Matrix Compaction Research Articles

Rapid Core Formation in Terrestrial Planets by Percolative Flow: In-Situ Imaging of Metallic Melt Migration Under High Pressure/Temperature Conditions

Core formation has left a lasting geochemical signature on the Earth. In order to constrain the composition of the Earth we must fully understand the processes by which newly formed Earth, and the bodies which accreted to it, differentiated. Percolation of iron-rich melt through solid silicate has been invoked as a mechanism for differentiation and core formation in terrestrial bodies in the early solar system. However, to date the contribution of percolation to core formation cannot be assessed due to the absence of data on Fe-rich melt migration velocities. Here we use a novel experimental design to investigate textural changes in an analogue system, Au melt in polycrystalline h-BN, under the high pressure/temperature (PT) of core formation at 3 GPa, relevant to core formation in the early solar system. Using a combination of high resolution, in-situ X-ray tomography and fast 2-D radiographic imaging, we obtain the first direct data on melt migration velocities at high PT. Melt migration is highly variable and episodic, driven by variations in differential pressure during melt migration and matrix compaction. Smaller scale melt processes, representing migration of melt along pre-existing melt networks, give comparatively fast velocities of 0.6-60 µms-1. Ex-situ experiments are used to compare melt networks in analogue systems to Fe-rich melt in silicates. Two competing processes for melt migration are percolation of melt along grain boundaries, and hydraulic fracturing induced by melt injection. Typically, both processes are noted in experimental and natural systems, although the relative importance of each mechanism is variable. Using a simple model for melt flow through a porous media, migration velocities determined here account for full differentiation of Earth-sized bodies within 101 to 103 Myr, for submicron diameter melt bands, or within a few Myr or micron-sized melt bands. This is consistent with rapid timescales inferred from geochemistry for core formation in planetesimals, implying that percolation may have had an important contribution to core differentiation in the Earth.

Modelling komatiitic melt accumulation and segregation in the transition zone

Komatiites are probably produced in very hot mantle upwellings or plumes. Under such conditions, melting will take place deep within the upper mantle or even within the mantle transition zone. Due to its compressibility at such pressures, melt might be denser than olivine, but would remain buoyant with respect to a peridotitic mantle both above and below the olivine–wadsleyite phase boundary because of the presence of its higher temperature and denser garnet. We studied the physics of melting and melt segregation within hot upwelling mantle passing through the transition zone, with particular emphasis on the effect of depth-dependent density contrasts between melt and ambient mantle. Assuming a 1D plume, we solved the two-phase flow equations of the melt-matrix system accounting for matrix compaction and porosity-dependent shear and bulk viscosity. We assumed a constant ascent velocity and melt generation rate. In a first model series, the level of neutral buoyancy zneutr is assumed to lie above the depth of onset of melting, i.e. there exists a region where dense melt may lag behind the solid phases within the rising plume. Depending on two non-dimensional numbers (accumulation number Ac, compaction resistance number Cr) we find four regimes: 1) time-dependent melt accumulation in standing porosity waves that scale with the compaction length. The lowermost of these waves broadens with time until a high melt accumulation zone is formed in steady state. During this transient solitary porosity waves may cross the depth of neutral density and escape. 2) steady-state weak melt accumulation near zneutr, 3) no melt accumulation due to small density contrast or, 4) high matrix viscosity. In regime 4 the high mantle viscosity prevents the opening of pore space necessary to accumulate melt. In a second series, the rising mantle crosses the olivine–wadsleyite phase boundary, which imposes a jump in density contrast between melt and ambient mantle. A sharp melt porosity contrast develops and a large melt porosity accumulates immediately above the phase boundary. Both model series show 1) that not only melt density, but also porosity-dependent matrix viscosity controls the melt ascent or accumulation, 2) that there are parameter ranges and physical conditions which may lead to the accumulation of very large melt porosities (> degree of melting), 3) that in spite of melt being denser than olivine at some depths, in general these melts escape these regions and continue to percolate upward faster than the rising mantle. Melting and melt transport under the conditions predicted by the numerical modelling is able to reproduce the compositions of the main types of komatiite. Thus, the accumulation of large melt fractions, and sequential escape of melt from porosity waves, explains several puzzling features of the geochemical compositions of komatiites.

Impact-induced compaction of primitive solar system solids: The need for mesoscale modelling and experiments

Primitive solar system solids were accreted as highly porous bimodal mixtures of mm-sized chondrules and sub-μm matrix grains. To understand the compaction and lithification of these materials by shock, it is necessary to investigate the process at the mesoscale; i.e., the scale of individual chondrules. Here we document simulations of hypervelocity compaction of primitive materials using the iSALE shock physics model. We compare the numerical methods employed here with shock compaction experiments involving bimodal mixtures of glass beads and silica powder and find good agreement in bulk material response between the experiments and models. The heterogeneous response to shock of bimodal porous mixtures with a composition more appropriate for primitive solids was subsequently investigated: strong temperature dichotomies between the chondrules and matrix were observed (non-porous chondrules remained largely cold, while the porous matrix saw temperature increases of 100’s K). Matrix compaction was heterogeneous, and post-shock porosity was found to be lower on the lee-side of chondrules. The strain in the matrix was shown to be higher near the chondrule rims, in agreement with observations from meteorites. Chondrule flattening in the direction of the shock increases with increasing impact velocity, with flattened chondrules oriented with their semi-minor axis parallel to the shock direction.

Subsurface deformation in hypervelocity cratering experiments into high-porosity tuffs

Hypervelocity impact experiments on porous tuff targets were carried out to determine the effect of porosity on deformation mechanisms in the crater's subsurface. Blocks of Weibern Tuff with about 43% porosity were impacted by 2.5 mm and 12.0 mm diameter steel spheres with velocities between 4.8 km s−1 and 5.6 km s−1. The postimpact subsurface damage was quantified with computer tomography as well as with meso- and microscale analyses of the bisected crater subsurface. The intensity and style of deformation in mineral clasts and the tuff matrix were mapped and their decay with subsurface depth was determined. Subsurface deformation styles include pore space compaction, clast rotation, as well as microfracture formation. Evaluation of the deformation indicates near-surface energy coupling at a calculated depth of burial of ~2 projectile diameters (dp), which is in conflict with the crater shape, which displays a deep, central penetration tube. Subsurface damage extends to ~2 dp beneath the crater floor in the experiments with 2.5 mm projectiles and increases to ~3 dp for 12 mm projectiles. Based on overprinting relationships and the geometrical orientation of deformation features, a sequence of subsurface deformation events was derived (1) matrix compaction, (2) intragranular crack formation in clasts, (3) deformation band formation in the compacted matrix, (4) tensile fracturing.

Laboratory measurement of deformation-induced hydro-mechanical properties of reservoir rock in deep saline aquifers: An experimental study of Hawkesbury formation

The long-term integrity of CO2 storage in deep saline aquifers has become uncertain due to the unsteady character of surrounding factors, and the time-dependent nature of the aquifer's overburden load (the vertical stress imposed on the aquifer by the weight of overlying materials (rock/soil layers), which may vary over time as a result of natural incidents such landslides and earthquakes) is critical. The aim of this study is to identify the influence of overburden load variations on the long-term integrity of the CO2 storage process in deep saline aquifers. High-pressure tri-axial strength and permeability tests, along with acoustic emission (AE) and scanning electron microscopy (SEM) analyses, were conducted on Hawkesbury sandstone obtained from the Gosford basin.According to the results, the injection of CO2 into the Hawkesbury formation may dissolve aquifer rock minerals, enhancing aquifer flow performance and reducing aquifer strength. Increasing the stress applied on the aquifer causes aquifer flow ability to reduce to some extent due to pore matrix compaction. Further increase of the overburden pressure may accelerate the aquifer's flow performance due to dilation-induced pore opening. This permeability transition point occurs earlier at greater CO2 injection pressures and overlaps with the crack formation point of the aquifer rock mass. Therefore, weakening of the rock mass after the transition point can be expected. Importantly, this permeability transition point occurs at lower overburden loads after longer interaction of CO2 with the saline aquifer. This exhibits the long-term risk associated with CO2 sequestration in saline aquifers. Permeability enhancement after the transition point may also produce environmental disasters, such as sudden leakages of injected CO2 from the reservoir to surrounding fresh water aquifers (Evans et al. 2004; Little and Robert 2010), exceeding the specific rates proposed by many regulatory frameworks. Therefore, it is essential to study the long-term integrity of the sequestration process in order to develop a regulatory structure to meet the demands of deep saline sequestration projects.

Effect of triaxial in situ stresses and heterogeneities on absolute permeability of laminated rocks

This work aims at improving our understanding of the effect of triaxial stress on absolute permeability of homogeneous and heterogeneous rocks. Measurements of absolute permeabilities of homogenous and heterogeneous laminated rock samples under hydrostatic and different laboratory-simulated triaxial in situ stress loadings were prepared. Experiments were conducted using homogenous, standard Berea and heterogeneous laminated sandstone cores (with lamination parallel to the flow direction). The effect of in situ stress variation on absolute permeability was investigated. Absolute permeability of homogenous sandstones sample decreased in a uniform manner as the axial load increased below the ultimate shear strength. As axial stress exceeds the radial confining stress, slight increase attributed to microcracks opening was noticed. For laminated sandstones, the scenario is quite different. Permeability shows exactly a similar trend of permeability drop as axial load increases due to inferred matrix compaction. At certain axial load, the permeability starts to increase due to inferred dilatancy of microcracks at the lamina faces and then drops again as axial load increases due to lamina compaction. If the axial load is further increased, pore collapses and grain-to-grain cementing breaks down into pore space followed by microcracks development predominantly parallel to the axial load leading to permeability enhancement. It has been concluded that absolute permeability changes due to lamination opening and closure as a result of loading magnitude and orientation. It is also concluded that permeability of the formation rock is affected by heterogeneity depending on the direction of lamination as well as the state of the stresses applied and loading type.

Cyclic Mechanical Loading Is Essential for Rac1-Mediated Elongation and Remodeling of the Embryonic Mitral Valve

During valvulogenesis, globular endocardial cushions elongate and remodel into highly organized thin fibrous leaflets. Proper regulation of this dynamic process is essential to maintain unidirectional blood flow as the embryonic heart matures. In this study, we tested how mechanosensitive small GTPases, RhoA and Rac1, coordinate atrioventricular valve (AV) differentiation and morphogenesis. RhoA activity and its regulated GTPase-activating protein FilGAP are elevated during early cushion formation but decreased considerably during valve remodeling. In contrast, Rac1 activity was nearly absent in the early cushions but increased substantially as the valve matured. Using gain- and loss-of-function assays, we determined that the RhoA pathway was essential for the contractile myofibroblastic phenotype present in early cushion formation but was surprisingly insufficient to drive matrix compaction during valve maturation. The Rac1 pathway was necessary to induce matrix compaction invitro through increased cell adhesion, elongation, and stress fiber alignment. Facilitating this process, we found that acute cyclic stretch was a potent activator of RhoA and subsequently downregulated Rac1 activity via FilGAP. On the other hand, chronic cyclic stretch reduced active RhoA and downstream FilGAP, which enabled Rac1 activation. Finally, we used partial atrial ligation experiments to confirm invivo that altered cyclic mechanical loading augmented or restricted cushion elongation and thinning, directly through potentiation of active Rac1 and active RhoA, respectively. Together, these results demonstrate that cyclic mechanical signaling coordinates the RhoA to Rac1 signaling transition essential for proper embryonic mitral valve remodeling.

Filamin A Mediates Wound Closure by Promoting Elastic Deformation and Maintenance of Tension in the Collagen Matrix

Cell-mediated remodeling and wound closure are critical for efficient wound healing, but the contribution of actin-binding proteins to contraction of the extracellular matrix is not defined. We examined the role of filamin A (FLNa), an actin filament cross-linking protein, in wound contraction and maintenance of matrix tension. Conditional deletion of FLNa in fibroblasts in mice was associated with ~4 day delay of full-thickness skin wound contraction compared with wild-type (WT) mice. We modeled the healing wound matrix using cultured fibroblasts plated on grid-supported collagen gels that create lateral boundaries, which are analogues to wound margins. In contrast to WT cells, FLNa knockdown (KD) cells could not completely maintain tension when matrix compaction was resisted by boundaries, which manifested as relaxed matrix tension. Similarly, WT cells on cross-linked collagen, which requires higher levels of sustained tension, exhibited approximately fivefold larger deformation fields and approximately twofold greater fiber alignment compared with FLNa KD cells. Maintenance of boundary-resisted tension markedly influenced the elongation of cell extensions: in WT cells, the number (~50%) and length (~300%) of cell extensions were greater than FLNa KD cells. We conclude that FLNa is required for wound contraction, in part by enabling elastic deformation and maintenance of tension in the matrix.

Cadherin-11 coordinates cellular migration and extracellular matrix remodeling during aortic valve maturation

Proper remodeling of the endocardial cushions into thin fibrous valves is essential for gestational progression and long-term function. This process involves dynamic interactions between resident cells and their local environment, much of which is not understood. In this study, we show that deficiency of the cell–cell adhesion protein cadherin-11 (Cad-11) results in significant embryonic and perinatal lethality primarily due to valve related cardiac dysfunction. While endocardial to mesenchymal transformation is not abrogated, mesenchymal cells do not homogeneously cellularize the cushions. These cushions remain thickened with disorganized ECM, resulting in pronounced aortic valve insufficiency. Mice that survive to adulthood maintain thickened and stenotic semilunar valves, but interestingly do not develop calcification. Cad-11 −/− aortic valve leaflets contained reduced Sox9 activity, β1 integrin expression, and RhoA-GTP activity, suggesting that remodeling defects are due to improper migration and/or cellular contraction. Cad-11 deletion or siRNA knockdown reduced migration, eliminated collective migration, and impaired 3D matrix compaction by aortic valve interstitial cells (VIC). Cad-11 depleted cells in culture contained few filopodia, stress fibers, or contact inhibited locomotion. Transfection of Cad-11 depleted cells with constitutively active RhoA restored cell phenotypes. Together, these results identify cadherin-11 mediated adhesive signaling for proper remodeling of the embryonic semilunar valves.

A tool for modelling the breathing of hydride powder in its container while cyclically absorbing and desorbing hydrogen

Hydrogen storage in metal compounds has been actively studied as a way to store energy by G. Sandrock (1999) and M. Latroche (2004) [1,2]. But even if the importance of studying the mechanical behaviour of hydride compounds has been shown early in M. Kawamura et al. (1981) [3] there is still a lack of phenomenological or predictive models for handling this difficulty. In this paper, the use of Discrete Element Modelling (DEM) is investigated as a way to improve our understanding of the mechanical behaviour of hydrides absorbing and desorbing hydrogen, which is also called the hydride breathing phenomenon, and to develop better macroscopic models in the future. Starting from elementary mechanical characterisation of the hydride powder, from matrix compaction dedicated to determine the powder compressibility, to rotating drum, dedicated to determine the flowing ability of the powder, the parameters of the Discrete Element Model are adjusted, and the model is then confronted to the results experimentally obtained on a volume of hydride breathing within an instrumented elementary cell. The method is developed on a TiVCr BCC alloy.The simulations are consistent with experimental results, and have thus been used for a parametric study. This study reveals a strong impact of the slenderness ratio of the hydride powder bed and the particle shape on both powder volume variations and stress variations during the cyclic absorption and desorption of hydrogen.

Strain localization associated with channelized melt migration in upper mantle lithosphere: Insights from the Twin Sisters ultramafic complex, Washington, USA

We present results of field, microstructural, and textural studies in the Twin Sisters ultramafic complex (Washington State) that document localized deformation associated with the formation of dunite channels in naturally deformed upper mantle. The Twin Sisters complex is a well-exposed, virtually unaltered section of upper mantle lithosphere comprised largely of dunite and harzburgite (in cm- to m-scale primary compositional layers), and variably deformed orthopyroxenite and clinopyroxenite dikes. A series of ∼N–S striking, m-scale dunite bands (typically with porphyroclastic texture) occur throughout the study area and crosscut both the primary compositional layers and older orthopyroxenite dikes. Structural relationships suggest that these dunite bands represent former zones of channelized melt migration (i.e., dunite channels), and that strain localization was associated with melt migration. Early formed orthopyroxenite dikes are either absent within cross-cutting dunite channels, or have been displaced within channels relative to their position in the adjacent host rocks. These pre-existing orthopyroxenite dikes provide strain markers illustrating that displacement was localized primarily along channel margins, which have opposite senses of shear. In all cases where offsets were noted, the center of the channel was moved southward relative to its margins. Material flow and strain was, therefore, partitioned within channels during melt migration, and dunite channels did not accommodate net shear displacement of the adjacent host peridotites. Primary compositional layers adjacent to dunite channels document opposite rotation of olivine [100] crystallographic axes on either side of channel margins, consistent with the kinematic reversal inferred from offset markers at the outcrop scale, suggesting that the formation of dunite channels also induced host rock deformation proximal to channels. Strain localization that was focused at the margin of the bands was likely facilitated by melt-induced weakening. Channelized movement within the dunite bands may have resulted from matrix compaction within channels, pressure gradients during melt migration, or a combination of these processes during coaxial deformation.

Effective shear and bulk viscosity of partially molten rock based on elastic moduli theory of a fluid filled poroelastic medium

SUMMARY The effective bulk and shear viscosity of the matrix of a partially molten rock are important properties for the process of melt migration and matrix compaction. A set of porosity-dependent effective bulk and shear viscosity models is presented based on a self-consistent poroelastic formulation for partially molten rock where the melt occurs in spherical, ellipsoidal, film-like or tubular inclusions. For these melt geometries a graphical user interface operated MATLAB program is provided which allows the calculation of effective bulk and shear viscosities as a function of porosity, as well as effective elastic moduli and seismic velocities. For all melt geometries an inverse porosity—dependence of the effective bulk viscosity is found. Depending on the assumed melt geometry, this formulation predicts both the effective bulk and shear viscosity to drop to zero at and above finite melt fractions of 20–50 per cent. Fitting equations are derived allowing direct implementation into two-phase flow melt–matrix formulations.

Serotonin Potentiates Transforming Growth Factor-beta3 Induced Biomechanical Remodeling in Avian Embryonic Atrioventricular Valves

Embryonic heart valve primordia (cushions) maintain unidirectional blood flow during development despite an increasingly demanding mechanical environment. Recent studies demonstrate that atrioventricular (AV) cushions stiffen over gestation, but the molecular mechanisms of this process are unknown. Transforming growth factor-beta (TGFβ) and serotonin (5-HT) signaling modulate tissue biomechanics of postnatal valves, but less is known of their role in the biomechanical remodeling of embryonic valves. In this study, we demonstrate that exogenous TGFβ3 increases AV cushion biomechanical stiffness and residual stress, but paradoxically reduces matrix compaction. We then show that TGFβ3 induces contractile gene expression (RhoA, aSMA) and extracellular matrix expression (col1α2) in cushion mesenchyme, while simultaneously stimulating a two-fold increase in proliferation. Local compaction increased due to an elevated contractile phenotype, but global compaction appeared reduced due to proliferation and ECM synthesis. Blockade of TGFβ type I receptors via SB431542 inhibited the TGFβ3 effects. We next showed that exogenous 5-HT does not influence cushion stiffness by itself, but synergistically increases cushion stiffness with TGFβ3 co-treatment. 5-HT increased TGFβ3 gene expression and also potentiated TGFβ3 induced gene expression in a dose-dependent manner. Blockade of the 5HT2b receptor, but not 5-HT2a receptor or serotonin transporter (SERT), resulted in complete cessation of TGFβ3 induced mechanical strengthening. Finally, systemic 5-HT administration in ovo induced cushion remodeling related defects, including thinned/atretic AV valves, ventricular septal defects, and outflow rotation defects. Elevated 5-HT in ovo resulted in elevated remodeling gene expression and increased TGFβ signaling activity, supporting our ex-vivo findings. Collectively, these results highlight TGFβ/5-HT signaling as a potent mechanism for control of biomechanical remodeling of AV cushions during development.

Vascular smooth muscle cells remodel collagen matrices by long-distance action and anisotropic interaction

While matrix remodeling plays a key role in vascular physiology and pathology, the underlying mechanisms have remained incompletely understood. We studied the remodeling of collagen matrices by individual vascular smooth muscle cells (SMCs), clusters and monolayers. In addition, we focused on the contribution of transglutaminase 2 (TG2), which plays an important role in the remodeling of small arteries. Single SMCs displaced fibers in collagen matrices at distances up to at least 300 μm in the course of 8–12 h. This process involved both ‘hauling up’ of matrix by the cells and local matrix compaction at a distance from the cells, up to 200 μm. This exceeded the distance over which cellular protrusions were active, implicating the involvement of secreted enzymes such as TG2. SMC isolated from TG2 KO mice still showed compaction, with changed dynamics and relaxation. The TG active site inhibitor L682777 blocked local compaction by wild type cells, strongly reducing the displacement of matrix towards the cells. At increasing cell density, cells cooperated to establish compaction. In a ring-shaped collagen matrix, this resulted in preferential displacement in the radial direction, perpendicular to the cellular long axis. This process was unaffected by inhibition of TG2 cross-linking. These results show that SMCs are capable of matrix remodeling by prolonged, gradual compaction along their short axis. This process could add to the 3D organization and remodeling of blood vessels based on the orientation and contraction of SMCs.

Interactions between TGFβ1 and cyclic strain in modulation of myofibroblastic differentiation of canine mitral valve interstitial cells in 3D culture

ObjectivesThe mechanisms of myxomatous valve degeneration (MVD) are poorly understood. Transforming growth factor-beta1 (TGFβ1) induces myofibroblastic activation in mitral valve interstitial cells (MVIC) in static 2D culture, but the roles of more physiological 3D matrix and cyclic mechanical strain are unclear. In this paper, we test the hypothesis that cyclic strain and TGFβ1 interact to modify MVIC phenotype in 3D culture. Animals, materials and methodsMVIC were isolated from dogs with and without MVD and cultured for 7 days in type 1 collagen hydrogels with and without 5 ng/ml TGFβ1. MVIC with MVD were subjected to 15% cyclic equibiaxial strain with static cultures serving as controls. Myofibroblastic phenotype was assessed via 3D matrix compaction, cell morphology, and expression of myofibroblastic (TGFβ3, alpha-smooth muscle actin – αSMA) and fibroblastic (vimentin) markers. ResultsExogenous TGFβ1 increased matrix compaction by canine MVIC with and without MVD, which correlated with increased cell spreading and elongation. TGFβ1 increased αSMA and TGFβ3 gene expression, but not vimentin expression, in 15% cyclically stretched MVIC. Conversely, 15% cyclic strain significantly increased vimentin protein and gene expression, but not αSMA or TGFβ3. 15% cyclic strain however was unable to counteract the effects of TGFβ1 stimulation on MVIC. ConclusionsThese results suggest that TGFβ1 induces myofibroblastic differentiation (MVD phenotype) of canine MVIC in 3D culture, while 15% cyclic strain promotes a more fibroblastic phenotype. Mechanical and biochemical interactions likely regulate MVIC phenotype with dose dependence. 3D culture systems can systematically investigate these phenomena and identify their underlying molecular mechanisms.

Growth factor regulation of corneal keratocyte mechanical phenotypes in 3-D collagen matrices.

To assess how wound healing cytokines and the extracellular matrix (ECM) environment regulate the keratocyte mechanical phenotype. Rabbit corneal keratocytes were plated within standard bovine or rat tail type I collagen matrices (2.5 mg/mL), compressed collagen matrices (approximately 100 mg/mL), or on collagen-coated dishes and cultured for up to 7 days in serum-free media, platelet derived growth factor BB (PDGF BB), insulin-like growth factor (IGF), TGFβ1, TGFβ2, or FGF2. F-actin, α-smooth muscle actin (α-SMA) and collagen fibrils were imaged using confocal microscopy. Cell morphology, local matrix reorganization, and global matrix contraction were quantified digitally. IGF and PDGF BB stimulated elongation of keratocytes and extension of dendritic processes within 3-D matrices, without inducing stress fiber formation or collagen reorganization. In contrast, treatment with TGFβ1 and TGFβ2 increased keratocyte contractility, as indicated by stress fiber formation and matrix compaction and alignment. This transformation was enhanced at higher cell densities within standard 3-D matrices, in which α-SMA was incorporated into stress fibers. In contrast, α-SMA was expressed within compressed 3-D matrices even at low cell density. FGF2 did not produce significant cytoskeletal or matrix reorganization in standard 3-D matrices; however, stress fibers were consistently expressed within compressed collagen matrices and on rigid two-dimensional substrates. Inhibiting Rho kinase blocked both TGFβ- and FGF2-induced stress fiber formation. Keratocytes cultured in IGF or PDGF BB maintain a quiescent mechanical phenotype over a range of matrix environments. In contrast, the mechanical phenotypes induced by FGF and TGFβ vary in response to the structural and/or mechanical properties of the ECM.

Melt segregation inside a partially molten zone: Theory, numerical models and implications

For the problem of matrix compaction and melt segregation a general mush continuity equation is derived, which explicitly expresses the coupling between the melt percolation and the inelastic matrix deformation and closes the governing equation set. Besides, a general equation is obtained, which describes the change in the volume of pore space due to all the possible reasons (inelastic matrix deformation, the phase transitions, and the advection of porosity by the matrix flow). The features of the isothermal melt segregation inside a partially molten zone are demonstrated using one-dimensional (1D) numerical solutions. It follows from the solutions that the pattern and the characteristic time of the melt segregation inside a partially molten zone of thickness L are controlled by the segregation parameter γc = (L/δc)2, where the compaction length δc = k(φ0)η/(φ0μ) depends on the permeability, k, the value of characteristic porosity, φ0, and the viscosities of the matrix, η, and melt, μ. The solutions demonstrate that at any value of γc, layers that are highly enriched in melt compared to the maximum initial porosity are formed in the upper part of the zone. At the same time, the evolution of the system and the segregation time differ considerably in the limits of γc ≪ γ* and γc ≫ γ*, where γ* depends on the boundary and initial conditions of the problem, and γ* is about 80 for the problem of melt segregation inside a partially molten zone with the maximum in the initial melt distribution located in the middle of the zone. At γc ≪ γ*, which corresponds to the segregation of low-viscosity ultrabasic melts (kimberlites, carbonatites), all the melt accumulates to the roof of the zone, and the segregation time does not depend on the matrix permeability and melt viscosity and decreases with an increase in the thickness of the zone as L−1. The latter can be the reason for the formation of clusters of the same age and same composition eruptions characteristic of the kimberlite provinces. In the opposite limiting case, γc ≫ γ*, the segregation time does not depend on the matrix viscosity and scales as L with a wave sequence forming in the upper part of the zone, which, probably, elucidates the origin of the rhythmical layering of the large tholeiitic basalt plutons.

Melt segregation and matrix compaction: the mush continuity equation, compaction/segregation time, implications

SUMMARY Two-phase aggregates, a special case of which is partially molten systems, are commonly modelled as an interpenetrating flow of two viscous liquids and are therefore described in terms of the fluid mechanics. The governing equation set of fluid mechanics describing a two-phase aggregate is incomplete as it consists of nine equations (momentum and mass conservation equations for each phase, and an energy conservation equation) in ten unknowns (six velocity components, two pressures, temperature and melt fraction). In this paper, the general equation closing the governing equation set is derived. It explicitly expresses the condition of the coupling between the liquid percolation and porosity volume change due to which the medium continuity is maintained. Therefore, the equation may be referred to as the mush continuity equation. The character of the closed set solutions is demonstrated using 1-D isothermal models by examples of melt segregation inside a bounded low-melting-degree zone and sediment compaction at the bottom of a reservoir. The compaction/segregation style and time are controlled by the compaction/segregation parameter γc= (L/δc)2 and compaction/segregation length depending on the mushy layer thickness, L, matrix permeability, k, characteristic porosity, φ0, and matrix, η, and fluid, μ, viscosities. At low γc, which approximately corresponds to low-viscosity liquids (kimberlites, carbonatites), the compaction/segregation time scales as L−1, which effectively constrains the molten region thickness at the moment of the segregation, and appears to explain the small volume and clustering of low viscosity magma eruptions characteristic of kimberlites. At high γc the porosity evolves through a formation of a series of isolated waves, which could provide an explanation for the rhythmicity observed in large layered plutons.

Morphology and biomechanics of articular cartilage

Articular cartilage is a hypocellular, aneural, avascular, and alymphatic connective tissue. In adults, articular cartilage comprises a small (1–5%) population of chondrocytes and mostly (80–95%) extracellular matrix. About 60–80% of the ECM’s wet weight consists of extracellular water, which is retained by the negatively charged proteoglycans. There is a strict relationship between cartilage composition and morphological organization and its biomechanical behavior. Water flows through the porous structure by matrix compaction, and the subsequent structural deformation increases with time under the constant compressive load until equilibrium is reached. This time-dependent behavior is described as viscoelastic. Moreover, the mechanical response to stresses differs depending on the direction of the loads applied, due to the inhomogeneous orientation of collagen fibers and other macromolecules. Under compression, the matrix is compacted and pressure in the interstitium rises, forcing water and soluble ions out of the tissue. However, cartilage has very low permeability, which means that very high pressures are required to move water through the tissue. As a consequence, in vivo, fluid pressure accounts for a significant component of total load support, dissipating and minimizing the stresses—a phenomenon called “stress shielding of the solid matrix.” The collagen-proteoglycan matrix is also responsible for the flow-independent viscoelastic shear resistance of articular cartilage. In vivo, shear stresses are observed mostly during compression. In fact, a compression applied to an expandable tissue results in an expansion of the tissue itself, perpendicular to the direction of the load applied. Fortunately, cartilage compression results in stiffening of the tissue: the stiffer the matrix, the more energy is required to stretch the fibers. This leads to an increase in cartilage resistance to shear as compression is applied. Nevertheless a “pitfall” in this mechanism is created by the firm attachment of deep zone cartilage to the tidemark. Here, thick collagen fibers connect the deep zone to the calcified cartilage. In this area, the hard bony substrate prevents any expansion and energy dissipation and, during compression, shear forces attain their highest values. This explains why a hard, blunt impact may cause cartilage to be sheared off the bone, by the unbalanced peak stresses at the bone interface. All these different biomechanical properties coexist during joint motion and they strongly interact with chondrocytes for cartilage matrix maintenance.

Starch–acrylics graft copolymers and blends: Synthesis, characterization, and applications as matrix for drug delivery

AbstractA series of acrylic monomers–starch graft copolymers were prepared by ceric ion initiation method by varying the amount of monomers. These graft copolymers were characterized by IR and 13C‐NMR spectroscopy. It was seen that as the concentration of monomer [acrylic acid (AA), methacrylic acid (MA), and methyl methacrylate (MMA)] increased the percent add‐on increased in all the graft copolymers, whereas grafting efficiency increased initially but showed a slight decrease with further increase in the monomer concentration (except for MMA). The release rate of paracetamol as a model drug from graft copolymers as well as their blends was studied at two different pH, 1.2 and 7.4, spectrophotometrically. The release of paracetamol in phosphate buffer solution at pH 1.2 was insignificant in the first 3 h for St‐g‐PAA‐ and St‐g‐PMA‐graft copolymers, which was attributed to the matrix compaction and stabilization through hydrogen bonding at lower pH. At pH 7.4, the release rate was seen to decrease with increase in add‐on. The tablet containing poly(methyl methacrylate) (PMMA) did not disintegrate at the end of 30–32 h, which may be attributed to the hydrophobic nature of PMMA. These results indicate that the graft copolymers may be useful to overcome the harsh environment of the stomach and can be used as excipients in colon‐targeting matrices. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009