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This paper addresses the stability of plane Couette flow in the presence of strong density and viscosity stratifications. It demonstrates the existence of a generalised inflection point that satisfies the generalised Fjørtoft criterion of instability when a minimum of kinematic viscosity is present in the base flow. The characteristic scales associated with this minimum are identified as the primary controlling parameters of the associated instability, regardless of the type of stratification. To support this finding, analytical stability models are derived in the long-wave approximation using piecewise linear base flows. Numerical stability calculations are carried out to validate these models and to provide further information on the production of disturbance vorticity. All instabilities are interpreted as arising from the interaction between two vorticity waves. Depending on the type of stratification, these two waves are produced by different physical mechanisms. When both strong density and viscosity stratifications are present, we show that they result from the concurrent action of shear and inertial baroclinic effects. The stability models developed for simple fluid models ultimately shed light on a recently observed unstable mode in supercritical fluids (Ren et al., J. Fluid Mech., vol. 871, 2019, pp. 831–864), providing a quantitative prediction of the stability diagram and identifying the dominant mechanisms at play. Furthermore, our study suggests that the minimum of kinematic viscosity reached at the Widom line in these fluids is the leading cause of their instability. The existence of similar instabilities in different fluids and flows (e.g. miscible fluids) is finally discussed.
The crystal structure of kaolinite(Pl, a = 5.153(1), b = 8.941 (1), c = 7.403 (1)Å, α = 91.692(3)°, β = 104.860(3)°, γ = 89.822(3)°, specimens from Keokuk geodes) has been refined in detail and that of dickite (Cc, a = 5.1460(3), b = 8.9376(5), c = 14.4244(6) Å, β = 96.761(5)°) has been re-refined, both from powder diffraction data with the Rietveld method. Except for the hydrogen atoms, the layer structures in both clays are very similar and are much as inferred or determined previously by others. The rotation in the tetrahedral sheet is 7(1)°. The two inner hydroxyl O-H bonds in kaolinite are differently oriented; one points into an octahedral vacancy and the other somewhat away from the octahedral sheet and toward the unoccupied center of an oxygen triangle formed by the two apical oxygens and shared basal oxygen of two adjacent SiO4 tetrahedra. All six of the inner surface hydrogen atoms appear to be nearly equally involved in the hydrogen bonding between kaolinite layers in kaolinite.
The formation of hydroxy-Al-interlayered montmorillonite was affected by complexing organic acids. Montmorillonite (<2.0 μm) was aged for three months at an initial pH of 5.0 or 6.0 in AlCl3 solutions containing citric or tannic acid at organic acid/Al molar ratios from 0 to 1.0. The Al/clay ratio in the system was 900 meq Al3+/100 g of montmorillonite. Ion-exchange experiments revealed that organically complexed Al ions have both positive and negative charges. Evidence from X-ray powder diffraction, electron microscopic examination, measurements of specific surface, cation-exchange capacity, organic carbon, and the nature of sorbed Al indicates that citric and tannic acids influence differently the hydroxy-Al interlayer formation in montmorillonite. Hydroxy-Al-citrate can be adsorbed as interlayers in montmorillonite, but hydroxy-Al-tannate exists principally as a separate phase binding the clay particles. The differences observed between the influence of citric and tannic acids on Al interlayering are probably due to their differences in molecular weight (size) and structure.
The diffusion of exchanged Yb, Ho, and Eu from interlayer positions in montmorillonite was studied using infrared spectroscopy (IR), X-ray powder diffraction, and cation-exchange measurements. Dehydration of exchanged montmorillonite between 100° and 280°C caused the ions to diffuse into the hexagonal rings of surface oxygens. Subsequent migration into vacant octahedral sites was small regardless of the radius of the cation. Considerable ion fixation in excess of the cation-exchange capacity of the clay was observed at 20°C in both water and a 1:1 water:95% ethanol mixture. Evidence for hydrolysis as a possible mechanism for cation fixation was obtained by observing frequency shifts for deuterated hydroxyl groups using IR spectroscopy. A major IR band centered at 2680 cm−1 was observed for all three lanthanide-exchanged montmorillonites studied and assigned to the OH-stretching frequency of a lanthanide hydroxide. This band intensified on heating at 300°C for 1 hr. An IR band between 690 and 710 cm−1 also was observed for all three lanthanide-exchanged montmorillonites and was assigned to a lanthanide-hydroxyl deformation mode. No hydrolysis was observed for Na-montmorillonite, as expected from the very low hydration energy of Na+.
Saponites and vermiculites may assume at least 11 ordered or semi-ordered layer stacking sequences. For a given relative humidity, the layer stacking type assumed is a function of the nature of the interlayer cation, the layer charge density, the mean size of the particles, and the di- or trioctahedral character of the sheets. For each interlayer cation, a succession of layer stacking types can be observed as relative humidity increases. For high relative humidity, some particular layer stacking types exist, but only for low-charge minerals. No other differences have been found for saponites and vermiculites in each successive layer stacking type. The degree of order that these layer stacking types imply is probably due to the existence of electrostatic bonds between hydrated interlayer cations and surface oxygens of the substituted tetrahedra. For octahedrally substituted 2:1 phyllosilicates, however, the disorder of the layer stacking sequences is related to a highly delocalized distribution of negative charges on the surface oxygens of the layers.
A study of the superstructures detected in saponites and vermiculites indicates that the interlayer cations tend to be located as far as possible from one another. The superstructures exist only with some cations and some layer stacking types and if the layer charge density is compatible with the charge produced by the cation distribution in this kind of superstructure.
Clays may catalyze chemical reactions by acting as Brönsted acids, Lewis acids, and/or Lewis bases. The changes occurring when limonene (p-menthadiene) is heated in the presence of montmorillonite illustrate how Brönsted and Lewis acidity may operate competitively, the nature of the interlayer cations determining which reaction dominates. The rate at which the starting material disappears increases with the acidity of the clay, which depends upon the interlayer cations (Na < Mg < Al < H). The concentration of disproportionation and isomerization products reaches a maximum after reaction times which decrease with increasing surface acidity of the clay, p-cymene is produced by oxidation in concentrations inversely related to the surface acidity of the clay. The course of the chemical reaction can thus be steered in the preferred direction by an appropriate choice of interlayer cations.
Aqueous Al passes from octahedral to tetrahedral coordination over a narrow pH interval, or threshold. This interval is 5.5–6.5 at 25°C and shifts to lower pH as temperature increases. The concentration of aqueous tetrahedrally coordinated Al is a quasi-step function of the solution pH, and, by the mass-action law, so should be the amount of tetrahedral Al incorporated by a silicate that crystallizes from the aqueous solution. Qualitative support for this prediction (which applies to quartz, opal-CT, kaolin-group minerals, pyrophyllite, micas, chlorites, and other low-temperature silicates) comes from the very topology of equilibrium activity diagrams and from several pairs of associated waters and authigenic silicates from weathering, hydrothermal, and diagenetic environments. The uptake of tetrahedral Al also depends on the aqueous concentrations of monovalent cations and silica, and on the mineral's structural constraints.
Solid solution of tetrahedral Al in halloysite in turn produces the characteristic bent or tubular crystals of this mineral. This genetic link between aqueous chemistry (mainly pH), tetrahedral-Al uptake by a low-temperature silicate, and the mineral's crystal morphology may operate also in other silicates.
Fourier-transform infrared (FTIR) spectroscopic studies were carried out on 1,6-hexanediamine hydrochloride (HDA)-treated synthetic fluorhectorite to determine the orientation of functional groups within the structure. Oriented crystal layers were prepared by flocculating the smectite slurry with glass fibers to obtain a 100-µm-thick paper. Orientations were determined by measuring integrated IR band intensities at various incident beam angles (≤60°), inasmuch as absorption occurred only if the oscillating dipole of the functional group interacted with the electric vector of the incident radiation. The H-N-H plane in amine groups was aligned parallel to the lamellar plane. The H-O-H plane of the small amount of sorbed water was inclined 45° or more to the interlamellar layer, and the OH groups were inclined 45° to this layer.
Even with the incorporation of HDA in the interlamellar structure, at high humidity, additional water sorbed. The sorbed water competed with and displaced amine groups from the surface, resulting in randomly oriented amine groups. Many of the amine groups were ionized, whereas the additional sorbed water showed little orientation.
This study demonstrated that the orientation of intercalated amines in fluorhectorite can be determined by following the intensity changes in infrared-active bands as a function of the incident beam angle. With intercalated HDA, the orientations were influenced by the presence of interlayer water.
Unraveling the neurobiological foundations of childhood maltreatment is important due to the persistent associations with adverse mental health outcomes. However, the mechanisms through which abuse and neglect disturb resting-state network connectivity remain elusive. Moreover, it remains unclear if positive parenting can mitigate the negative impact of childhood maltreatment on network connectivity. We analyzed a cohort of 194 adolescents and young adults (aged 14–25, 47.42% female) from the Neuroscience in Psychiatry Network (NSPN) to investigate the impact of childhood abuse and neglect on resting-state network connectivity. Specifically, we examined the SAN, DMN, FPN, DAN, and VAN over time. We also explored the moderating role of positive parenting. The results showed that childhood abuse was linked to stronger connectivity within the SAN and VAN, as well as between the DMN-DAN, DMN-VAN, DMN-SAN, SAN-DAN, FPN-DAN, SAN-VAN, and VAN-DAN networks about 18 months later. Positive parenting during childhood buffered the negative impact of childhood abuse on network connectivity. To our knowledge, this is the first study to demonstrate the protective effect of positive parenting on network connectivity following childhood abuse. These findings not only highlight the importance of positive parenting but also lead to a better understanding of the neurobiology and resilience mechanisms of childhood maltreatment.
Glauconites in early ankerite concretions, ferroan calcite-cemented sandstones, and uncemented sandstones in the first Wilcox sandstone of the Lockhart Crossing field, Livingston Parish, Louisiana, show a progressive substitution of Fe for octahedral Al with increasing diagenesis. An octahedral Fe content of 0.50 atoms was calculated from glauconite located in early ankeritic concretions. Octahedral Fe averaged 0.60 and 0.90 atoms in later ferroan calcite-cemented sandstone and uncemented sandstone, respectively. Corresponding octahedral Al averages were 1.16, 1.03, and 0.67, respectively. A systematic increase in average interlayer K from 0.49 to 0.54 to 0.61 was also observed, with apparent increases in diagenesis. All element determinations were made with an electron microprobe and recast on an anion equivalent basis to structural formulae based on the O10(OH)2 unit. The clay preserved in the early ankerite concretions was found to be an illite/smectite containing about 20% expandable layers, and the mineral in the glauconite pellets from uncemented areas of the sandstone, an ordered glauconite. “Minus cement” porosities of the sandstone indicate that glauconitization may have taken place at burial depths greater than 0.6 to 1.8 km, but the mechanism for the incorporation of Fe3+ in the glauconite at that depth is not apparent.