled to shear-thinning and viscoelastic magmas, hence bubble chain phenomena could form in magmas. Our analysis also suggests that the viscoelastic rheology of HEC plays a fundamental role in the observed bubble chain phenomena.

Numerical-experimental approach to identify the effect of relative humidity on the material parameters of a rate-dependent damage model for polyamide 66

This work aims at identifying the behavior of polyamide 66 (PA66) under different Relative Humidity (RH) conditions using a phenomenological model that accounts for viscoelastic and viscoplastic rheology coupled to ductile damage. An experimental approach is designed considering different loading conditions, namely: monotonic at several strain rates, loading–unloading, creep-recovery, and cyclic tests. These experiments are chosen to discriminate the various active mechanisms governing the nonlinear behavior of PA66. The thermodynamic background of the phenomenological model, the evolution laws, and the accompanying RH-dependent material parameters are presented and discussed. Using the experimental findings, an optimization algorithm is adopted to identify the model parameters. The latter are investigated with regard to the relative humidity, leading hence to the development of a model that accounts for the effect of RH on all inelastic mechanisms and ductile damage. Validation through experimental data for RH = 0%, 25%, 50%, 65%, and 80% reveals that the current model captures the effect of RH and yields mechanical responses in good agreement with experimental findings, notably at higher RH levels. The current numerical-experimental framework presents a unified model for a wide range of humidity conditions and provides a better insight into material properties and rate-dependent inelastic mechanisms under humidity exposure, which typical models do not provide. In addition, the present constitutive law is easily adoptable in micromechanics schemes for the study of polymer based composite materials and structures.

Frequency varying rheology-based fluid–structure-interactions waves in liquid-filled visco-elastic pipes

This contribution proposes a new rheology-based model for water-hammer wave propagation in visco-elastic pipes. Using a long wavelength analysis and a generalized frequency-dependent Hooke-law for the stress/strain relation, the pressure/longitudinal stress coupled wave system is derived. In this general framework, a visco-elastic Fluid–Structure Interaction (FSI) four equations model is derived by having four visco-elastic kernels associated with the non-local time response of the visco-elastic solid. The explicit dependence of these kernels with the material creep function and the pipe dimension is found. Considering a general linear visco-elastic rheology, the four visco-elastic kernels, and the corresponding creep function are explicitly derived in frequency and time-domain versus four visco-elastic parameters. For a given set of boundary conditions, a general analytical solution for the pressure/stress water hammer wave is obtained in frequency domain. The model’s predictions are successfully compared with experimental measurements as well as with other models adjusted to the same experimental data set by calibrating the model’s parameter. The proposed model can be used in many other contexts with the specific ability to distinguish the intrinsic visco-elastic rheology from the considered pipe geometry and boundary conditions.

The Stefan problem in a thermomechanical context with fracture and fluid flow

The classical Stefan problem, concerning mere heat‐transfer during solid‐liquid phase transition, is here enhanced towards mechanical effects. The Eulerian description at large displacements is used with convective and Zaremba‐Jaumann corotational time derivatives, linearized by using the additive Green‐Naghdi's decomposition in (objective) rates. In particular, the liquid phase is a viscoelastic fluid while creep and rupture of the solid phase is considered in the Jeffreys viscoelastic rheology exploiting the phase‐field model and a concept of slightly (so‐called “semi”) compressible materials. The ‐theory for the heat equation is adopted for the Stefan problem relaxed by allowing for kinetic superheating/supercooling effects during the solid‐liquid phase transition. A rigorous proof of existence of weak solutions is provided for an incomplete melting, employing a time discretization approximation.

Evolution of flow reversal and flow heterogeneities in high elasticity wormlike micelles (WLMs) with a yield stress

The formation and evolution of a heterogeneous flow and flow reversal are examined in highly elastic, gel-like wormlike micelles (WLMs) formed from an amphiphilic triblock poloxamer P234 in 2M NaCl. A combination of linear viscoelastic, steady shear, and creep rheology demonstrate that these WLMs have a yield stress and exhibit viscoelastic aging, similar to some soft glassy materials. Nonlinear shear rheology and rheoparticle tracking velocimetry reveal that these poloxamer WLMs undergo a period of strong elastic recoil and flow reversal after the onset of shear startup. As flow reversal subsides, a fluidized high shear rate region and a nearly immobile low shear rate region of fluid form, accompanied by wall slip and elastic instabilities. The features of this flow heterogeneity are reminiscent of those for aging yield stress fluids, where the heterogeneous flow forms during the initial stress overshoot and is sensitive to the inherent stress gradient of the flow geometry. Additionally, macroscopic bands that form transiently above a critical shear rate become “trapped” due to viscoelastic aging in the nearly immobile region. This early onset of the heterogeneous flow during the rapidly decreasing portion of the stress overshoot differs from that typically observed in shear banding WLMs and is proposed to be necessary for observing significant flow reversal. Exploring the early-time, transient behavior of this WLM gel with rheology similar to both WLM solutions and soft glassy materials provides new insights into spatially heterogeneous flows in both of these complex fluids.

History‐Dependent Volcanic Ground Deformation From Broad‐Spectrum Viscoelastic Rheology Around Magma Reservoirs

AbstractGeodetic timeseries suggest that volcanoes exhibit a wide range of deformation patterns. Viscoelastic deformation around crustal magma storage zones is an expected contributor to such observations, but is challenging to characterize robustly. Here we present a novel approach to modeling crustal deformation around magma reservoirs that identifies frequency‐domain signatures of viscoelastic response for temperature‐dependent crustal rheology. We develop a transfer function that links unsteady reservoir pressure forcing to surface displacement, finding that thermomechanical properties and geometry of the magmatic system are encoded in viscoelastic response on timescales where geodetic observations are routinely made. Inhomogeneous viscoelasticity is reflected by spatially variable relaxation of host rocks that results in a viscous aureole whose size depends on the frequency spectrum of forcing. We explore viscoelastic signatures of broadband pressurization episodes, identifying a history dependence of volcano deformation in which past activity influences the stress state and surface deformation patterns of future episodes.