Local Isotherm Research Articles

Three-temperature radiation hydrodynamics with PLUTO: Thermal and kinematic signatures of accreting protoplanets

In circumstellar disks around young stars, the gravitational influence of nascent planets produces telltale patterns in density, temperature, and kinematics. To better understand these signatures, we first performed 3D hydrodynamical simulations of a 0.012 M⊙ disk with a Saturn-mass planet orbiting circularly in-plane at 40 au. We tested four different disk thermodynamic prescriptions (in increasing order of complexity: local isothermality, β cooling, two-temperature radiation hydrodynamics, and three-temperature radiation hydrodynamics), finding that β cooling offers a reasonable approximation for the three-temperature approach when the planet is not massive or luminous enough to substantially alter the background temperature and density structure. Thereafter, using the three-temperature scheme, we relaxed this assumption, simulating a range of different planet masses (Neptune-mass, Saturn-mass, and Jupiter-mass) and accretion luminosities (0 and 10−3 L⊙) in the same disk. Our investigation revealed that signatures of disk–planet interaction strengthen with increasing planet mass, with circumplanetary flows becoming prominent in the high-planet-mass regime. Accretion luminosity, which adds pressure support around the planet, was found to weaken the midplane Doppler flip, which is potentially visible in optically thin tracers such as C18O, while strengthening the spiral signature, particularly in upper disk layers sensitive to thicker lines, such as those of 12CO.

New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants.

New sorption isotherms for heterogeneous sorbents are derived by combining a Gamma distribution of binding constants with a local isotherm defined by a Langmuir or Hill equation. The new "Gamma isotherms" are expressed as Stieltjes transforms of the distribution and involve generalized exponential integrals. The related energy distributions are asymmetric and present a peak corresponding to the mean binding constant. The advantages of the new isotherms are (1) at low pressures or concentrations, with a Langmuir local isotherm, the global "Gamma-Langmuir" isotherm retrieves Henry's law; (2) contrary to the power Freundlich or hypergeometric Freundlich global isotherms, these Gamma isotherms do not need a redefinition of the standard state; (3) with a Hill local isotherm, the global "Gamma-Hill" isotherm allows a separate estimation of the cooperativity and heterogeneity parameters; and (4) the condensation approximation is a good approximation if the local isotherm is Hill and displays a high degree of cooperativity. The Gamma-Langmuir model is applied to three examples from the literature, with rather different Gamma distributions.

Intraseasonal variability of the deep scattering layer induced by mesoscale eddy

The deep scattering layer (DSL), a stratum of the marine diel vertical migration (DVM) organisms inhabiting the mesopelagic ocean, plays a crucial role in transporting carbon and nutrients from the surface to depth through the migration of its organisms. Using 18 months of in-situ observations and altimeter sea level data, we reveal for the first time the intraseasonal variations and underlying mechanisms of the DSL and the DVM to the east of the Taiwan Island. Substantial vertical speeds acquired from the Acoustic Doppler Current Profiler were used to examine the distribution and variation of the DVM. Innovatively, the results for the power spectrum analysis of the scattering intensity demonstrated a significant intraseasonal variability (ISV) with an 80-day period in the DSL. Furthermore, the variation in the DVM was closely linked to the DSL and showed an 80-day ISV during the observation. A dynamic relationship between the ISV of the DSL east of Taiwan Island and the westward-propagating mesoscale eddies was established. Anticyclonic (cyclonic) eddy movement toward Taiwan Island triggers downward (upward) bending of the local isotherms, resulting in a layer of DSL warming (cooling) and subsequent upper boundary layer deepening (rising). These findings underscore the substantial influence of mesoscale eddies on biological activity in the mesopelagic ocean, establishing a novel understanding of ISV dynamics in the DSL and their links to eddy-induced processes.

Three-temperature radiation hydrodynamics with PLUTO

In circumstellar disks around T Tauri stars, visible and near-infrared stellar irradiation is intercepted by dust at the disk’s optical surface and reprocessed into thermal infrared. It subsequently undergoes radiative diffusion through the optically thick bulk of the disk. The gas component, overwhelmingly dominated by mass but contributing little to the opacity, is heated primarily by gas-grain collisions. However, in hydrodynamical simulations, typical models for this heating process (local isothermality, β-cooling, and two-temperature radiation hydrodynamics) incorporate simplifying assumptions that limit their ranges of validity. To build on these methods, we developed a “three-temperature” numerical scheme, which self-consistently models energy exchange between gas, dust, and radiation, as a part of the PLUTO radiation-hydrodynamics code. With a range of test problems in 0D, 1D, 2D, and 3D, we demonstrate the efficacy of our method and make the case for its applicability across a wide range of problems in disk physics, including hydrodynamic instabilities and disk-planet interactions.

Electron microscopy approach to the wetting dynamics of single organosilanized mesopores

Columnar mesoporous silicon (PSi) with hydrophobic vs. hydrophilic chemistries was chosen as a model for the local (pore-by-pore) study of water-pore interactions. Tomographic reconstructions provided a 3D view of the ramified pore structure. An in situ study of PSi wetting was conducted for categorized pore diameters by environmental scanning TEM. An appropriate setting of the contrast allows for the normalization of the gray scale in the images as a function of relative humidity (RH). This allows constructing an isotherm for each single pore and a subsequent averaging provides an isotherm for each pore size range. The isotherms systematically point to an initial adsorption through the formation of water adlayers, followed by a capillary filling process at higher RH. The local isotherms correlate with (global) gravimetric determination of wetting. Our results point at the validation of a technique for the study of aging and stability of single-pore nanoscale devices.

Clustering function and minimum change in spreading pressure as key factor to predict storage conditions for black pepper oleoresin encapsulated by spray drying

Black pepper oleoresin was encapsulated by spray drying using gum arabic (GA) and whey protein concentrate (WPC) as wall materials. The physical surface features were examined using low-temperature adsorption of nitrogen at 77 K. Clustering function and spreading pressure were evaluated to predict optimal storage conditions of the microcapsules, through analyzing the data from the water adsorption isotherms determined using a gravimetric method at 25, 35, and 45 °C. Kinetic studies of the color changes and loss of piperine of the microcapsules stored at different water activities at 35 °C were carried out. It was found that the GAB, BET and Condon models adequately describe the sorption characteristics. The monolayers calculated with the clustering function and minimum change in spreading pressure (MCSP) were close to those obtained by the adsorption models. The isotherms local from the Condon model coincided with the levels of stability of the microcapsules. Two local isotherms were found for GA microcapsules, which exhibited two regions of chemical stability during storage. One region with high stability in the range of 0.108–0.515 aw, and the other with poor stability of 0.515–0.821 aw. Conversely, WPC microcapsules showed one isotherm local, which had high stability in the entire water activity range studied. For both microcapsules, the lowest values of color changes were of 1.5–4, while the degradation rate constants were −0.017 day−1 and -0.002 day−1 for GA and WPC, respectively. The water activities where occurred the optimal stability fall within of the MCSP zone.

Approximate analytical overall isotherms: lateral interactions of adsorbate species and patchwise topology

Approximate analytical solutions for the overall adsorption functions based on the Fowler-Guggenheim local isotherm with a patchwise topology of adsorption centres location and four different adsorption heat distribution functions have been obtained. The Gaussian, constant, linear (as a particular case of power distribution), and exponential distribution functions have been applied. Overall adsorption functions have been analytically obtained, studied and commented. The Gaussian-related adsorption function reproduces the classic computational result nearly perfectly.

Xenon adsorption isotherms on chabazite. Statistical physics modeling investigation: Adsorption energy and pore size distributions computation

In order to investigate the toxic Xenon removal by an adsorption process on chabazite, the grand canonical formalism of statistical physics has been used. This conducted statistical physics treatment enabled us to draw information about the interactions between Xenon atoms and chabazite surface through the determined physico-chemical parameters. The adsorption energy and pore size distributions have been derived by using an integral expression based on a monolayer model as local isotherm. The fitted values of the steric coefficient showed that one chabazite active site can trap only one Xenon atom. The evaluated densities of receptor sites played an important role in the assess of the adsorption capacity. Ca−CHA sample showed the maximum adsorption capacity (2.36 mmol.g−1). By using the adsorption energy distributions (GD), the physisorbed character of the Xenon adsorption on chabazite samples was brought out. The diversification of the active sites is noticed for all chabazite samples. The highest adsorption energies are observed in the case of the Xenon adsorption on CA−CHA sample. Furthermore, by using the pore size distribution (PSD), the microporous character of all samples (Ca−CHA, Cs−CHA, Li−CHA, K−CHA and Rb−CHA) has been showed. The maximum surface area was found to be 187.23 m2. g−1 for Ca−CHA. The calculated surface tensions are in the range [10.07E-5 N.m−1-13.46E-5 N.m−1]. Finally, by combining the thermodynamical and statistical physics treatments, the chemical potential describing the Xenon adsorption, is calculated at different pressures.

The Henry constant and isosteric heat at zero loading for adsorption on energetically heterogeneous solids absolute versus excess

We present a self-consistent analysis of adsorption of gases on energetically heterogeneous solids and derive expressions for the Henry constant and the isosteric heat at zero loading, qst(0), for both excess and absolute amounts of molecules; the latter being amenable to thermodynamic analysis. Results obtained by Monte Carlo integration are shown to depend on the system size for calculations using the total number of molecules in the adsorbed and gas phases of the system. In the limit when loading approaches zero, the thermodynamic variables obtained from the fluctuation theory in a grand canonical simulation are in agreement with the Henry constant and the isosteric heat at zero loading calculated from Monte Carlo integration, establishing the consistency of the analysis of isotherm and isosteric heat for the full range of loading. The equations for the isotherm (and the Henry constant), and the isosteric heat for a complex substrate, can be written in terms of the local isotherms and the local isosteric heats of the components comprising the substrate for all loadings. This results in a significant saving in computing time for the calculation of the thermodynamic variables of a complex substrate.

Stereographic and energetic studies of acid blue 9 adsorption onto Spirulina platensis (strain LEB-52) based on statistical physics approach

A monolayer model extended to two energy levels (monolayer model 2) has been developed to fit the adsorption isotherms of acid blue 9 on Spirulina platensis (Sp LEB-52). These isotherms were obtained at different values of pH and different temperatures. The adsorption isotherm modeling was based on a statistical physics approach. The evolutions of stereographic and energetic parameters involved in the model equation were presented in this work. The obtained values of nd1 and nd2 are always higher than unity, indicating that the adsorption of acid blue 9 molecules on Sp LEB-52 is a multimolecular adsorption. The highest adsorption capacity (Qs = 1251.8 mg g−1) is signaled at pH = 4 and T = 298.15 K. Furthermore, we have used the monolayer model 2 as local isotherm to determine the adsorption energy distribution (AED) and the pore size distribution (PSD). The adsorption energy values corresponding to active sites of type 1 and type 2 are, respectively, in the intervals [10.5 − 27.5 kJ mol−1] and [15 − 25 kJ mol−1]. Obtained PSDs indicate that acid blue 9 molecules are adsorbed on macro-pores of Sp LEB-52.

Effect of organic matter on phosphorus adsorption and desorption in a black soil from Northeast China

Phosphorus (P) adsorption–desorption in soil is an important internal cycle related to soil fertility problems, as well as for determining the environmental fate of P. Soil organic matter (SOM) has been identified as an important factor affecting the adsorption–desorption of soil P through different mechanisms. In this study, humic acids were added to change the SOM content in black soil. Following an incubation period of 30 days, the changes in soil P adsorption–desorption capacity were studied. The results indicated that increased SOM led to increases in the soil available P and the P activation coefficient. All soil treatments fitted well with both Langmuir and Freundlich equations. The P adsorption and desorption characteristics were analyzed using the Langmuir equation as a local isotherm. The maximum adsorption capacity of P increased with the increase in SOM, but the P bonding energy and maximum buffering capacity first decreased, and then increased, with the lowest values obtained with a SOM content of 75.3 mg kg−1. Both the maximum desorption capacity of P and the ratio of soil P desorption showed a fluctuating trend, which were the greatest when the SOM content reached 75.3 g kg−1 in black soil, showing an improved ability to release P. Thus, the addition of organic matter could efficiently enhance P availability by reducing the strength of P adsorption and the maximum phosphate buffering capacity and increasing the desorption of P to some extent, with the greatest P availability obtained at a SOM content of 75.3 g kg−1.

Theoretical modelling for calculation of the energy densities of adsorption sites using inverse gas chromatography

The inverse gas chromatography is used to determine the energy densities of the adsorption sites of the stationary solid phase. The use of this technique is old and dates back to the 1940s. The many possibilities offered by this method are described in several works. This work is an attempt to explore some adsorption local isotherm models in order to determine the energy density of the adsorption sites. It involves the use of integral equations of the first kind which are known to be numerically instable. These integral equations were solved by two different methods of solution. One is based on the use of Taylor series expansions and the other uses the Stieltjes transform. Some interesting theoretical and numerical results are presented.

A concurrent approach for process design and multicomponent adsorption modeling with local isotherms

An iterative approach is proposed to predict the optimal concentration profiles in an adsorption process and to simultaneously obtain parameters for a multicomponent isotherm by selecting representative liquid compositions for experimental measurements. The proposed approach was demonstrated for xylene adsorption on zeolite 13X that has undergone a barium ion exchange. Breakthrough experiments were performed at liquid compositions predicted by the process model, which was refined in an iterative manner with the experimental data. Robustness of the isotherm parameters for model uncertainty and variations in the process design were also analyzed.

Second-generation kernel for characterization of carbonaceous material by adsorption

A complete Monte Carlo heterogeneous kernel of N2 adsorption isotherms for activated carbon characterization was developed based on experimental insights from the carbon oxidative etching mechanism. The local isotherms of the kernel were split into four degrees of etching. With this new kernel, we analyzed microstructure evolution with burn-off and surface discrimination, two important carbon characterization problems. New atomic-level information of the development of porosity as the microstructure evolves with burn-off was obtained. This same kernel can differentiate between graphitized and non-graphitized surfaces, a promising new feature of such a kernel, creating an opportunity to apply adsorption as a large-scale method for the characterization of high-end graphene devices. The study also highlights that for both tested applications (microstructure evolution and surface discrimination), a heterogeneous multikernel, as opposed to the standard single kernel available in commercial equipment, is essential to improve characterization.

BSMV as a Biotemplate for Palladium Nanomaterial Synthesis.

The vast unexplored virus biodiversity makes the application of virus templates to nanomaterial synthesis especially promising. Here, a new biotemplate, Barley stripe mosaic virus (BSMV) was successfully used to synthesize organic-metal nanorods of similarly high quality to those produced with Tobacco mosaic virus (TMV). The mineralization behavior was characterized in terms of the reduction and adsorption of precursor and nanocrystal formation processes. The BSMV surface-mediated reduction of Pd(2+) proceeded via first-order kinetics in both Pd(2+) and BSMV. The adsorption equilibrium relationship of PdCl3H2O- on the BSMV surface was described by a multistep Langmuir isotherm suggesting alternative adsorbate-adsorbent interactions when compared to those on TMV. It was deduced that the first local isotherm is governed by electrostatically driven adsorption, which is then followed by sorption driven by covalent affinity of metal precursor molecules for amino acid residues. Furthermore, the total adsorption capacity of palladium species on BSMV is more than double of that on TMV. Finally, study of the BSMV-Pd particles by combining USAXS and SAXS enabled the characterization of all length scales in the synthesized nanomaterials. Results confirm the presence of core-shell cylindrical particles with 1-2 nm grains. The nanorods were uniform and monodisperse, with controllable diameters and therefore, of similar quality to those synthesized with TMV. Overall, BSMV has been confirmed as a viable alternate biotemplate with unique biomineralization behavior. With these results, the biotemplate toolbox has been expanded for the synthesis of new materials and comparative study of biomineralization processes.

Equilibrium sorption isotherms of Moringa oleifera leaves at different temperatures

Adsorption and desorption isotherms for Moringa oleifera leaves were investigated using concentrated H2SO4 solutions to vary the micro-climate over different temperatures (27, 32, 37°C) and water activity (aw) (0.1–0.8). Plots of equilibrium moisture content (EMC) against aw were used to generate isotherm curves, local isotherm (Li) concept and stability. The experimental data obtained were compared with four widely recommended models in the literature for food sorption isotherms [GAB, modified GAB (MGAB), modified Oswin (MOE) and OSWIN models]. Results obtained showed that the moisture sorption isotherms were sigmoidal in shape and were influenced by temperature. The four sorption models adequately predicted the adsorption and desorption isotherms for Moringa oleifera leaves at the evaluated temperatures, with R2 values between 0.980 and 0.998. The sequence in which the evaluated models effectively fitted the moisture sorption, were GAB, MGAB, MOE and OSWIN models, with GAB being the best. While the GAB model was most suitable for fitting the adsorption [Mean square error (MSE = 183.08), standard error of estimate (SEE = 549.24), R2 = 0.980)], MGAB was better for desorption isotherm [(MSE = 141.950), SSE = 425.86), R2 = 0.998] of Moringa oleifera leaves under practical storage temperature and water activity used in this study.

ON SHOCKS DRIVEN BY HIGH-MASS PLANETS IN RADIATIVELY INEFFICIENT DISKS. I. TWO-DIMENSIONAL GLOBAL DISK SIMULATIONS

Recent observations of gaps and non-axisymmetric features in the dust distributions of transition disks have been interpreted as evidence of embedded massive protoplanets. However, comparing the predictions of planet–disk interaction models to the observed features has shown far from perfect agreement. This may be due to the strong approximations used for the predictions. For example, spiral arm fitting typically uses results that are based on low-mass planets in an isothermal gas. In this work, we describe two-dimensional, global, hydrodynamical simulations of disks with embedded protoplanets, with and without the assumption of local isothermality, for a range of planet-to-star mass ratios 1–10 for a 1 star. We use the Pencil Code in polar coordinates for our models. We find that the inner and outer spiral wakes of massive protoplanets () produce significant shock heating that can trigger buoyant instabilities. These drive sustained turbulence throughout the disk when they occur. The strength of this effect depends strongly on the mass of the planet and the thermal relaxation timescale; for a planet embedded in a thin, purely adiabatic disk, the spirals, gaps, and vortices typically associated with planet–disk interactions are disrupted. We find that the effect is only weakly dependent on the initial radial temperature profile. The spirals that form in disks heated by the effects we have described may fit the spiral structures observed in transition disks better than the spirals predicted by linear isothermal theory.

On the use of the Hill’s model as local isotherm in the interpretation of the behaviour of the adsorption energy distributions

Activated carbons are reported to show promise for separation processes and natural gas storage, since they have a strongly heterogeneous surface. In that context, a thorough investigation of the energetic heterogeneity of activated carbon surfaces is essential for the development and improvement of materials designed for specific applications. We have carried out this study, to determine the Adsorption Energy Distribution (AED) corresponding to the adsorption of methane, ethane, and nitrogen on activated carbon at different temperatures by using the Hill model as local isotherm. At first, the integral equation itself is deduced by a reasoning based on the local adsorption isotherm. Then, to solve the integral equation a numerical method is proposed. The Hill isotherm was established by applying the grand canonical ensemble in a statistical physics treatment. This treatment allowed us to define the parameter n, which represents the number of molecules adsorbed per site. We have supposed as a first approach that the energy distribution function has the shape of the normal Gaussian distribution. The influence of the adsorbate type and the values of parameter n at different temperatures on the behaviour of the AED, have been studied. Keywords: Adsorption energy distribution; Activated carbon; Statistical physics; Integral equation; Hill isotherm.

Fluids in nanospaces: molecular simulation studies to find out key mechanisms for engineering

We have analyzed various phenomena that occur in nanopores, focusing on elucidating their key mechanisms, to advance the effective engineering use of nanoporous materials. As ideal experimental systems, molecular simulations can effectively provide information at the molecular level that leads to mechanistic insight. In this short review, several of our recent results are presented. The first topic is the critical point depression of Lennard-Jones fluid in silica slit pores due to finite size effects, studied by our original Monte Carlo (MC) technique. We demonstrate that the first layers of adsorbed molecules in contact with the pore walls act as a “fluid wall” and impose extra finite size effects on the fluid confined in the central portion of the pore. We next present a new kernel for pore size distribution (PSD) analysis, based entirely on molecular simulation, which consists of local isotherms for nitrogen adsorption in carbon slit pores at 77 K. The kernel is obtained by combining grand canonical Monte Carlo (GCMC) method and open pore cell MC method that was developed in the previous study. We show that overall trends of the PSDs of activated carbons calculated with our new kernel and with conventional kernel from non-local density functional theory are nearly the same; however, apparent difference can be seen between them. As the third topic, we apply a free energy analysis method with the aid of GCMC simulations to investigate the gating behavior observed in a porous coordination polymer, and propose a mechanism for the adsorption-induced structural transition based on both the theory of equilibrium and kinetics. Finally, we construct an atomistic silica pore model that mimics MCM-41, which has atomic-level surface roughness, and perform molecular simulations to understand the mechanism of capillary condensation with hysteresis. We calculate the work required for the gas–liquid transition from the simulation data, and show that the adsorption branch with hysteresis for MCM-41 arise from spontaneous capillary condensation from a metastable state.

Discrimination between adsorption isotherm models based on nonlinear frequency response results

A number of criteria are established for distinguishing between different adsorption isotherm types. These criteria are defined based on the adsorption isotherm derivatives up to the third order, which, on the other hand, can be estimated from nonlinear frequency response data. The criteria for five favourable (Langmuir, Freundlich, Sips, Toth and Unilan) isotherms and two complex isotherms (BET and quadratic) are presented. These criteria enable unique identification of the underlying adsorption isotherm relation if the values of the local first, second and third order isotherm derivatives at several points are known. The method is applied to experimental data from our previous publications, for one case of a favourable and one case of a complex isotherm.