Viscoelastic Shell Research Articles

Review of transport processes and particle self-assembly in acoustically levitated nanofluid droplets

Acoustic levitation has been the cornerstone of many interesting studies across multiple application domains ranging from biomedical engineering to spray drying. In the sphere of colloidal or nanofluid droplets, acoustic levitation allows researchers to probe deep into the physical mechanisms concerning stability, heat and mass transfer processes, and subsequent particle self-assembly. It also offers a plethora of opportunities to custom engineer the transport mechanisms, thereby enabling unique morphological features of the dried precipitate. The high degree of spatial control in a levitator and ease of experimental diagnostics ensure one to study any such transport process in great detail. In this review, we have systematically elucidated three important paradigms in acoustic levitation of nanofluid droplets. First, we have provided a detailed understanding of the fluid mechanics of the process by delving into the pressure and velocity fields the droplet encounters. We have provided descriptions about the key nondimensional number responsible for successful levitation of the droplet. Second, we have studied the transport processes in nanofluid droplets and investigated the important transport mechanisms that are affected by flow and the acoustic field of the levitator. In particular, we look into the heat and mass transfer limitation for particle laden droplets. Third, we have analyzed the particle self-assembly and formation of nanoporous viscoelastic shell. Subsequently, we provided detailed insights into the morphological transitions of the shell through buckling and cavity ingression. We also showcase how the morphology of the shell can be controlled using differential heating and doping. Finally, we conclude by showcasing some unique application context-like photonic crystal behavior that can emerge from unique particle assembly in acoustic levitation.

Modelling of thin viscoelastic shell structures under Reissner–Mindlin kinematic assumption

In this paper, we study thin viscoelastic shell structures using a constitutive equation in hereditary integral form. An alternative mathematical formulations for several viscoelastic shell structures under the Reissner–Mindlin kinematical assumptions are obtained. The resulting equations are written as a Volterra equation of the second kind to allow further mathematical analysis. A locking-free finite element formulation, with selective reduced integration is used to approximate the equation. To perform numerical experiments we consider several situations suffering from locking in both cases dynamic and quasi-static. We show the good behavior of the model compared with other models from the literature.

Parametric study of three-dimensional vibration of viscoelastic cylindrical shells on different boundary conditions

In this research based on theory of elasticity, free vibration behavior of a viscoelastic cylindrical shell with different boundary conditions is studied. A constitutive equation for viscoelastic material is assumed to obey the Boltzmann model and Poisson's ratio is held to be constant. Moreover, the Prony series is used to model time dependent modulus of elasticity. Governing equations of motions for simply-supported edges conditions are solved analytically using the state-space technique along the radial coordinate and the Fourier series method along the axial and circumferential directions. In the case of other edges condition a semi-analytical solution is employed by using the differential quadrature method instead of Fourier series solutions. It is worthy to note before solving the problem, that the Laplace transform is employed to convert governing differential equations from the time-domain into the Laplace domain. Then, validation of the present formulation is performed by comparing the numerical results with those published in the literature. Finally, effect of viscoelastic properties, boundary conditions, the thickness-to-radius ratio and length-to-radius ratio on the frequency behavior are studied.

Viscoelastic relaxation: A mechanism to explain the decennial large surface displacements at the Laguna del Maule silicic volcanic complex

Silicic systems generate the most explosive eruptions on Earth. In contrast to basaltic systems, they can accumulate large volumes of magma without systematically erupting, confronting the classical interpretation that a volcano inflates when a magmatic intrusion occurs. Understanding the mechanisms of volcanic inflation and unrest is thus one of the most important challenges in volcanic risk assessment. Laguna del Maule (LdM) in the Southern Volcanic Zone (SVZ) of Chile, is one of the most active Holocene silicic complexes in the world and it has been inflating since 2007, accumulating 2 m of uplift without erupting. Several geophysical and geochemical studies conclude that a large crystal rich reservoir would be residing beneath LdM, in consistency with other multi-disciplinary studies showing that such crystal-rich reservoirs (“mush zones”) can be maintained beneath silicic volcanoes, fed by mafic magma recharge from below. Nevertheless, the mechanical state of such reservoirs remains unclear. Here, we characterize for the first time the mechanical properties of such a mush reservoir, able to promote large surface displacements such as those measured at LdM. Using a 3D finite element method we simulate a recharge of magma at the base of a crystal rich reservoir, by assuming an overpressurized source surrounded by a large viscoelastic shell. Inversion results show that this model fits the observed temporal and spatial evolution of ground displacements measured with InSAR data and GNSS data between 2007 and 2017. We interpret the temporal behavior of ground displacement at LdM as resulting from two contributions. A magma recharge occurred within the first 4 yr of the active inflation, followed by the viscous response of the large viscoelastic shell, set to a viscosity of 1017 Pas. Compared to a purely elastic solution, our model suggests that up to 50% of the accumulated surface displacement during the ten-year period can be explained by this viscous response, and predicts ongoing displacements 50 yr after the onset of inflation. This model agrees with geophysical and geochemical observations and offers a simple explanation of the temporal evolution of surface displacements. It further allows to reconsider the mechanical behavior of large partially crystallized domains in the upper crust; such significant transient stress transfer over large viscoelastic areas should thus be accounted for in other studies of silicic volcanic complexes.

Experimental research on gel-stabilized foam designed to prevent and control spontaneous combustion of coal

The gel-stabilized foam was prepared successfully by forming gel structure in the bubble film using thickening agent (TA) and crosslinking agent (CLA). The viscosity characteristic, foamability, stability, and microstructure of gel-stabilized foam were investigated systematically. The formation of gel structure reduced the foamability of foaming solution due to the increased viscosity, whereas it increased the foam stability significantly. By comprehensively considering foam expansion ratio >5 and half-life >120 h, the effective component range of gel-stabilized foam was determined as 3.4–5.5 g/L for TA and 2.1–4.0 g/L for CLA. Microstructure and liquid drainage kinetics analysis indicated that gel-stabilized foam demonstrated the smaller average bubble size, lower growth rate of bubble size and drainage rate compared to the traditional aqueous foam, mainly ascribing to the thickened bubble film and the formation of a viscoelastic shell on the bubble surface. The simulation experiment of spontaneous combustion of coal indicated the better inhibition efficiency of gel-stabilized foam to spontaneous combustion of coal than that of traditional foam, as evidenced by higher crossing point temperature, lower emission of carbon monoxide and ethylene for treated coal by gel-stabilized foam, which revealed its better water-retaining property to retard the oxidation of coal. Moreover, gel-stabilized foam will form a complete film on the surface of coal particles to isolate coal from the oxygen to inhibit spontaneous combustion.

Hyperchaos and multistability in the model of two interacting microbubble contrast agents.

We study nonlinear dynamics of two coupled contrast agents that are micrometer size gas bubbles encapsulated into a viscoelastic shell. Such bubbles are used for enhancing ultrasound visualization of blood flow and have other promising applications like targeted drug delivery and noninvasive therapy. Here, we consider a model of two such bubbles interacting via the Bjerknes force and exposed to an external ultrasound field. We demonstrate that in this five-dimensional nonlinear dynamical system, various types of complex dynamics can occur, namely, we observe periodic, quasiperiodic, chaotic, and hypechaotic oscillations of bubbles. We study the bifurcation scenarios leading to the onset of both chaotic and hyperchaotic oscillations. We show that chaotic attractors in the considered system can appear via either the Feigenbaum cascade of period-doubling bifurcations or the Afraimovich-Shilnikov scenario of torus destruction. For the onset of hyperchaotic dynamics, we propose a new bifurcation scenario, which is based on the appearance of a homoclinic chaotic attractor containing a saddle-focus periodic orbit with its two-dimensional unstable manifold. Finally, we demonstrate that the dynamics of two bubbles can be essentially multistable, i.e., various combinations of the coexistence of the above mentioned attractors are possible in this model. These cases include the coexistence of a hyperchaotic regime with an attractor of any other remaining type. Thus, the model of two coupled gas bubbles provides a new example of physically relevant system with multistable hyperchaos.

Experiment and simulation analysis on noise reduction of cylindrical shells with viscoelastic material

In order to solve the problem of mid-low frequency noise reduction in cylindrical shells, the experimental and simulation methods are used to study the noise reduction performance of cylindrical shells with different acoustic covering layers in the mid-low frequency range. Firstly, a cylindrical shell noise reduction experimental device was established, the experiment for cylindrical shell structure and laying a viscoelastic material shell structure were carried out. Acoustic commercial software (LMS Virtual. Lab) was used to establish a finite element model for simulation analysis, the numerical results then compared with the experimental results. Finally, the finite element simulation was applied to study the noise response in the cylindrical cavity of lining different materials and the influence of the laying scheme and thickness of the layer. The results show that, in the case of the same laying rate, the oblique laying has a better noise reduction effect and the amount of noise reduction increases as the laying thickness increases. Under a constant thickness of the foam-butyl rubber, as the proportion of butyl rubber increases, the noise reduction per unit thickness increases, while the noise reduction per unit mass decreases.

Acoustic Waves in a Liquid with Gas Bubbles Covered by a Viscoelastic Shell

The propagation of acoustic waves in a mixture of a liquid with gas bubbles encapsulated with a viscoelastic shell is investigated. The system of differential equations of the disturbed motion of the mixture is given and the dispersion relation is derived. Low-frequency asymptotics of the phase velocity and attenuation coefficient are obtained. The dependence of the equilibrium speed of sound on the perturbation frequency and the dimension of encapsulated bubbles is established and illustrated. The theory is compared with available experimental data.

Magma chambers: what we can, and cannot, learn from volcano geodesy.

Geodetic observations on volcanoes can reveal important aspects of crustal magma chambers. The rate of decay of deformation with distance reflects the centroid depth of the chamber. The amplitude of the deformation is proportional to the product of the pressure change and volume of the reservoir. The ratio of horizontal to vertical displacement is sensitive to chamber shape: sills are efficient at generating vertical displacement, while stocks produce more horizontal deformation. Geodesy alone cannot constrain important parameters such as chamber volume or pressure; furthermore, kinematic models have no predictive power. Elastic response combined with influx proportional to pressure gradient predicts an exponentially decaying flux, leading to saw-tooth inflation cycles observed at some volcanoes. Yet many magmatic systems exhibit more complex temporal behaviour. Wall rock adjacent to magma reservoirs cannot behave fully elastically. Modern conceptual models of magma chambers also include cumulate and/or mush zones, with potentially multi-level melt lenses. A viscoelastic shell surrounding a spherical magma chamber significantly modifies the predicted time-dependent response; post-eruptive inflation can occur without recharge if the magma is sufficiently incompressible relative to the surrounding crust (Segall P. 2016 J. Geophys. Res. Solid Earth, 121, 8501-8522). Numerical calculations confirm this behaviour for both oblate and prolate ellipsoidal chambers surrounded by viscoelastic aureoles. Interestingly, the response to a nearly instantaneous pressure drop during an explosive eruption can be non-monotonic as the rock around the chamber relaxes at different rates. Pressure-dependent recharge of a non-Newtonian magma in an elastic crust leads to an initially high rate of inflation which slows over time; behaviour that has been observed in some magmatic systems. I close by discussing future challenges in volcano geodesy. This article is part of the Theo Murphy meeting issue 'Magma reservoir architecture and dynamics'.

The lateral growth and coalesence of magma systems.

Thermal and mechanical models of magma reservoir growth need to be reconciled with deformation patterns and structural relationships observed at active magma systems. Geophysical observations provide a series of short time-scale snap-shots (100–102 years) of the long-term growth of magmatic bodies (103–106 years). In this paper, we first review evidence for the growth of magmatic systems along structural features and the associated deformation patterns. We then define three distinct growth stages, (1) aligned melt pockets, (2) coalesced reservoirs, (3) highly evolved systems, which can be distinguished using short-term surface observations. We use two-dimensional thermal models to provide first-order constraints on the time scales and conditions associated with coalescence of individual magma bodies into large-scale reservoirs. We find that closely spaced intrusions (less than 1 km apart) can develop combined viscoelastic shells over time scales of 10s kyr and form laterally extensive mush systems over time scales of 10–100 kyr. The highest temperatures and melt fractions occur during a period of thermal relaxation after melt injection has ceased, suggesting that caldera-forming eruptions may preferentially occur long after the main intrusive activity. The coalescence of eruptible melt-rich chambers only occurs for the highest melt supply rates and deepest systems. Thus, these models indicate that, in most cases, conductive heat transfer alone is not sufficient for a full coalescence of magma chambers and that other processes involving mechanical ruptures and mush mobilization are necessary; individual melt lenses can remain isolated for long periods within growing mush systems, and will only mix during eruption or other catastrophic events. The long-term history of the magmatic system is therefore critical in determining rheological structure and hence short-term behaviour. This framework for the development of magmatic systems in the continental crust provides a mechanical basis for the interpretation of unrest at the world's largest volcanoes.This article is part of the Theo Murphy meeting issue ‘Magma reservoir architecture and dynamics'.

Dynamics of a physically nonlinear viscoelastic cylindrical shell with a concentrated mass

Dynamics of a physically nonlinear viscoelastic cylindrical shell with a concentrated mass

Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness

The problem of parametric oscillations of an isotropic viscoelastic shallow shell of variable thickness under periodic load is considered. It is believed that under the influence of specified load, the shallow shell allows displacements (in particular, deflections), commensurate with its thickness. In a geometrically nonlinear statement, taking into account the viscoelastic properties of material, a mathematical model of the problem has been developed using the classical Kirchhoff-Love hypothesis. Using the Bubnov-Galerkin method based on the polynomial approximation of the deflections, the problem is reduced to the study of the system of integro-differential equations, where time is the independent variable. The solution of the system of integrodifferential equations is determined by the proposed numerical method. Based on this method, a numerical solution algorithm is described. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. At the same time, the effect of geometric nonlinearity, viscoelastic properties of material, as well as other physicomechanical and geometric parameters and factors (rheological parameters, thickness, initial shape imperfections, aspect ratios, boundary conditions, excitation coefficient) on the area of dynamic instability is taken into account. The results obtained in this study are in good agreement with the results and data obtained by other authors.

Acoustics of a Liquid with Bubbles Covered by a Viscoelastic Shell

The problem of propagation of acoustic waves in a liquid with gas bubbles covered by a viscoelastic shell has been considered. The dependence of the wave number on the perturbation frequency has been found. The low-frequency asymptotes for the phase velocity and the attenuation coefficient have been deduced. The dependence of the equilibrium sound velocity on the perturbation frequency and size of covered bubbles has been established and illustrated. A comparison of the theory with the known experimental data is presented.

Acoustic of a Liquid with Bubbles, Covered with a Viscoelastic Shell

Acoustic of a Liquid with Bubbles, Covered with a Viscoelastic Shell

Renewed Posteruptive Uplift Following the 2011–2012 Rhyolitic Eruption of Cordón Caulle (Southern Andes, Chile): Evidence for Transient Episodes of Magma Reservoir Recharge During 2012–2018

AbstractThe VEI 4 rhyolitic eruption of Cordón Caulle volcano in 2011–2012 was immediately followed by ∼0.77 m of exponentially decaying uplift during 2012–2015. In this study, we present evidence of additional transient pulses of inflation with interferometric synthetic aperture radar (InSAR) time series during 2016–2018. We also assess whether the 2012–2015 uplift can be explained by viscoelastic relaxation or not. InSAR detected ∼12 cm of uplift during 2016–2017 and ∼5 cm during 2017–2018. The three inflation episodes have very similar spatial scales and can be modeled with the same inflating sill (z ∼ 6 km), but their time evolution is significantly different. Numerical models of a pressurized reservoir surrounded by a viscoelastic shell do not have a better fit than a magma injection model to the 2012–2015 InSAR time series, indicating that magma injection is the most likely mechanism to explain this uplift signal. The spatial similarities of the three pulses suggest that they are produced by episodic magma injection. These magma injection pulses provide the heat to remobilize the crystal mush beneath the volcano on timescales of a few months, but the end of the uplift is not predicted by existing models. None of these uplift pulses were related to abnormal seismicity, and we speculate that they are mostly aseismic because they caused stresses of lower magnitude than the coeruptive stresses. The meter scale displacement observed at Cordón Caulle between 2007 and 2018 suggests that the volcano undergoes episodic cycles of inflation like those observed in silicic calderas.

On the Mechanical Effects of Poroelastic Crystal Mush in Classical Magma Chamber Models

AbstractImproved constraints on the mechanical behavior of magma chambers is essential for understanding volcanic processes; however, the role of crystal mush on the mechanical evolution of magma chambers has not yet been systematically studied. Existing magma chamber models typically consider magma chambers to be isolated melt bodies surrounded by elastic crust. In this study, we develop a physical model to account for the presence and properties of crystal mush in magma chambers and investigate its impact on the mechanical processes during and after injection of new magma. Our model assumes the magma chamber to be a spherical body consisting of a liquid core of fluid magma within a shell of crystal mush that behaves primarily as a poroelastic material. We investigate the characteristics of time‐dependent evolution in the magma chamber, both during and after the injection, and find that quantities such as overpressure and tensile stress continue to evolve after the injection has stopped, a feature that is absent in elastic (mushless) models. The time scales relevant to the postinjection evolution vary from hours to thousands of years, depending on the micromechanical properties of the mush, the viscosity of magma, and chamber size. We compare our poroelastic results to the behavior of a magma chamber with an effectively viscoelastic shell and find that only the poroelastic model displays a time scale dependence on the size of the chamber for any fixed mush volume fraction. This study demonstrates that crystal mush can significantly influence the mechanical behaviors of crustal magmatic reservoirs.

Tidal Deformations of a Viscoelastic Planet

This article studies the tidal deformations of a viscoelastic planet in the gravitational field of the attracting center and satellite. The planet is modeled either as a body consisting of a solid core and a viscoelastic shell rigidly attached to it, or as a uniform isotropic viscoelastic ball. The attracting center and the satellite are modeled by material points. The function describing the dependence of the height of the tidal hump at a fixed point on the planet’s surface on time has been found. Graphs of this function were constructed for the planet “Earth” moving in the gravitational field of the Sun and the Moon. To obtain the result, the method of separation of movements developed by V.G. Vilke for mechanical systems with an infinite number of degrees of freedom is used.

Rolling Dynamics of Nanoscale Elastic Shells Driven by Active Particles.

Self-propelled elastic shells capable of transducing energy to rolling motion could have potential applications as drug delivery vehicles. To understand the dynamics of the nanoscale size elastic shells, we performed molecular dynamics simulations of shells filled with a mixture of active and passive beads placed in contact with an elastic substrate. The shell skin is made of cross-linked polymer chains. The energy transduction from active beads to elastic shell results in stationary, steady rolling, and accelerating states depending on the strength of the shell–substrate adhesion and the magnitude of a force applied to the active beads. In the stationary state, the torque produced by a friction (rolling resistance) force in the contact area balances that due to the external force generated by the active beads, and the shell sticks to the substrate. In the steady rolling state, a rolling friction force balances the driving force, and the shell maintains a constant rolling velocity. The scaling relationship between the magnitude of the driving force and the shell velocity reflects a viscoelastic nature of the shell skin deformation dynamics. In the accelerating state, the energy supplied to a system by active beads exceeds the energy dissipation due to viscoelastic shell deformation in the contact area. Furthermore, the contact area of the shell with a substrate decreases with increasing shell instantaneous velocity.

Nonlinear supersonic flutter for the viscoelastic orthotropic cylindrical shells in supersonic flow

On the example of an orthotropic shell, the problems of the dynamics of thin-walled structures under aerodynamic loading are studied, taking into account the viscoelastic properties of material and geometric nonlinearity. The aerodynamic pressure is determined using the AA. Ilyushin's piston theory. Equations of motion relative to displacements are described by a system of integro-differential equations in partial derivatives. Using the Bubnov–Galerkin method, based on the polynomial approximation of deflections, the problem is reduced to a system of ordinary integro-differential equations, where time is an independent variable. Solutions of integro-differential equations are determined by a numerical method based on the elimination of the singularity in the relaxation kernel of the integral operator. Computational algorithms and applied programs have been developed to solve the problems on the nonlinear flutter for viscoelastic elements of an aircraft. The critical flutter speed for the viscoelastic orthotropic cylindrical shells is determined. It is established that an account of viscoelastic properties of shell material leads to a decrease in the critical flutter.

The inflation of viscoelastic balloons and hollow viscera

For the first time, the problem of the inflation of a nonlinear viscoelastic thick-walled spherical shell is considered. Specifically, the wall has quasilinear viscoelastic constitutive behaviour, which is of fundamental importance in a wide range of applications, particularly in the context of biological systems such as hollow viscera, including the lungs and bladder. Experiments are performed to demonstrate the efficacy of the model in fitting relaxation tests associated with the volumetric inflation of murine bladders . While the associated nonlinear elastic problem of inflation of a balloon has been studied extensively, there is a paucity of studies considering the equivalent nonlinear viscoelastic case. We show that, in contrast to the elastic scenario, the peak pressure associated with the inflation of a neo-Hookean balloon is not independent of the shear modulus of the medium. Moreover, a novel numerical technique is described in order to solve the nonlinear Volterra integral equation in space and time originating from the fundamental problem of inflation and deflation of a thick-walled nonlinear viscoelastic shell under imposed pressure.