Desorption Model Research Articles

Optimizing the secondary drying phase of a continuous Spin-Freeze Drying process: A semi-mechanistic modelling approach

Over the past decade, continuous spin freeze-drying technology has emerged as a promising alternative to conventional batch freeze-drying, effectively addressing many of the latter’s inherent disadvantages. Much of the focus during this period has been on controlling and optimizing the primary drying phase of this process. However, optimizing the secondary drying step is equally critical for the overall efficiency of the process. The primary aim of this study was to develop a comprehensive semi-mechanistic model for the secondary drying phase in continuous spin freeze-drying, accounting for the effects of process settings such as freezing rate and product temperature on desorption kinetics. Additionally, the study aimed to address discrepancies between conventional desorption models, typically applied in batch freeze-drying, and the observed data in this research. To achieve this, a residual moisture-dependent activation energy was introduced to improve the accuracy of the desorption model. Using NIR spectroscopy and IR-thermography, unknown model parameters could reliably be estimated using a simple and fast procedure. The calibrated model successfully predicted the final moisture content with an accuracy within 0.11% of the measured value under previously untested process conditions. Ultimately, the proposed semi-mechanistic model demonstrated its reliability in predicting the impact of new process conditions on both product temperature and residual moisture over time, enabling the development of a practical design space.

Enhancing anti-diabetic activity and reducing cytotoxicity of T. crispa extracts through sustainable approach of pressurized hot water extraction and micelle-mediated separation

In this study, pressurized hot water extraction (PHWE) was evaluated for the recovery of anti-diabetic borapetoside C (BPC) from T. crispa stems. The maximum BPC extraction efficiency obtained at 100 ˚C, 2.5 MPa and 5.0 mL/min was considerably higher than that obtained by the conventional methods. Under optimized conditions, one-site kinetic desorption model could most accurately describe the PHWE behavior, suggesting an intra-particle diffusion-controlled mechanism. The undesirable compounds in the extract were further removed by micelle-mediated separation (MMS), in which Tween 80 was added, followed by NaCl addition and slight temperature increase to induce phase separation. At the most suitable MMS condition, with 0.028 mM Tween 80, 0.4 M NaCl, at 85 ˚C, the majority (87 %) of BPC could be recovered in the aqueous phase after 40 min. After MMS, the resulting extract exhibited low cytotoxicity against L6 and HepG2 cells while maintaining significant α-glucosidase and α-amylase inhibition activities.

Cluster dynamics modeling of hydrogen retention and desorption in tungsten with saturation and multi-trapping effect of sinks

Hydrogen (H) retention and desorption in tungsten (W)-based plasma-facing materials are still not well understood, largely due to the limitations of ex-situ observations in experimental detection methods like thermal desorption spectroscopy (TDS). In order to reveal the fundamental mechanisms behind H retention and desorption, we developed a cluster dynamics model, IRadMat-TDS, for theoretical modeling of depth distribution and TDS of deuterium (D) in polycrystalline W. The model newly includes the saturated absorption and emission of D in inherent sinks like grain boundaries (GBs), as well as the multi-trapping effect of D in various types of GBs with different trapping energies. The simulated TDS spectra are in agreement with experimental ones. For polycrystalline W under D ion irradiation within keV-energy range, two typical thermal desorption peaks in TDS at around 490 and 550 K are explicitly attributed to D emission from GBs and vacancies, respectively. And GBs play a major role in D retention. Moreover, the broad peaks in TDS come from the convolution of multi-trapping of D in sinks with different types of trapping sites rather than a single-site approximation.

Cathode cooling effects on the neutron production rate in the glow discharge type of fusion neutron source

Fusion reactions on the cathode surface of glow discharge deuterium–deuterium fusion neutron sources contribute significantly to the neutron production rate (NPR). While the NPR shows a linear relationship with current in the low current regime, a rise in cathode temperature in the high-current regime causes stagnation of the NPR. This tendency may be caused by high-temperature-induced desorption of deuterium on the cathode. This study aims to clarify the relationship between NPR and deuterium desorption. The present study utilized a water-cooling system to prevent deuterium desorption on the cathode. A stainless-steel 304 cathode and a diamond-like carbon (DLC)-coated cathode were tested. The cooling system kept the cathode temperature below 315 K throughout the experiment. In the case of the DLC-coated cathode, the water-cooling system improves the NPR in a high-current regime (30 mA or more in the present study). At 50 kV and 60 mA, the NPRs were 1.87 × 106 and 8.39 × 105 (n/s), with and without water cooling, respectively. Furthermore, without the cooling system, the NPR correlation with the cathode temperature indicates good agreement with the estimation model of deuterium desorption on the DLC-coated cathode. This study demonstrates that suppression of deuterium desorption in the cathode improves NPR, especially in the high-current regime.

Simulation and optimization of fatty acid extraction parameters from Nannochloropsis sp. using supercritical carbon dioxide

Microalgae, which are rich in fatty acids, have potential applications in various sectors such as bioenergy, health, food, and biomaterials. The Supercritical Fluid Extraction (SFE) method is commonly used to extract microalgae. This research estimated the process parameters of desorption rate constant (kd) and binary diffusion coefficient (DAB) for SFE fatty acid from Nannochloropsis sp. using a mathematical model called as hot sphere diffusion. Desorption models were used to model the release of fatty acids into the solvent (supercritical carbon dioxide). The parameter estimation process was conducted at temperatures of 313 and 333 K and pressures of 12.5, 20, and 30 MPa. The value of kd increased with increasing pressure and temperature and DAB values were obtained at varying pressures and temperatures.

Desorption model of volatile Ru species induced by partial chlorination on Ru(0001) under an O2/Cl2-based plasma process

Ruthenium (Ru) is known to be effectively etched by O2-based plasma with a 10%–20% amount of Cl2, while it is less etched by pure O2-based or Cl2-rich plasma. In this work, reaction paths and energy profiles on a metallic Ru surface were calculated in density functional theory (DFT) simulations to reveal the chemical role of the small amount of Cl2 in the O2-based plasma for Ru etching. We prepared three Ru(0001) surfaces with (1 × 1) adatoms in which chemisorption sites were occupied by O and Cl adatoms. Subsequently, we assumed that convex Ru moieties, which are precursors to form volatile Ru species, were formed on the surface and that they were oxidized by the irradiation of O2-rich plasma. In each Ru(0001) surface, we calculated the production and activation energies of each elementary reaction path to desorb the volatile Ru products. Compared with the surface where all chemisorption sites were covered with O, both energies decreased in locations where some chemisorption sites were replaced by Cl. Our DFT-based research showed that a small amount of Cl2 in the O2/Cl2 plasma contributes to decreasing the production and activation energy to form volatile Ru products on the Ru surface, resulting in the etching rate being increased.

Improving pressurized liquid extraction of passion fruit (P. edulis) bagasse: Exploring the effects of high-temperature, particle size, and extraction bed dimensions

Extraction techniques to obtain bioactive molecules from passion fruit bagasse have emerged recently. The driving force behind this effort lies in the array of biological properties related to its compounds, including anti-carcinogenic, antioxidant, anti-inflammatory, and vasorelaxant properties. Given this background, this work proposes improvements to the extraction process from defatted passion fruit bagasse (DPFB). The effect of pressurized liquid extraction (PLE) temperature was examined at 70, 90, and 110 °C, revealing an increase in global yield and total reducing content (TRC) with rising temperature. However, the yield of piceatannol was statistically equal between 70 and 90 °C and decreased at 110 °C, suggesting thermal degradation. These findings were corroborated by thermal stability analysis and oxygen radical absorbance capacity assessment. The impact of raw material particle size was investigated and showed that granulometric classification led to an increase in the TRC and piceatannol yields by 35% and 84%, respectively, and allowed identifying the piceatannol's location within the outer layer of the passion fruit seed (FR1). Mathematical modelling was applied to the kinetic extraction of DPFB-FR1 to assess the effect of bed height to diameter ratio (H/D). The two-site desorption model has properly fitted experimental data and indicated an enhancement in piceatannol mass transfer rate when increasing H/D. In summary, the present work presents findings and conclusions not previously documented in the literature, contributing to the improvement of PLE and pre-treatment methods for passion fruit bagasse.

Desorption Characteristics of CH4-C2H6 Mixed Gas in Heavy Hydrocarbon-Rich Coal Seams.

The gas desorption characteristics of coal are closely related to the gas content of the coal seam. The gas in heavy hydrocarbon-rich coal seams contains CH4 and C2H6 heavy hydrocarbons. However, most current research on the gas desorption characteristics of coal seams focuses on CH4 analysis, ignoring the influence of the C2H6 heavy hydrocarbon gas. To accurately determine the gas content of a heavy hydrocarbon-rich coal seam, methods based on CH4 analysis are inadequate and the desorption characteristics of CH4-C2H6 mixed gas must be clarified. This work experimentally and theoretically studies the desorption characteristics of single-component gas and CH4-C2H6 mixed gas from coal samples. The results show that increasing the adsorption-equilibrium pressure was found to increase the desorption quantity and desorption speed of single-component gas and increase the desorption quantity, desorption ratio, and diffusion coefficient of mixed gas. Under the same adsorption-equilibrium pressure, the desorption quantity and rate of single-component CH4 gas exceeded those of C2H6. The quantity and speed of mixed gas desorption increased with rising CH4 concentration and decreased with rising C2H6 concentration. The change in the mixed gas concentration during desorption reflects the distribution characteristics of light hydrocarbon components on the outer surface and heavy hydrocarbon components on the inner surface of coal. From the desorption characteristics of mixed gas, desorption models of mixed gas were obtained at different concentrations, laying a theoretical foundation for accurate determinations of gas contents in heavy hydrocarbon-rich coal seams.

Adsorption and Desorption Behavior of Partially Hydrolyzed Polyacrylamide on Longmaxi Shale

Large-scale volumetric fracturing is generally used during shale gas development. The return rate of fracturing fluid is low, and a large amount of slickwater is retained in the reservoir. The adsorption and desorption of partially hydrolyzed polyacrylamide (HPAM), an additive commonly used in slickwater, on the surface of shale was studied using Longmaxi shale from the Sichuan Basin. The experimental results showed that the mass ratio of the HPAM solution to shale reached saturation adsorption at 20:1 when the concentration of HPAM solution was 1000 mg/L and 25:1 when the concentration of HPAM solution was 500 mg/L. The mass ratio of the HPAM solution to shale was fixed at 25:1, and the adsorption equilibrium was reached at a HPAM concentration of 1000 mg/L when the aqueous solution temperature was 30 °C and 800 mg/L when the aqueous solution temperature was 60 °C. The Langmuir adsorption model yielded a better fit than the Freundlich adsorption model. The adsorption equilibrium time at 30 °C was at 60 min for a HPAM concentration of 500 mg/L, while for a concentration of 1000 mg/L, it was at 90 min. The adsorption equilibrium time at 60 °C was 40 min for a HPAM concentration of 500 mg/L, whereas it was 60 min for a HPAM concentration at 1000 mg/L. The pseudo-second order (PSO) kinetics model yielded better fits than the pseudo-first order (PFO) kinetics model. The adsorption of HPAM on shale was strong, and the adsorbed HPAM resembled cobwebs adhering to the shale surface. HPAM on the surface of shale after adsorption was able to resist the desorption capacity of water. However, when the amount of adsorbed HPAM on shale increased significantly, the amount of residual HPAM on the surface of the shale decreased rapidly during desorption in deionized water. The desorption of HPAM on the shale surface followed a modified desorption model. The higher the concentration of HPAM adsorbed on the shale surface was, the easier it was to desorb and the easier it was to be removed from the shale.

Comparison of the Adsorption and Desorption Dynamics of Biological Molecules on Alginate Hydrogel Microcapsules-The Case of Sugars, Polyphenols, and Proteins.

The aim of this work was to analyze and compare the adsorption and desorption processes of carbohydrates (glucose as a model molecule), polyphenols (gallic acid as a model molecule), and proteins (bovine serum albumin, BSA as a model molecule) on alginate microcapsules. The adsorption and desorption processes were described by mathematical models (pseudo-first-order, pseudo-second-order, and Weber-Morris intraparticle diffusion model for adsorption, and first-order, Korsmeyer-Peppas, and the Higuchi model for desorption) in order to determine the dominant mechanisms responsible for both processes. By comparing the values of adsorption rate (k2) and initial adsorption rate (h0) based on the pseudo-first-order model, the lowest values were recorded for BSA (k1 = 0.124 ± 0.030 min-1), followed by glucose (k1 = 0.203 ± 0.041 min-1), while the model-obtained values for gallic acid were not considered significant at p < 0.05. For glucose and gallic acid, the limiting step of the adsorption process is the chemical sorption of substances, and the rate of adsorption does not depend on the adsorbate concentration, but depends on the capacity of the hydrogel adsorbent. Based on the desorption rates determined by the Korsmeyer-Peppas model (k), the highest values were recorded for gallic acid (k = 3.66236 ± 0.20776 g beads/mg gallic acid per min), followed by glucose (k = 2.55760 ± 0.16960 g beads/mg glucose per min) and BSA (k = 0.78881 ± 0.11872 g beads/mg BSA per min). The desorption process from alginate hydrogel microcapsules is characterized by the pseudo Fickian diffusion mechanism.

Characterization of Coal Particle Methane Desorption and Optimization of Desorption Model Based on Desorption Damage.

In view of the current situation where most studies on gas desorption characteristics are limited to the atmospheric pressure desorption environment, we have independently developed a coal methane desorption instrument to test the nonatmospheric pressure desorption characteristics for coal particle gas beneath the condition of desorption damage. The instrument can arbitrarily adjust the gas pressure in the range of measurement while controlling the instantaneous release of excess gas to keep the desorption environment pressure constant. We measured the methane desorption amount of coal samples with different desorption times within 3 h and calculated the desorption velocity. The results show that the final desorption amount and desorption velocity of gas scale up with the increase of times, and the final desorption amount of coal sample W-01 increases the most, which is 18.5%. With the passage of time, the diffusion coefficient decreases gradually, and the number of desorption times is directly proportional to the diffusion coefficient. Its relative deviation of diffusion coefficient between different desorption times of the same coal sample can reach up to 40%, and the desorption time in the range of 5 to 30 min is the area with high relative deviation. A quantitative index Ki of a double-parameter damage model based on desorption conditions and adsorption pressure is proposed, and the damage extent of each sample is evaluated. The damage quantitative index of coal sample W-01 is the highest, which is 0.87. The methane desorption model of coal under the condition of desorption damage is constructed, and more than 30 groups of experiments are verified.

Effect of Coal Particle Breakage on Gas Desorption Rate during Coal and Gas Outburst

The gas contained in coal plays a crucial role in triggering coal and gas outbursts. During an outburst, a large quantity of gas originally absorbed by coal is released from pulverized coal. The role this part of the gas plays in the process of coal and gas outbursts has not been clearly elucidated yet. Therefore, investigating the changes in gas desorption rate from coal particles of different sizes could provide some meaningful insights into the outburst process and improve our understanding of the outburst mechanism. First, combining the diffusivity of coal of different particle sizes and the distribution function of broken coal, we present a gas desorption model for fragmented gas-bearing coal that can quantify gas desorption from coal particles within a certain range of size. Second, the gas desorption rate ratio is defined as the ratio of the gas desorption rate from coal being crushed to that from coal before breaking. The desorption rate ratio is mainly determined by the desorption index (γ) and the granularity distribution index (α). Within the limit range of coal particle sizes, the ratio of effective diffusion coefficient for coal particles with different sizes is directly proportional to the reciprocal of the ratio of particle sizes. Under uniform particle size conditions before and after fragmentation, the gas desorption rate ratio is the square root of the reciprocal of the effective diffusion coefficient. The gas desorption model quantitatively elucidates the accelerated desorption of adsorbed gas in coal during the continuous fragmentation process of coal during an outburst.

Pressure-dependent characteristics of the diffusion coefficient during the gas desorption process in coal cuttings: Numerical modelling and analysis

Determining the diffusion coefficient is crucial in coalbed methane development. Existing models have limitations, as they often apply only to spherical systems, cannot describe nonlinear adsorption, and do not quantify the impact of gas pressure on diffusion coefficients. Additionally, traditional trial methods struggle to accurately compute diffusion coefficients in numerical solutions. To address these challenges, our study builds two unipore diffusion models (EPDDM and PPDDM) by introducing exponential and power pressure-dependent diffusion coefficients, considering three-dimensional coordinates and Langmuir adsorption. And then proposes a diffusion coefficient determination method using a particle swarm optimization algorithm. Through desorption experiments, numerical modelling, and model comparisons, we analyze the evolution law of diffusion coefficient, gas pressure, and desorption volume during the desorption process. Our results show that the proposed models quantitatively depict the positive correlation between diffusion coefficient and gas pressure. Furthermore, they accurately reflect changes in desorption volume. During early-stage desorption, the diffusion coefficient of EPDDM is 1.63–1.85 times greater than that of PPDDM, while their desorption volumes are similar. This observation motivates the proposal of a more versatile Logistic pressure-dependent diffusivity model, aiming to unify the above two models. These achievements are anticipated to serve as a foundational framework for exploring the mechanisms governing gas diffusion.

Insights into carbon dioxide sequestration into coal seams through coupled gas flow-adsorption-deformation modelling

Injecting carbon dioxide (CO2) into coal seams may unlock substantial carbon sequestration potential. Since the coal acts like a carbon filter, it can preferentially absorb significant amounts of CO2. To explore this further, desorption of the adsorbed gas due to pressure drop is investigated in this paper, to achieve an improved understanding of the long-term fate of injected CO2 during post-injection period. This paper presents a dual porosity model coupling gas flow, adsorption and geomechanics for studying coupled processes and effectiveness of CO2 sequestration in coals. A new adsorption−desorption model derived based on thermodynamics is incorporated, particularly, the desorption hysteresis is considered. The reliability of the proposed adsorption-desorption isotherm is examined via validation tests. It is indicated that occurrence of desorption hysteresis is attributed to the adsorption-induced pore deformation. After injection ceases, the injected gas continues to propagate further from the injection well, while the pressure in the vicinity of the injection well experiences a significant drop. Although the adsorbed gas near the well also decreases, this decrease is less compared to that in pressure because of desorption hysteresis. The unceasing spread of CO2 and drops of pressure and adsorbed gas depend on the degree of desorption hysteresis and heterogeneity of coals, which should be considered when designing CO2 sequestration into coal seams.

Nondimensional analysis and application of gas desorption and diffusion driven by density gradient in coal particles.

An in-depth understanding of gas diffusion characteristics in coal is of great value to coalbed methane (CBM) production planning and coal mine safety management. However, the mechanism and model of gas diffusion is still unclear, and some methods for determining diffusion coefficients are not accurate enough. Accordingly, a free gas density gradient (FGDG)-driven coal particle gas desorption and diffusion model was established in this work, and numerical solutions were performed via finite difference method (FDM) and dimensionless method. The variation rules of dimensionless gas pressure, gas content, desorption capacity, and desorption rate were obtained. Finally, the application of the dimensionless method in diffusion modeling and diffusion coefficient inversion was discussed. The results show that the dimensionless method can simplify mathematical equation processing and analyze the common phenomena of desorption and diffusion under different parameters. The gas desorption diffusion in coal particles is from the surface to the inside, and there is obvious desorption hysteresis effect. The larger the dimensionless radius or dimensionless time, the smaller the dimensionless gas pressure, gas content, and dimensionless desorption rate. The dimensionless cumulative gas desorption amount increased rapidly first and then tended to flat with dimensionless time. The simulated curve can be easily converted into the variation curves of several different measured parameters, and the diffusion coefficient can be calculated accurately. The prediction curve of the FGDG diffusion model is in good agreement with the experimentally measured data, which verifies its reasonableness. The research content aims to provide some ideas for modeling gas desorption and diffusion behavior.

Molecular Ion Desorption from LiF(110) Surfaces by Positron Annihilation.

We have studied the desorption of positive ions from a LiF(110) crystal surface using positron and electron irradiation at 500eV to examine the interaction between positrons and ionic crystals. Only monatomic ions, such as H^{+}, Li^{+}, and F^{+}, are detected under electron irradiation. However, positron irradiation leads to the significant desorption of ionic molecules, specifically, FH^{+} and F_{2}^{+}. Molecular ion yields are more sensitive to temperature than atomic ion yields. Based on the findings, we propose a desorption model in which positronic compounds are initially produced at the surface and subsequently desorbed as molecular ions via Auger decay following positron annihilation.

A mathematical model for ammonium removal and recovery from real municipal wastewater using a natural zeolite

A study was carried out to remove/recover ammonium (NH4+) from residual effluents in tertiary treatment by sorption/desorption processes onto a natural clinoptilolite zeolite (NZ) in batch and fixed-bed column systems. Batch equilibrium and kinetic experiments were performed at different loading of NZ and contact time intervals, respectively. The results obtained in batch were fitted by the Freundlich and Langmuir isotherms and mass action law model. The Freundlich isotherm showed better agreement with experimental data than the Langmuir model. The isotherm studies revealed a type III with a maximum capacity of 2.8 ± 0.2 mg/g at 40 mgNH4+/L. Moreover, the data from the fixed-bed column studies was well fitted by a mass transfer model, considering the intraparticle diffusion resistance given by the linear driving force model (LDF). Finally, the capacity of NH4+ recovery of activated zeolite was measured experimentally and by a robust dynamic desorption model. The column desorption results demonstrated that higher recoveries (92–99.99%) were observed when increasing the flow rate to 0.12 mL/min. The uniqueness of this study is its capability to simulate both the sorption and desorption processes of the naturally derived sorbent for the effective removal and recovery of NH4+-N from real wastewater stream.

Modeling of intrinsic photon-stimulated desorption yields under readsorption effect

In synchrotron radiation and electron storage rings, photon-stimulated gas desorption is a major contributor to gas load, leading to vacuum degradation and compromising the stability and quality of the beamline. Therefore, it is imperative to investigate the underlying mechanisms of photon-stimulated gas desorption to enhance the reliability of the experiments. In this paper, a theoretical model for analyzing the process of photon-stimulated desorption is presented, and the equations are solved numerically by considering the evacuation, bulk diffusion, thermal outgassing, adsorption, and desorption of surface gas molecules. The modified model can predict the yield of H2 gas desorption induced by photon stimulation when synchrotron radiation is directed vertically onto various sample surfaces, utilizing the coupled multi-physics solution. The calculated results are consistent with the experimental measurements obtained from the Shanghai Synchrotron Radiation Facility. The results show that the photodesorption yield is related to the amount of surface-adsorbed molecules, which explains the observed decrease in the photodesorption yield with increasing accumulated photon dose. Furthermore, the study provides a theoretical approach to predicting the pressure evolution of photon-stimulated desorption.

Modeling of Water Vapor Adsorption and Desorption in an Industrial Medical Air Dryer

Modeling of Water Vapor Adsorption and Desorption in an Industrial Medical Air Dryer

Kinetic Study of Total Phenolic Content from Piper betle Linn. Leaves Extract Using Subcritical Water

The green plant-based extraction of phenolic compounds is still challenging and attractive due to their benefit. The mechanism controlling of desorption rate of phenolic compounds, measured as total phenolic content (TPC), from Piper betle Linn. (PBL) leaves using subcritical water, and a one-site kinetic desorption model (first order) was studied. One-site kinetic desorption model has well explained the extraction mechanism of phenolic compounds from PBL leaves using subcritical water through desorption and diffusion mechanism. This model fits with the experimental data and presents a good description of the extraction mechanism with R-squared of 0.94. The recovery of TPC from PBL leaves using subcritical water was influenced by intraparticle diffusion, temperature, and extraction time. The desorption rate constant in the one-site kinetic desorption model increased from 100 to 200 °C (0.3975±0.02 to 3.3045±0.00 min-1) and then decreased to 250 °C (3.2093±0.00 min-1). The highest TPC was recovered quickly for 5 min at 200 °C. In addition, a high yield of TPC was also obtained at a slow desorption process for 30 min at a lower temperature of 175 °C. The low activation energy for the diffusion of phenolic compounds from PBL leaves of this study was 8.964 kJ/mol. This result showed that the one-site kinetic desorption model of subcritical water extraction has an excellent opportunity to be applicable in phenolic compounds recovery from PBL leaves. The one-site kinetic desorption rate constant and mathematical kinetic model equation achieved in this study might control the quality of phenolic compounds extracted from PBL leaves through subcritical water.