Viscous Buckling Research Articles

Evaluation of Physico-Mechanical Properties and Thermal Conduction to Energy-Saving Effects of Wood Compression Layered Structural Materials.

In this study, specimens were prepared from Japanese cedar (Cryptomeria japonica) with different thicknesses to determine the best hot-pressing conditions for wood compression layered structural materials (WCLS) through densification at various temperatures and compressing time conditions. However, residual stress-releasing after densification recovery can cause dimensional instability. To address this issue, the drying set method was combined with the compression-set recovery test to determine the best setting time. As a result, the bending strength and modulus of rupture (MOR) of WCLS increased by 9.98 ± 9.71 to 20.87 ± 13.09% and the modulus of elasticity (MOE) increased by 9.87 ± 11.92 to 22.40 ± 17.97%. The volumetric swelling coefficient (S), water absorption percent (WAP), and equivalent moisture content (EMC) decreased as the drying time increased. The anti-swelling efficiency (ASE) and moisture excluding efficiency (MEE) were found to be the highest at a drying time of 12 h, with values ranging from 13.20 ± 15.11 to 36.46 ± 6.83% and 15.18 ± 1.11 to 19.58 ± 8.31%, respectively. The drying method was found to be effective in increasing dimensional stability. The glass transition temperature (Tg) moved to a lower temperature as the compression-set increased, which was due to plasticization of wood caused by high temperature and pressure. The cell walls of WCLS presented viscous buckling, which provided effective dimensional stability. The thermal conductivity of Japanese cedar and each compression-set WCLS were 0.1863 ± 0.0071, 0.1520 ± 0.0147, 0.1817 ± 0.0106, and 0.1423 ± 0.0137 W/mK, respectively. The thermal conductivity of each WCLS increased with an increase in compression-set, but decreased by 10.67 to 22.52% compared to Japanese cedar. The total electricity energy consumption of each WCLS after 24 h of testing decreased with a trend of 30.50 ± 0.84, 29.83 ± 0.42, 29.57 ± 0.51, and 29.4 ± 0.36 kWH.

Enigmatic surface rolls of the Ellesmere Ice Shelf

Abstract The once-contiguous Ellesmere Ice Shelf, first reported in writing by European explorers in 1876, and now almost completely disintegrated, has rolling, wave-like surface topography, the origin of which we investigate using a viscous buckling instability analysis. We show that rolls can develop during a winter season (~ 100 d) if sea-ice pressure (depth-integrated horizontal stress applied to the seaward front of the Ellesmere Ice Shelf) is sufficiently large (1 MPa m) and ice thickness sufficiently low (1–10 m). Roll wavelength initially depends only on sea-ice pressure, but evolves over time depending on amplitude growth rate. This implies that a thinner ice shelf, with its faster amplitude growth rate, will have a shorter wavelength compared to a thicker ice shelf when sea-ice pressure is equal. A drawback of the viscous buckling mechanism is that roll amplitude decays once sea-ice pressure is removed. However, non-Newtonian ice rheology, where effective viscosity, and thus roll change rate, depends on total applied stress may constrain roll decay rate to be much slower than growth rate and allow roll persistence from year to year. Whether the viscous-buckling mechanism we explore here ultimately can be confirmed as the origin of the Ellesmere Ice Shelf rolls remains for future research.

Solid and hollow metallic glass microneedles for transdermal drug-delivery

Metallic microneedles are attractive for painless transdermal drug-delivery. However, fabrication techniques for metal microneedles are often complex and multi-step. In this study, a scalable manufacturing of metallic microneedle arrays is presented using thermoplastic drawing of metallic glasses. Microneedles with tunable lengths and tips are produced by controlling the rheology and fracture of metallic glass. The same drawing process can generate solid and hollow microneedles simply by varying the thickness of metallic glass. The mechanism of thickness dependent transition from solid to hollow profiles is described by the viscous buckling of metallic liquid. In vitro skin insertion tests demonstrate that both solid and hollow metallic glass microneedles can pierce porcine skin and deliver model drugs.

An adaptive variational finite difference framework for efficient symmetric octree viscosity

While pressure forces are often the bottleneck in (near-)inviscid fluid simulations, viscosity can impose orders of magnitude greater computational costs at lower Reynolds numbers. We propose an implicit octree finite difference discretization that significantly accelerates the solution of the free surface viscosity equations using adaptive staggered grids, while supporting viscous buckling and rotation effects, variable viscosity, and interaction with scripted moving solids. In experimental comparisons against regular grids, our method reduced the number of active velocity degrees of freedom by as much as a factor of 7.7 and reduced linear system solution times by factors between 3.8 and 9.4. We achieve this by developing a novel adaptive variational finite difference methodology for octrees and applying it to the optimization form of the viscosity problem. This yields a linear system that is symmetric positive definite by construction, unlike naive finite difference/volume methods, and much sparser than a hypothetical finite element alternative. Grid refinement studies show spatial convergence at first order in L ∞ and second order in L 1 , while the significantly smaller size of the octree linear systems allows for the solution of viscous forces at higher effective resolutions than with regular grids. We demonstrate the practical benefits of our adaptive scheme by replacing the regular grid viscosity step of a commercial liquid simulator (Houdini) to yield large speed-ups, and by incorporating it into an existing inviscid octree simulator to add support for viscous flows. Animations of viscous liquids pouring, bending, stirring, buckling, and melting illustrate that our octree method offers significant computational gains and excellent visual consistency with its regular grid counterpart.

Buckling of metallic glass supercooled liquid layer during embossing

Embossing of metallic glass supercooled liquids into templates is emerging as a precision net-shaping and surface patterning technique for metals. Here, we report the effect of thickness of metallic glass on template-based embossing. The results show that the existing embossing theory developed for thick samples fails to describe the process when the thickness of metallic glass becomes comparable to the template cavity diameter. The increased flow resistance at the cavity entrance results in viscous buckling of supercooled liquid instead of filling. A phenomenological equation is proposed to describe the thickness dependent filling of template cavities. The buckling phenomenon is analyzed based on the folding model of multilayer viscous media. We show that controlled buckling can be harnessed in the fabrication of metal microtubes, which are desirable for many emerging applications.

Normal faulting and viscous buckling in the Tibetan Plateau induced by a weak lower crust

Flow of weak lower crust has been invoked to reconcile observed topographic gradients, uniform elevations, slow seismic velocity, and high conductivity measured in the Tibetan Plateau, with viscosity estimates of 1016–1021 Pa·s. Here we investigate the dynamic response resulting from a range of lower crust viscosities in a 3-D lithospheric-scale geodynamic simulation of the India–Eurasia collision zone to determine bounds of physically viable lower crustal strengths. We show that thickening of the plateau is accommodated through viscous buckling of the upper crust in response to lower crustal flow for a lower crustal viscosity on the order of 1020 Pa·s. This generates two east–west trending bands of surface subsidence and dilatation consistent with observed normal faulting and estimates of vertical velocity. These results suggest viscous buckling of the upper crust, induced by lower crustal flow from gravitational pressure gradients due to high topography, is responsible for the observed extension in Tibet.

Thermo-mechanical Densification of Populus tomentosa var. tomentosa with Low Moisture Content

This study used thermo-mechanical densification technology to compress low-moisture content (3~5%) rapid-growth Populus tomentosa var. tomentosa trees to produce specimens with a low-compression ratio (small volume loss) and a uniform density profile and desirable properties. Furthermore, the densified specimens were subjected to post-heat treatment at 180, 190, and 200 °C for 2, 3, and 4 h, respectively. Microscopic examination was performed to observe the changes that occurred in the wood vessels after densification. To determine the influence of post-heat treatment on the set recovery, the specimens were subjected to eight cycles of soaking and drying in 20 °C water and two cycles in boiling water. The density profile tendencies of the densified specimens were in accord with undensified specimens. Microscopic observation revealed that the deformations present in the densified wood resulted from the viscous buckling of cell walls without fracture. The volume of the void areas in the specimens decreased uniformly. Post-heat treatment can decrease compressive deformation, especially when applied at 200 °C for 4 h. After two boiling water cycles of soaking and drying, the densified wood still had a certain set recovery. Therefore, densified wood should be used sparingly in high temperature and high humidity environments.

Thermoplastic deformation of poplar wood plasticized by ionic liquids measured by a nonisothermal compression technique

Abstract The in situ thermoplasticization of poplar wood with ionic liquids (ILs) has been investigated. The thermoplastic deformation of wood samples treated with four types of ILs at various concentrations was determined through nonisothermal compression tests by means of a rotational rheometer. Results show that increasing the concentration of ILs reduced softening temperature and increased deformation compared to the untreated control. Scanning electron microscopy revealed that plastic deformation of wood cells from the applied compression stress varied, depending on cell type, and occurred without cell wall fracture. X-ray diffraction analysis of compressed wood showed that wood treated with ILs exhibits a greater crystallinity index than the untreated control. The recovered strain in compressed samples decreased with increasing temperature and concentration of ILs to 18% weight percent gain (WPG) and then decreased slightly to 36% WPG. In treated samples, the combined wood/IL blends demonstrated less thermal stability than wood and ILs alone. Results also show that plastic deformation of IL-treated wood resulted in viscous buckling of unfractured cell walls. This deformation mode likely resulted from the disintegration of intermolecular and intramolecular hydrogen bonding between cell wall polymers through the combined effect of ILs, pressure, and high temperature.

Buckling of Viscous Filaments of a Fluid under Compression Stresses

We study the compression of viscous filaments at constant velocity. If slender enough, the filament bends, a viscous analogue of Euler elastic buckling. We measure the characteristic time of this viscous buckling and discuss the link with the elastic critical compression. We show that the analogy only holds in the limit of large capillary numbers. Otherwise capillarity has a stabilizing effect, which suppresses buckling.

Lubrication of Highly Viscous Core-Annular Flows in Microfluidic Chambers

We investigate the lubrication transition of high-viscosity fluid threads flowing in sheaths of less viscous fluids, i.e., viscous core-annular flows, in microchannels. Focus is given on the flow behavior of threads as they traverse a quasi-two-dimensional diverging-converging slit microfluidic chamber. The role of the viscosity contrast is examined for both miscible and immiscible fluids, and, for the later case, both partially wetting and nonwetting threads are considered. The conditions for lubrication are established in relation to flow rates of injection, interfacial properties, viscosities, and phenomena such as viscous buckling, wetting, breakup, and coalescence.

Density profile and morphology of viscoelastic thermal compressed wood

The viscoelastic thermal compression (VTC) of low-density hybrid poplar (Populus deltoides × Populus trichocarpa) from fast growing trees was performed in order to produce specimens with three different degrees of densification (63, 98, and 132%). The morphology and density profile of the VTC specimens were studied. Three different methods for the preparation of specimens for microscopy were used in order to find a technique that makes it possible to examine the VTC wood microscopically in the completely deformed state. It was found that the abrasive surface preparation of oil-embedded blocks was the most promising technique. Microscopic observation revealed that the deformations in the VTC wood were mostly the result of the viscous buckling of cell walls without fracture. The volume of the void areas in the specimens decreased with the degree of densification. The results showed that the density profile of the VTC wood varied with the degree of densification as a consequence of different temperature and moisture gradients formed before and during wood compression. The density profile is also visible on the cross-section of the VTC specimens.

Numerical simulation of moving free surface problems in polymer processing using volume‐of‐fluid method

AbstractWe have developed a numerical algorithm based on 2D/3D finite element method for solving non‐Newtonian fluid flow with the moving free surface encountered in polymer processing. The power law model is considered as a rheological constitutive equation. The standard Galerkin finite element formulation/penalty formulation are applied to discrctize the governing equations, the volume‐of‐fluid (VOF) scheme is used to track the moving free surface, and the donor‐acceptor model introduced by Hirt and Nichols is modified and implemented on FEM. We applied the numerical scheme to simulate fountain flow and viscous buckling problems. For fountain flow, the numerical prediction of this study is in good agreement with the experimental results of other investigators. For viscous buckling, both 2D and 3D numerical simulations show that the shear thinning effect retards buckling. As this algorithm is very effective in treating moving free surface problems and requires less memory than previous algorithms, it may help solve challenging problems in polymer processing such as transient visroelastic flow simulations with moving free surfaces.

Models for thin viscous sheets

Leading-order equations governing the dynamics of a two-dimensional thin viscous sheet are derived. The inclusion of inertia effects is found to result in an ill-posed model when the sheet is compressed, and the resulting paradox is resolved by rescaling the equations over new length-and timescales which depend on the Reynolds number of the flow and the aspect ratio of the sheet. Physically this implies a dominant lengthscale for transverse displacements during viscous buckling. The theory is generalized to give new models for fully three-dimensional sheets.

Origin of periodically spaced wrinkle ridges on the Tharsis Plateau of Mars

Ridged plains are a major geologic unit on Mars and are a predominant unit on the Tharsis Plateau, a region that has undergone uplift, extension, and extensive shield and flood volcanism. These units, probably flood volcanic in origin, are characterized by landforms classed as wrinkle ridges. Wrinkle ridges are interpreted to be folds, resulting from buckling followed by reverse to thrust faulting (flexure‐fracture). A prominent characteristic of many of the wrinkle ridges on Mars, particularly those in the Tharsis ridge system, is the periodic nature of their spacing. The periodic spacing has been evaluated in six major provinces on the Tharsis Plateau with regions further divided into domains based largely on variation in ridge orientation. The average spacing of the Tharsis ridges, based on 2934 measurements, is 30 km. In an effort to account for the periodic nature of the wrinkle ridges, the ridged plains material is modeled as both a single member and a multilayer with frictionless contacts that has buckled at a critical wavelength of folding. Free slip between layers is assumed based on the possible existence of mechanically weak interbeds in the ridged plains sequence separating groups of flows. The near‐surface mechanical structure in the area of ridged plains is approximated by a strong layer or layers overlying a weak megaregolith of finite thickness overlying a strong basement. Buckling of the ridged plains is assumed to be decoupled from the basement by the weak megaregolith. Decoupling is enhanced if the megaregolith were water‐ or ice‐rich at the time of deformation. The rheologic behavior of the ridged plains and megaregolith is approximated by a linear elastic and linear viscous material. The models are examined for a range in (1) the strength contrast between the ridged plains material and the underlying megaregolith; (2) thickness of the ridged plains material; (3) thickness of the megaregolith; and (4) number of layers. The elastic model can explain the observed ridge spacing only if the ridged plains are relatively thick (≥2400 m) with multiple layers (n > 1) and relatively high contrasts in Young's modulus (E/E0 ≥ 100). The high E/E0 required is possible only if the megaregolith was water‐rich at the time of deformation. Over the same range in values of the parameters, viscous buckling is much less restricted. The viscous model can explain the observed ridge spacing over a wide range in ridged plains thickness (250 m to several kilometers), megaregolith thickness, number of layers (n = 1 to 8) and contrasts in viscosity (η/η0 ≥ 10). In addition, viscous buckling is viable if the megaregolith were dry, water‐rich or ice‐rich at the time of deformation. The absence of folds with a cross‐sectional geometry in the shape of a sinusoid (anticline‐syncline pairs) may be the result of initial deformation of the ridged plains material into low‐amplitude folds (in infinitesimal strain) followed by plastic yielding in the cores of the anticlines (in finite strain). Initial elastic or viscous buckling, coupled with plastic yielding confined to the hinge area followed by the development of reverse to thrust faulting, could account for the asymmetric fold geometry of many of the wrinkle ridges.

Comments on ‘‘Viscous buckling of thin fluid layers’’

Comments on viscus buckling of thin fluid layers are pretented. (AIP)

THEORY OF VISCOUS BUCKLING AND GRAVITY INSTABILITY OF MULTILAYERS WITH LARGE DEFORMATION

An exact treatment of the stability of multilayered viscous fluids in slow motion with large deformations leads to an analog model which includes the effect of gravity. A distinction can be made between true mechanical instability and an apparent instability of purely kinematic nature. A mechanism for concentric folding is derived, leading to predictions in good agreement with experimental results (De Sitter, 1939). Exact equations are obtained for the time history of viscous buckling of multilayered fluids for small deflections superimposed upon a large variable compressible strain. A numerical application to the single embedded layer checks the practical validity of the simplified thin-layer theory with interfacial slip. For gravity instability, the analog model provides a method of analysis applicable to very large deformations in salt structures.

Theory of Viscous Buckling of Multilayered Fluids Undergoing Finite Strain

The equations of fluid mechanics are applied to the problem of small perturbations upon a finite initial strain-rate of a viscous fluid. The magnitude of the viscosity is such that inertia forces are negligible. General solutions are developed for the time history of buckling of a fluid with an arbitrary number of layers of different viscosities under finite compressive deformation. The effect of gravity is taken into account. Numerical solutions are derived for the single layer. Results are compared with values obtained from the theory of elasticity and viscoelasticity. The interest of the theory lies in its application to problems of folding of geological structures.

Fluid Dynamics of Viscous Buckling Applicable to Folding of Layered Rocks

For slow creep under relatively small differential stress rocks may in a first approximation be treated as very viscous fluids. Under such conditions it is therefore possible to apply the theory of fluid dynamics to the evolution of strain in complexes consisting of coherent assemblages of rock bodies with unlike shape and unlike effective viscosities. In this paper fluid dynamics is applied to models simulating layered rocks exposed to compression parallel with layering. As basis for discussion and experimental tests presented in the paper the fluid dynamic theory of the following models is briefly reviewed. (1) Single layer enclosed in uniform surroundings whose dimension normal to the layer is large relative to the characteristic wavelength. (2) Multilayers consisting of alternating competent and incompetent layers; (a) unrestricted by surrounding media, and (b) restricted by surrounding media. In all cases the contacts between adjacent layers are considered welded to prevent free slip. Layer-parallel shear is consequently included in the models. This unfortunately makes the mathematics somewhat cumbersome but also makes the models more realistic representatives of rock structures than free-slip models. The welded-contact model of an embedded single layer gives a somewhat smaller wavelength/thickness ratio than the free-slip model of Biot and others. For multilayers (unrestricted, case b) consisting of many alternating competent and incompetent layers, the welded-contact model gives results very different from the free-slip model. If the spacing between the competent layers, i.e., the thickness of the incompetent layers, is greater than a certain limit, the multilayer will buckle in many folds, whereas at smaller spacing the multilayer will buckle to 1 or ½ wave. Many of the theoretical predictions of the behavior of viscous models apply to elastic models if viscosity coefficients are replaced by rigidity modula in the equations. All important predictions of the theory have been tested by rubber models. Excellent agreement between theory and experiment has been established. The multilayers which buckle to a single wave if unrestricted (by adjacent bodies) will buckle to many waves with a characteristic wavelength if surrounded by uniform viscous materials. Equations for enclosed multilayers of this kind are also developed. A theory is developed for viscous buckling of a thin competent layer embedded in an incompetent layer of limited thickness which in turn is sandwiched between thick competent layers. The latter layers remain straight during compression whereas the middle layer buckles. The wavelength of the buckles is shown to be a function of the spacing between the buckling layer and the straight walls. The case of a multilayer taking the place of the thin central layer in the foregoing case is discussed. The approach throughout the work has been to develop the stream function ^psgr and the derivative velocity components U and V which satisfy the particular boundary conditions of the models. When the correct stream function is found for a particular situation, the situation is completely known from a fluid dynamic point of view because the velocities, the rate of change of strain, the stress variations and the variations of pressure throughout the system all follow by way of the general fluid dynamic equations. The models have been chosen with application to common rock structures in mind.

Contact strain and folding instability of a multilayered body under compression

The contact strain which develops in a host rock during compression-folding of a more “competent” layer is treated mathematically and demonstrated by tests on composite models of rubber sheets and blocks with different rigidities. The contact strain is found to be negligible outside a zone about one initial wavelength wide on either side of the folded sheet. This theoretical conclusion based upon the contact deformation resulting from the initial small-amplitude buckles is also, according to the experimental tests, valid for rather strong buckling. Second-order folding of a thin “competent” layer laying within the contact zone of a thicker buckled “competent” layer is demonstrated by experimental tests. Considerations of the stresses connected with the contact strain and the stress distribution in the buckling “competent” layer itself give a simple expression for the initial stable wavelength which develops in response to compression parallel to the layering. The strain distribution in folded multilayers consisting of a set of thin “competent” sheets evenly spaced in an uniform less “competent” body is considered theoretically. In such multilayers the stable initial wavelength as developed during compression will, according to the theory, increase somewhat with decreasing spacing between the “competent” layers if all other conditions are equal. If the spacing is close enough (the limit depends upon the relative mechanical properties of the two substances) the multilayer will buckle as an unit in the sense that one half-wave covers the whole length of the body. This agrees with compression tests on multilayered rubber blocks. In the last two sections of the paper a theory of viscous buckling of thick layers is developed both for the case of a single layer enclosed in a large uniform body and for the case of a multilayer of alternating “competent” and “incompetent” layers. In this theory shear parallel to layering plays an important part. For a single embedded layer the thick-layer model gives a little smaller wavelength/thickness ratio than the simple but less realistic thin-layer model. For multilayers strain parallel to layering becomes very significant, particularly when the spacing between the competent layers is small, and the thick-layer model differs considerably from the simpler thin-layer model. A theory of buckling of a multilayer withn alternating competent-incompetent layers sandwiched between two very thick uniform bodies is also developed.