Viscoelastic Medium Research Articles

Effect of geometric disorder on chaotic viscoelastic porous media flows

Many practical applications, such as enhanced oil recovery or groundwater remediation, encounter the flow of viscoelastic fluids in porous media. Once the flow rate exceeds a critical value in such flows, an elastic instability with a fluctuating flow field is observed, which ultimately transits to a more chaotic and turbulence-like flow structure as the flow rate further increases. In this study, we present an extensive numerical investigation of the viscoelastic fluid flows in a model porous media consisting of a microchannel with many micropillars placed in it by considering both their initial staggered and aligned configurations. Within the present range of conditions encompassed in this study, we find that the geometric disorder always increases the chaotic fluctuations irrespective of the initial arrangement of micropillars. We propose that it is due to the formation of preferential paths or lanes and the formation of highly curved streamlines, which results in the local stretching of polymer molecules and, hence, significant origin in the local elastic stresses. We further show that this chaotic flow behavior strongly depends on the competitive influence between the strain-hardening and shear-thinning behaviors of a viscoelastic fluid, which again strongly depends on the polymer extensibility parameter, polymer viscosity ratio, and geometric disorder parameter. In particular, we show that the strain-hardening behavior of a viscoelastic fluid promotes these chaotic fluctuations, whereas the shear-thinning behavior tends to suppress these. Therefore, it is not a general phenomenon that can always be seen in the flows of a viscoelastic fluid in porous media.

Review of Approaches to Formulating Coupled Equations of Interdiffusion in Viscoelastic Media

Review of Approaches to Formulating Coupled Equations of Interdiffusion in Viscoelastic Media

An analytical solution of a horizontally vibrating pile considering water-pile-soil interaction on viscoelastic half-space

The water-pile-soil model on viscoelastic half-space is developed to investigate the dynamic responses of an end-bearing pile subjected to the horizontal dynamic loads. The pile is assumed to be viscoelastic material with a circular cross-section and can be divided into several pile segments in a water-pile-soil system, in which the soil and water are modeled as linear viscoelastic media and linear acoustic media, respectively. The pile-soil with viscoelastic half-space and pile-water with rigid ground vibration are solved by the potential function decomposition and the variable separation method, respectively. The displacement response of the pile is then obtained based on the continuity conditions between the pile and soil and water. The predictions of the present solution are compared with numerical method. Moreover, the present solution can be degenerated into a rigid foundation and verified the rationality with existing analytical solutions and numerical methods. Parametric analyses are further conducted by using the present solution to evaluate the relationships between water and pile-soil parameters, especially focus on the influence of the soil viscoelastic half-space shear modulus. The results indicate that it is necessary to consider the influence of the viscoelastic half-space at the pile end soil when the pile elastic modulus is relatively small in the design of offshore cast-in-place piles.

Modified Generalized R/T Coefficient Method for Surface-Wave Dispersion-Curve Calculation in Elastic and Viscoelastic Media

ABSTRACT This article presents an efficient and effective modified generalized reflection and transmission (R/T) (mGRT) coefficient method for dispersion-curve calculation of the Rayleigh and Love waves. We construct a novel dispersion function based on the kernel function for calculating synthetic seismograms in an elastic layered half-space model. It improves the root searching using the monotonicity of the dispersion function in sections between roots. We introduce an auxiliary function to accelerate the root-searching procedure by approximating the number of roots of the dispersion equation. To solve the low-velocity-layer problem for the generalized R/T coefficient method, we turn to the dispersion function of multiple depths. Numerical results indicate that the proposed method is slightly slower than the other most efficient methods including the delta-matrix method and the fast delta-matrix method. Then, we present a technique for the velocity and attenuation dispersion curves in viscoelastic media. The technique is based on jumping features of the dispersion function and converts 2D root-searching problem to 1D minimization problem. The mGRT method is expected to be a useful candidate for calculating dispersion curves in both elastic and viscoelastic media.

Evaluation of the thermal and mechanical waves in anisotropic fiber-reinforced magnetic viscoelastic solid with temperature-dependent properties using the MGT thermoelastic model

The main objective of the current paper is to provide a modified thermo-viscoelastic mathematical model based on the Moore-Gibson-Thompson (MGT) equation to study the behavior of fiber-reinforced viscoelastic media. To describe the viscoelastic behavior of the fiber-reinforced material, the Kelvin-Voigt type is used. The relaxation time coefficient is included in the Green and Naghdi type III model (GN-III) to solve the problem of the infinite velocity propagation of heat waves. For an infinite viscosity-reinforced elastic solid with a cylindrical cavity, the proposed model was applied to investigate the effects of thermo-mechanical coupling and thermal relaxation coefficients on the studied fields. The cavity surface is considered to be traction-free and subject to temperature changes that fluctuate harmoniously. The Laplace transform tool was used to find analytical solutions for the distributions of different physical fields. The inverse Laplace transforms were calculated numerically using the Fourier series approximation approach. The effect of viscosity and the frequency of heat pulses on the fields under study are shown graphically. A comparison was made between several related models to confirm the effectiveness of the proposed system by presenting the numerical results in tables.

Effects of rocking impedance and soil shear stress of the free-field on the dynamic response of an end-bearing pile during horizontal earthquakes

An increasing number of pile foundation with large diameter are utilized in civil and offshore engineering in areas of active seismicity. This paper focuses on studying the effects of rocking impedance and soil shear stress of the free-field on the horizontal seismic responses of pile foundation. A substructure model in frequency domain is utilized to simulate pile-soil dynamic interaction during horizontal earthquakes. The soil is considered as viscoelastic media and the pile considered as one-dimensional (1D) rod modelled by Timoshenko beam theory. First, the analytical expressions of the horizontal and rocking impedances for an end-bearing pile are obtained. Further, the earthquake input method for 1D finite element analysis of pile-soil interaction on rigid bedrock during horizontal earthquakes are developed, where the soil shear stress of the free-field is considered. Finally, the proposed model is used to investigate the effects of rocking impedance and soil shear stress of the free-field on the seismic response of the pile with different soil and pile parameters.

Deriving the slip-front propagation velocity with slip-dependent and slip-velocity-dependent friction laws via the use of the linear marginal stability hypothesis.

We investigate analytically and numerically the determining factors of the slip front propagation (SFP) velocity. The slip front has two forms characterized by an intruding or extruding front. We assume a one-dimensional viscoelastic medium on a rigid and fixed substrate, and we employ the friction law depending on the slip and slip velocity. Despite this dependency potentially being nonlinear, we use the linear marginal stability hypothesis, which linearizes the governing equationfor the slip, to investigate the intruding and extruding front velocities. The analytically obtained velocities are found to be consistent with the numerical computation where we assume the friction law depends nonlinearly on both the slip and slip velocity. This implies that the linearized friction law is sufficient to capture the dominant features of SFP behavior.

Finite element analysis of viscoelastic media used in abrasive flow machining process

The surface roughness of a part is the most important parameter in view of tribological applications and it also affects the working life of the part during application. The abrasive flow machining (AFM) process is an advanced non-conventional finishing process, used to deburr, polish, and to remove the recast layer from the surface as well as at the edges of the components. In AFM viscoelastic media is used to finish the workpiece with close dimensional tolerance and precision. The viscoelastic media used in the AFM process is laden with abrasive particles. In the present work, a finite element analysis of viscoelastic abrasive media is performed considering the AFM process. A mixture of polyborosiloxane and silicon carbide is used as viscoelastic abrasive media and the AFM process is modeled using ANSYS Polyflow. In the analysis, the flow of viscoelastic abrasive media is assumed to follow the Maxwell model of viscoelastic fluid. The simulations were performed for varying the extrusion pressure for the finishing of an internal cylindrical surface. The results of the simulations were validated with the experimental observation and found in good agreement.

P-094 Fundamental understanding of sperm motion in viscoelastic media

Abstract Study question How does viscosity influence the flagellar beating behaviour of free-swimming bull, mouse, and human sperm? Summary answer Sperm flagellar beating behaviour exhibits a transition from an irregular three-dimensional (3D) beating at 5 mPa·s to an organized two-dimensional (2D) waveform at 20 mPa·s. What is known already Sperm migrate in a complex viscoelastic environment through the female reproductive tract. The viscoelastic properties of the oviductal fluid significantly influence the progressive motility of sperm, acting as one of the key guidance mechanisms in vivo. However, the biomechanics of sperm flagellar activity in response to varying viscosity of the oviductal fluid is poorly understood. Understanding sperm flagellar behaviour in physiologically relevant environments is crucial to understanding reproduction and may help to describe unknown causes of infertility. Lack of high-speed high-resolution imaging techniques and automated image-analysis capabilities have been the main barriers to fully describe the flagellar beating behaviour. Study design, size, duration We used a custom-built high-speed high-resolution dark-field microscopy platform to resolve the flagellar dynamics of human, bull, and mouse sperm near surfaces in viscoelastic media ranging in viscosity from 1 to 250 mPa·s. The imaging system includes an automated image analysis algorithm to quantify sperm flagellar waveform and motility characteristics by extracting the flagellar centreline, reconstructing the waveform and calculating tangent-angle profiles. 20 sperm from 3 different bull, mice and humans were analyzed. Participants/materials, setting, methods Bull, mouse, and human sperm were used in this study. In each experiment, a diluted sperm sample in a buffer supplemented with methylcellulose was used and free-swimming sperm were imaged using dark-field microscopy at 200 frames per second. An automated image analysis algorithm was used to extract sperm flagellar centreline and Proper Orthogonal Decomposition (POD) was then used to study sperm flagellar waveform. Statistical analysis was performed using one-way ANOVA. Main results and the role of chance The reconstructed flagellar beating pattern was different for sperm swimming in low and high-viscosity media. Bull sperm exhibited a lower flagellar beating amplitude along the end piece when swimming in a high-viscosity media, a potential energy-efficient strategy to navigate a high viscosity fluid. The first two dominant POD modes (shape modes) describe more than 90% of the beating pattern for all species. Bull sperm exhibited a transition mode with irregular loops in 5 mPa·s buffer, but the flagellar shape cycle created an organised repetitive circular cycle in 1 mPa.s (3D beating) buffer and at viscosities higher than 5 mPa·s (2D beating). Human sperm also indicated a similar behaviour but with the transition happening at higher viscosities. Mouse sperm in high-viscosity media had a lower flagellar beating amplitude across the principal piece and higher beating amplitude across the end piece. The flagellar shape cycle in mouse sperm showed a periodic flagellar beating behaviour at high-viscosities (>20 mPa·s), but a shape cycle with distorted loops at lower viscosities. Our results showed in quantitative detail that increasing viscosity alters sperm flagellar beating pattern, and how sperm migration behaviour in low viscosity media can be distinct from their swimming behaviour in vivo. Limitations, reasons for caution A more comprehensive study of sperm motility parameters such as curvilinear velocity, average path velocity and straight line velocity with a larger sample size is required to fully characterise sperm swimming behaviour as a function of viscosity. Wider implications of the findings The increasing viscosity of the oviductal fluid regulates the sperm flagellar beating behaviour to switch from a 3D swimming behaviour with irregular shape cycles at lower viscosities to a 2D slithering mode with repetitive circular shape cycles at higher viscosities to achieve a more energy-efficient beating pattern for navigation. Trial registration number Not applicable

Modeling cardiomyocyte mechanics and autoregulation of contractility by mechano-chemo-transduction feedback

SummaryThe heart pumps blood into circulation against vascular resistance and actively regulates the contractile force to compensate for mechanical load changes. Our experimental data show that cardiomyocytes have a mechano-chemo-transduction (MCT) mechanism that increases intracellular transient to enhance contractility in response to increased mechanical load. This study advances the cardiac excitation- signaling-contraction (E-C) coupling model on conceptual and technical fronts. First, we developed analytical and computational models to perform 3-dimensional mechanical analysis of cardiomyocytes contracting in a viscoelastic medium under mechanical load. Next, we proposed an MCT feedback loop in the E-C coupling dynamic system to shift the feedforward paradigm of cardiac E-C coupling to an autoregulation model. Our combined modeling and experimental studies reveal that MCT enables autoregulation of E-C coupling and contractility in single cardiomyocytes, which underlies the heart’s intrinsic autoregulation in compensatory response to load changes in order to maintain the stroke volume and cardiac output.

Probing local chromatin dynamics by tracking telomeres

Chromatin dynamics is key for cell viability and replication. In interphase, chromatin is decondensed, allowing the transcription machinery to access a plethora of DNA loci. Yet, decondensed chromatin occupies almost the entire nucleus, suggesting that DNA molecules can hardly move. Recent reports have even indicated that interphase chromatin behaves like a solid body on mesoscopic scales. To explore the local chromatin dynamics, we have performed single-particle tracking on telomeres under varying conditions. We find that mobile telomeres feature, under all conditions, a strongly subdiffusive, antipersistent motion that is consistent with the monomer motion of a Rouse polymer in viscoelastic media. In addition, telomere trajectories show intermittent accumulations in local niches at physiological conditions, suggesting that the surrounding chromatin reorganizes on these timescales. Reducing the temperature or exposing cells to osmotic stress resulted in a significant reduction of mobile telomeres and the number of visited niches. Altogether, our data indicate a vivid local chromatin dynamics, akin to a semidilute polymer solution, unless perturbations enforce a more rigid or entangled state of chromatin.

Ambient Fluid Rheology Modulates Oscillatory Instabilities in Filament-Motor Systems

Semi-flexible filaments interacting with molecular motors and immersed in rheologically complex and viscoelastic media constitute a common motif in biology. Synthetic mimics of filament-motor systems also feature active or field-activated filaments. A feature common to these active assemblies is the spontaneous emergence of stable oscillations as a collective dynamic response. In nature, the frequency of these emergent oscillations is seen to depend strongly on the viscoelastic characteristics of the ambient medium. Motivated by these observations, we study the instabilities and dynamics of a minimal filament-motor system immersed in model viscoelastic fluids. Using a combination of linear stability analysis and full non-linear numerical solutions, we identify steady states, test the linear stability of these states, derive analytical stability boundaries, and investigate emergent oscillatory solutions. We show that the interplay between motor activity, filament and motor elasticity, and fluid viscoelasticity allows for stable oscillations or limit cycles to bifurcate from steady states. When the ambient fluid is Newtonian, frequencies are controlled by motor kinetics at low viscosities, but decay monotonically with viscosity at high viscosities. In viscoelastic fluids that have the same viscosity as the Newtonian fluid, but additionally allow for elastic energy storage, emergent limit cycles are associated with higher frequencies. The increase in frequency depends on the competition between fluid relaxation time-scales and time-scales associated with motor binding and unbinding. Our results suggest that both the stability and oscillatory properties of active systems may be controlled by tailoring the rheological properties and relaxation times of ambient fluidic environments.

Study of the SH-wave propagation in an MEFR layer bounded by heterogeneous viscoelastic layer and elastic half-space

PurposeThe purpose of this study is stated regarding the impact of the horizontally polarized shear wave vibration on a composite medium in the terms of phase and damped velocity.Design/methodology/approachThe assumed composite is composed of magneto-elastic fiber-reinforced (MEFR) layer constrained between heterogeneous viscoelastic layer and heterogeneous elastic half-space. The considered heterogeneity is associated with the directional rigidity and mass density in the uppermost layer and half-space of quadratic and trigonometric types, respectively. The coupled field equations related to the respective medium are solved analytically by employing the method of separation of variables.FindingsThe dispersion relation of the stated problem is secured by using the continuity assumptions, imposed at the stress-free surface and the interfaces of the expressed medium. The adopted numerical examples are used to compute the dispersion relation and plot the graphs between phase/damped velocity and wave number. Parametric studies on the phase and damped velocity yield five main conclusions: (1) Phase velocity decreases with increasing value of wave number and damped velocity increases up to a certain number and then starts falling simultaneously with increasing magnitude of wave number while keeping the rest parametric values fixed. (2) The presence of heterogeneity in the upper layer enhances the phase velocity and diminishes the damped velocity, but the presence of heterogeneity in the half-space enhances both the phase and damped velocity. (3) The appearance of reinforced parameters enhances the phase velocity for the considered crystalline graphite material and diminishes the phase velocity for the rest materials (carbon fiber-epoxy resin and steel) of the MEFR layer. Similarly, damped velocity decreases for the assumed crystalline graphite material of the MEFR layer and increases for the rest materials of the MEFR layer. (4) The induced dissipation factor due to viscoelastic property shows reversal decreasing and increasing effect on phase and damped velocity of SH-wave. (5) Ascending values of the angle at which the wave crosses the magnetic field increase the phase velocity and decrease the damped velocity for all the considered MEFR examples.Originality/valueTill date, the mathematical modeling as well as vibrational analysis of wave propagation through the composite structure consisting of MEFR layer constrained between viscoelastic media and elastic half-space under the effect of different varying properties with depth remains a new challenging issue for the researchers around the globe. The current analysis is an approach to move ahead in the era of wave propagation in different realistic models based on their parametric studies. Also, these studies are very helpful to find their applications in the field of mechanical, construction, aerospace, automobile, biomedical, marine, manufacturing industries and many branches of science and technology where magnetic fields induced in elastic deformation occur.

Combination of FEM-DQM for nonlinear mechanics of porous GPL-reinforced sandwich nanoplates based on various theories

In this novel work, applying boundary shape function differential quadrature hierarchical finite element method (DQHFEM) will be employed to analyze frequency, damping, bending, and buckling of an embedded sandwich nanoplate using different plate theories such as refined zigzag theory (RZT), sinusoidal shear deformation theory (SSDT), first-order shear deformation theory (FSDT) and classical plate theory (CPT). The face sheets as well as the core layer of the sandwich structure respectively are formed by porous material and nanocomposites reinforced with graphene platelets (GPLs) considering various dispersion. According to the Halpin–Tsai micromechanics model, Young’s modulus, as well as the rule of mixture for density as well as Poisson’s ratio related to the face sheets, can be obtained. Further, for modeling the mentioned sandwich structure much more realistic, Kelvin–Voigt model is applied. In order to gain motion of equations, D’Alembert’s principle is utilized where size influences can be contemplated as well using higher-order strain gradient nonlocal theory. In this comprehensive research, diverse parameters featuring the influences of structural damping, strain gradient parameters, GPL volume percent, dispersion, viscoelastic medium, porosity, boundary edges, and geometric variables upon vibration, buckling, and bending behaviors correlative to this structure. It is ascertained that RZT is the most accurate theory among other mentioned theories in estimating the static and dynamic response of structure which needs no shear correction factors. Moreover, the presence of GPLs can make the entire sandwich structure stiffer and dispersion patterns of pores, as well as GPLs, can affect the vibration, buckling, and bending of the structure.

Hi-C embedded polymer model of Escherichia coli reveals the origin of heterogeneous subdiffusion in chromosomal loci

Underneath its apparently simple architecture, the circular chromosome of Escherichia coli is known for displaying complex dynamics in its cytoplasm, with past investigations hinting at inherently diverse mobilities of chromosomal loci across the genome. To decipher its origin, we simulate the dynamics of genome-wide spectrum of E. coli chromosomal loci, via integrating its experimentally derived Hi-C interaction matrix within a polymer-based model. Our analysis demonstrates that, while the dynamics of the chromosome is subdiffusive in a viscoelastic media, the diffusion constants are strongly dependent of chromosomal loci coordinates and diffusive exponents (α) are widely heterogenous with α≈ 0.36-0.60. The loci-dependent heterogeneous dynamics and mean first-passage times of interloci encounter were found to be modulated via genetically distant interloci communications and is robust even in the presence of active, ATP-dependent noises. Control investigations reveal that the absence of Hi-C-derived interactions in the model would have abolished the traits of heterogeneous loci diffusion, underscoring the key role of loci-specific genetically distant interaction in modulating the underlying heterogeneity of the loci diffusion.

Size effects in adhesive contacts of viscoelastic media

Is the maximum force required to detach a rigid sphere from a viscoelastic substrate dependent on the initial value of the contact radius? Experimental and theoretical investigations reported in the literature have given opposite responses.Here, we try to answer the above question by exploiting a fully deterministic model in which adhesive interactions are described by Lennard-Jones potential and the viscoelastic behaviour with the standard linear solid model.When the approach and retraction phases are performed under quasi-static conditions, the substrate behaves as an elastic medium and, as expected, the pull-off force FPO (i.e., the maximum tensile force) is found to be independent of the maximum contact radius amax reached at the end of loading. Size-dependent effects are instead observed (i.e., the pull-off force FPO changes with amax) when transient effects occur as the larger the contact area, the greater the size of the bulk volume involved in the dissipation. Results are also discussed in the light of viscoelastic crack Persson’s theory, which is modified to capture size effects related to amax.

Microcavitation dynamics in viscoelastic tissue during histotripsy process

Monitoring bubble cavitations and bubble dynamics are essential in enhancing non-invasive ultrasonic ablation methods like histotripsy that mechanically fractionates tissue into acellular debris using microcavitation. Histotripsy can totally fractionate tissue into a liquid-appearing homogenate with no cellular features with enough pulses. In this paper, we present the analysis of the dynamics of cavitation bubbles in a viscoelastic medium subjected to a histotripsy pulse using different fidelities in depicting compressibility and viscoelasticity effects. The mathematical formulation is described based on the Keller–Miksis equation in two models for cavitation bubbles in viscoelastic tissue through histotripsy process; the first model is in neo-Hookean, and the second is in quadratic law Kelvin–Voigt model. The governing model is solved analytically based on the modified Plesset–Zwick method. Analysis of the results reveals that the parameters of Young modulus, viscosity effects and stiffening parameter reduce the growth of cavitation microbubbles through the histotripsy process. The cavitation bubble growth increases when the gel concentration decreases during the histotripsy process.

Research on the underlying mechanism behind abrasive flow machining on micro-slit structures and simulation of viscoelastic media

Research on the underlying mechanism behind abrasive flow machining on micro-slit structures and simulation of viscoelastic media

A comparative study for calculating dispersion curves in viscoelastic multi-layered plates

This study examines and critically compares various commonly used models for calculating complex wavenumbers in viscoelastic orthotropic multi-layer materials (e.g. fiber reinforced polymer laminates). Both exact 3D elasticity theory based methods and approximate methods are considered for wave propagation analysis: (i) global matrix method (GMM), (ii) stiffness matrix method (SMM), (iii) hybrid compliance-stiffness matrix method (HCSMM), (iv) semi analytical finite element (SAFE) method, (v) Legendre polynomial method (LPM), and (vi) fifth order shear deformation theory (5-SDT). A detailed mathematical formulation is provided for each of these techniques.The accuracy and the computational efficiency for calculating complex wavenumbers over a wide frequency range are analyzed for both homogenized and multi-layered viscoelastic orthotropic media. This information is helpful to select the proper method to be used in inversion schemes for material characterization. A comparative analysis is also performed on the computed through thickness displacement fields within the solid medium. The different implemented methods have been compiled in a toolbox with a graphical user interface, called “The Dispersion Box”, and can be freely downloaded from Orta et al. (2022).

On the Long and Short-Range Adhesive Interactions in Viscoelastic Contacts

Recently, tribologists have shown increasing interest in rate-dependent phenomena occurring in viscoelastic fractures. However, in some cases, conflicting results are obtained despite the use of similar theoretical models. For this reason, we try to shed light on the effects that long and short-range adhesion has on the pull-off force in the contact of viscoelastic media by exploiting a recently developed numerical model. We find that, in the limit of long-range adhesion, the unloading velocity has little effect on the pull-off force, which is close to the value predicted by Bradley for rigid bodies. In such case, the detachment process is characterized by a uniform bond-breaking of the contact area, and viscous dissipation involves the bulk material. For medium(short)-range adhesion, the pull-off force is instead a monotonic increasing function of the pulling velocity and, at high speeds, reaches a plateau that is a function of the adiabatic surface energy. In this case, the detachment process is similar to the opening of a circular crack, and viscous dissipation is localized at the contact edge.