Equilibrium Separation Research Articles

Optical matter based on graphene surface plasmons.

In this work, we have proposed a graphene planar structure as an optical binding device of dielectric nanoparticles. Surface plasmons (SPs) on a graphene sheet, generated thanks to the near field scattering of the incident plane wave by the nanoparticles placed close to the graphene sheet, act as a powerful intermediary for enhancing the optical force between nanoparticles to organize the particle structure at length scales comparable with the plasmon wavelength, i.e., at the light sub-wavelength scale. In particular, we have paid attention to the formation of one-dimensional arrays of nanoparticles. Our results show that both the equilibrium separation between particles and the energy potential binding depend on the number of particles forming the array and that the former tends to the plasmon wavelength (the array constant) for a number of particles large enough. We have obtained simple analytical expressions that explain the main results obtained by using the rigorous theory. Our contribution can be valuable for the knowledge in the low-frequency optical binding framework, from terahertz to far-infrared spectrum.

Efficient adsorption separation of methane from C2–C3 hydrocarbons in a Co(II)-nodes metal–organic framework

Methane (CH4) as a substitute for other mineral fuels plays a crucial role in reducing energy consumption and preventing environmental pollution. The present study employs a solvothermal method to fabricate a porous framework Co-metal–organic framework (Co-MOF) containing two distinct secondary building units (SBUs): an anionic [Co2(μ2-OH)(COO)4(H2O)] and a neutral [CoN2(COO)2]. Notably, within the anionic SBUs, the coordinated water molecules induce the generation of divergent unsaturated Co(II) centers in the unidirectional porous channels, thereby creating open metal sites. The adsorption performance of Co-MOF towards pure component gases was systematically investigated. The results demonstrated that Co-MOF exhibits superior adsorption capacity for C2–C3 hydrocarbons compared to CH4, which offering the potential for efficient adsorption and separation of CH4 from C2–C3 hydrocarbons. The gas selectivity separation ratios of Co-MOF for C2H6/CH4 and C3H8/CH4 were calculated using the ideal adsorbed solution theory method at 273/298 K and 0.1 MPa. The results revealed that Co-MOF achieved remarkable equilibrium separation selectivity for CH4 and C2–C3 hydrocarbon gases among non-modified MOFs, signifying the potential of the synthesized Co-MOF for efficient recovery and purification of CH4 from C2–C3 hydrocarbons. Breakthrough experiments further demonstrate the ability of Co-MOF to purify methane from C2–C3 hydrocarbons in practical gas separation scenarios. Additionally, molecular simulation calculations further substantiate the propensity of anionic SBUs to interact with C2–C3 hydrocarbon compounds. This study provides a novel paradigm for the development of porous MOF materials in the application of gas mixture separation.

COMPARISON OF EQUILIBRIUM AND IDEAL SEPARATION FACTORS IN DISTILLATION PROCESSES

The effective, equilibrium, and ideal separation factors in distillation processes (β, β0, and βi respectively) are considered in relation to dependences β(β0), β0(βi), and β(βi). On the examples of substances “base (Cd, Те, S, Zn, Se or As) – impurity”, a comparison of β0 and βi was made. The conclusion is made about the limited possibility of using the factor βi instead of β0 in distillation calculations: β0 ~ βi if βi differs from unity by no more than one order of magnitude; the divergency β0/βi increases with increasing deviation βi from unity.

ON DEPENDENCE OF EFFECCTIVE SEPARATION FACTOR ON DEGREE OF DISTILLATION

By using the example of the experimental data of the distillation of Pb-Sb (with Pb as the base) it is shown that the efficiency of distillation purification can be determined not only by the dependence of the effective separation factor on the degree of distillation, in the known distillation equation, but also by two others parameters: the equilibrium separation factor and the Peclet number.

CALCULATION OF DISTRIBUTION OF IMPURITIES IN SOLIDIFIED CONDENSATE INTO ACCOUNT OF PECLET NUMBER

The results of calculations of the distribution of impurities in the condensate obtained by condensation of vapor into a solid phase in the process of evaporation of the “base-impurity” substance are presented at the values of the equilibrium separation factor β0 in the range of 0.001…10 and the values of the diffusion Peclet number (Pe) in the range of 0.1…1∙104 . One can see the influence of both parameters on the formation of the distribution: at given values of β0 and Pe, the condensates have larger or smaller areas with a uniform distribution of impurities. The graphs of the averaged impurity concentration in the condensates are also presented depending on the degree of distillation at the same values of β0 and Pe.

EVALUATING THE EFFICIENCY OF EVAPORATIVE REFINING USING THE BURTON-PRIM-SLICHTER EQUATION

The efficiency of distillation or sublimation is assessed by the value β/β0, calculated at the melting temperature of the substance being refined using the Burton-Prim-Slichter equation (β and β0 are effective and equilibrium separation factors). Examples of calculations are given for a number of substances with a simple base: Sb, Yb, Mg, Eu, Te, Zn, Cd, Be.

Large Casimir Flipping Torque in Quantum Trap.

Casimir torque between parallel plates, a macroscopic quantum electrodynamics effect, is known to be induced by dielectric anisotropy and related to the rotational degree of freedom. We here reveal a different type of Casimir torque generated on a Au plate suspended in a quantum trap without recourse to materials anisotropy. As the Au plate deflects from the equilibrium plane with a nonzero flipping angle, the regions departing from and approaching the Teflon-coated Au substrate are subjected to attractive and repulsive Casimir forces, respectively, resulting in a restoring torque about the axis of flipping. For a quantum trap with an equilibrium separation of ∼10 nm, the stiffness per unit area of the Casimir flipping torque can be an order of magnitude larger than those of previously reported dielectric anisotropy-induced rotational torques at the same separation. The large Casimir flipping torque provides the possibility of designing a mechanical oscillator completely dominated by quantum and thermal fluctuations.

On Application of Burton-Prim-Slichter Equation in Calculations of Evaporation Refining

Using examples of substances with a simple base (Sb, Yb, Mg, Eu, Te, Zn, Cd, Be), the application of the Burton-Prim-Slichter equation is shown to assess the possibility of evaporative refining of substances by calculations at the values of the parameter δ/D, known from the study of crystallization (δ is the thickness of the surface layer in the evaporated material, D is the diffusion coefficient of the impurity). Calculations of β/β0 were performed for the indicated substances at melting points. (β and β0 are the effective and equilibrium separation coefficients.)

A stable ultramicroporous Cd(II)-MOF with accessible oxygen sites for efficient separation of light hydrocarbons with high methane production

Metal-organic frameworks (MOFs) have garnered increasing attention for their effective separation of light hydrocarbons owing to their prominent separation selectivity and energy-efficient adsorption process. Here, we constructed a robust stable ultramicroporous Cd(II)-MOF ([Cd5(NTA)4(H2O)2] (Me2NH2+)2·10H2O (1)) with abundant accessible oxygen sites and investigated its adsorption performance for recovering high-purity methane (CH4) from natural gas (NG) including C1(CH4)/C2(C2H6)/C3(C3H8) mixtures. At ambient conditions, the theoretical equilibrium separation selectivity of 1 for C2H6/CH4 (v/v = 10/85) and C3H8/CH4 (v/v = 5/85) were found to be 34.3 and 223.8, respectively. The CH4/C2H6/C3H8 (v/v/v = 85/10/5) mixture breakthrough experiments for 1, conducted at 298 K, demonstrated effective separation performance with breakthrough times of up to 136 and 280 min·g−1 for C2H6 and C3H8. Particularly, the CH4 productivity (purity > 99.9 %) with 9.8 mmol·g−1 ranked the third in reported literatures, lower to the reported maximum value of 13.28 mmol·g−1 for Ni(TMBDC)(DABCO)0.5. Furthermore, Grand Canonical Monte Carlo (GCMC) simulations and first-principles density functional theory (DFT) calculations revealed that the high uptake and selectivity for C3H8 and C2H6 can be attributed to the abundant oxygen sites present in the pores. The dynamic breakthrough experiments comprehensively demonstrated that the proposed MOF can be an effective potential adsorbent for the practical separation of CH4/C2H6/C3H8 mixtures.

Performance evaluation of bimetallic ion exchanged clinoptilolite for potential equilibrium and kinetic adsorption separations of CO2 from CO2/CH4 mixture

The bimetallic ion exchanged clinoptilolites (M1xM2y-CPs, M1 = Li+, Na+ or Cs+, M2 = Li+ or Cs+, x, and y = the exchange degree of the first and second cation) were prepared. Their physic-chemical parameters were characterized using various methods. The results demonstrated that the relative crystallinity of M1xM2y-CPs gradually decreased with the increase of the secondary cationic introduction. Meanwhile, M1xM2y-CPs presented the surface fractal features, particularly, the values of M1xM2y-CPs were higher than that of single ion exchanged CPs, suggesting that the surface of M1xM2y-CPs was rougher and more disordered. The effects of the type, size, and distributions of the used various cations on the gas adsorption and separation properties were evaluated via their equilibrium adsorbed performances of CO2 and CH4 demonstrate. The results indicated that the CO2 uptake of NaxLiy-CP increased with the increase of Li+ exchange degree, in which, Na67.95Li17.15-CP presented the maximum adsorption capacity of 2.45 mmol/g for CO2. While, the CO2/CH4 selective factors of NaxCsy-CP were around 10.82–12.75 at 273 K and 9.92–12.44 at 298 K, much higher than that of other bimetallic ion exchanged samples. The breakthrough experiments displayed a longer breakthrough time and a stronger CO2 absorption capacity. The cycling tests indicated an excellent CO2 adsorption stability and reversibility. Furthermore, the kinetics adsorption of pseudo-first-order and intraparticle model were used to investigate their adsorption mechanism. Finally, the CO2 adsorption mechanism between the adsorption amount and the average total energy of the CO2 adsorption system was preliminary elucidated using Material Studio simulation software.

Air preoxidation and Fe-catalyzed cooperative effect for preparation of high-performance coal-based granular activated carbon: Enhancing low-concentration CH4 recovery and utilization

Low-cost and efficient recovery of low-concentration CH4 is important in enhancing energy utilization and mitigating climate issues. The primary objective of this study was to develop a novel coal-based granular activated carbon through an improved preparation process. By utilizing anthracite as a precursor and coal tar as a binder, the present investigation highlights the cooperative effects of air preoxidation and Fe catalysis on the development and regulation of the pore structure in activated carbon. The efficiency of the modified activated carbon in separating CH4/N2 was tested and compared to that of commercial activated carbon. The modified activated carbon ACAFe exhibited an equilibrium separation factor of 3.23 for CH4/N2 at 25 °C. At 25 °C and 400 kPa, a single-column vacuum pressure swing adsorption (VPSA) process enriched CH4 from 40 mol% to 53.49 mol% and provided a CH4 recovery rate of 76.39%. ACAFe also demonstrated excellent cyclic regenerability. In conclusion, the cooperative effect of air preoxidation and Fe catalysis is an operationally simple, cost-effective, and highly efficient process with considerable industrial potential for recovering and utilizing low-concentration methane from unconventional natural gas sources.

Pair interaction of localized topological structures in confined chiral media.

We study pairwise interactions between localized topological structures in chiral magnetic and cholesteric liquid crystal (CLC) systems confined in the planar geometry. Our calculations for magnetics are based on the lattice model that takes into account the bulk and surface anisotropies along with the exchange and the Dzyaloshinskii-Moriya interactions. In CLC cells, these anisotropies describe the energy of interaction with an external magnetic or electric field and the anchoring energy assuming that the magnetic or electric anisotropy is negative and the boundary conditions are homeotropic. We have selected the region of the phase diagram, where various localized solitonlike structures, including skyrmion tubes, torons, and leeches, embedded in the ground state of the z-cone (conical phase) coexist, and carried out numerical analysis of the distance dependencies of the effective intersoliton interaction potentials. For skyrmions and torons, the potentials are found to be attractive in the large separation region. It turned out that for these potentials, the effects of axial asymmetry are negligible. By contrast, it turned out that for the intermediate structures between the skyrmions and torons known as the leeches, the leech-leech potentials generally depend on the orientation of the intersoliton separation vector and their large distance parts may become repulsive at certain directions of the vector. All the potentials have the short distance repulsive parts and the local minima located at the equilibrium separations. It is found that the skyrmion-skyrmion potential has an additional metastable configuration shifted towards the short-distance region.

Performance Evaluation of Batchwise Multistage Countercurrent Extraction in a LiCl–KCl/Cd System to Separate Actinides from Rare Earth Fission Products

The electrorefining of spent metallic fuels is conducted in LiCl–KCl eutectic–based salt to recycle U, Pu, and minor actinides when chemically active fission products of rare earth, alkali, and alkaline-earth metals accumulate in the salt. For removing the fission products from the salt, a batchwise multistage countercurrent extraction technique using a liquid Cd solvent and a Li reductant was investigated and found to achieve both a high recovery ratio of actinides and a sufficient degree of separation from rare earths. Vessels containing salt were prepared in accordance with the number of stages, and a smaller vessel containing liquid Cd was immersed in them sequentially to extract actinides from the salt. This operation is simple and reliable. The results calculated using the equilibrium separation factors reported in the literature suggested that four-stage extraction offers satisfactory performance for the separation of actinides from rare earths: more than 80% of Nd remained in the salt when 99.9% of Pu was recovered. Moreover, demonstration tests were conducted using Nd and Dy as surrogates of actinides and rare earths, respectively. The separation factor between Dy and Nd was determined to be 21, which was approximately equal to that between Nd and Pu reported in the literature. It was shown that the experimental results of extracting Nd while leaving Dy in the salt were in good agreement with the calculated results. In conclusion, batchwise multistage countercurrent extraction was proved to be a promising actinide separation method.

Nanobubble-Induced Aggregation of Ultrafine Particles: A Molecular Dynamics Study.

Nanobubble-induced aggregation (NBIA) of fine and ultrafine particles in liquid is a promising method for enhancing floatation rates in mineral processing, cleaning contaminants from water, and reviving marine ecosystems. Although the current experimental techniques can measure the nanobubble capillary force between two surfaces with controlled approach speed, they are not capable of imaging NBIA dynamics of fine/ultrafine particles by real-time observation with nanoscale spatial resolution. In this work, we use molecular dynamics (MD) simulations to study dynamics of NBIA of Ag particles in a Lennard-Jones fluid system. The molecular-level modeling allows us to study microscopic details of NBIA dynamics that are inaccessible by current experimental means. Using MD simulations, we investigated the effects of NB size, surface wettability, surface roughness, and contact line pinning on NBIA dynamics. Our modeling results show that both concave NB bridges between two hydrophobic surfaces and convex NB bridges between two hydrophilic surfaces can result in an attractive nanobubble capillary force (NBCF) that causes the aggregation of Ag particles in liquids. The equilibrium separation between two fully aggregated particles can be well predicted by the improved capillary force model. We also observe that the change of contact angle after the contact line pinning occurs at the sharp edge of a particle, which slows the aggregation process. Our thermodynamics analysis shows that there is a critical contact angle below which the merged surface NBs will detach from the surface instead of causing aggregation. The prediction of the critical contact angle is corroborated by our MD simulation results.

On Parameters of Evaporation Refining

The previously presented theory of evaporation refining which takes into account the difference in the vapor pressure of the components and the diffusion of impurities (but not other possible factors) is analyzed. The complexity of the theory is noted: to calculate the refining efficiency depending on the yield at a given temperature, a large number of parameters (nine) of the substance and material are required: molar mass M, density ρ, melting point Tm, equilibrium separation factor β0, vapor pressure of the main component p, the impurity diffusion activation energy in the refined substance Q, the impurity diffusion coefficient Dm at temperature Tm and the material size factor X. The conceptual character of the theory under consideration is noted due to the lack of knowledge of most of these parameters and the neglect of all process factors.

Molecular modeling of gaseous mercury species adsorption and transport in nanoporous silica membranes

The separation of Hg and HgO from industrial flue gas is an issue of much interest in the control of heavy metal emissions, and its feasibility for kinetic and equilibrium separation of Hg and HgO from N2 using disordered silica is theoretically investigated here using a combination of pore level transport modelling and effective medium theory. It is found that the classical Knudsen model generally leads to considerable over-prediction of the effective diffusion coefficient in the nanoporous silica compared to the more accurate Oscillator model that considers fluid–solid interaction. It is seen that nanoporous silica membranes are kinetically selective to nitrogen, the major component of flue gas, relative to Hg and HgO. Nevertheless, the kinetic selectivity for N2 is low, and only about 2–3, indicating that the kinetic separation of mercury species from flue gas is not practically feasible. On the other hand, the equilibrium selectivity of HgO over N2 is over 50 at 0.75 nm modal radius, while that for Hg exceeds 30 at 0.3 nm radius, suggesting this method of separation to be appropriate. Narrow pore silica materials of uniform nanopore size of about 0.3–0.75 nm are found to be optimal for the removal of mercury species.

The role of Saturn’s magnetism in the equilibrium separation of particles of dense rings

For the first time we have demonstrated that, taking into account the interaction of Saturn's magnetic field with the diamagnetic ice particles of the rings, it is possible to explain the separation of particles. It is shown that there is an equilibrium distance between the particles when the force of gravitational attraction between them is compensated by the force of magnetic repulsion. An expression for calculating the equilibrium distance is obtained. It also becomes clear why the ring particles do not stick together.

Optimized conditions for the design and operation of a vacuum distillation column for the purification of crude glycerol from biodiesel production

AbstractDue to the growth in global demand for biodiesel, there is a tendency for the volume of its main by‐product, glycerol, available on the market to increase. This has led to a search for new uses for this by‐product and the development of new processes that use glycerol as a raw material because it has wide industrial applications. However, to be used in many of these processes, the glycerol must go through a purification stage before reaching the purity required for the application (which can reach 99.7% w/w). Taking this into account, the optimization of the parameters for the main glycerol purification stage (vacuum distillation) is essential to reduce the cost of this stage as much as possible. In this article, optimization of the vacuum distillation column was carried out using an artificial neural network (ANN) and a genetic algorithm (GA) together. With the optimization, it was found that four theoretical stages of equilibrium (separation) is the optimal value, in economics terms, for the distillation column on an industrial scale, leading to better performance (in terms of glycerol purity) than patents that used a smaller number of theoretical stages and an equal performance in relation to the patents that used a greater number of stages, which in this case reduces the cost with the size of the column. This result helps to increase the financially viability of using glycerol as a raw material, which can make several processes cheaper, thus generating greater added value to this sustainable by‐product. © 2023 Society of Industrial Chemistry and John Wiley & Sons Ltd.

The Zero Regrets Algorithm: Optimizing over Pure Nash Equilibria via Integer Programming

Designing efficient algorithms to compute Nash equilibria poses considerable challenges in algorithmic game theory and optimization. In this work, we employ integer programming techniques to compute Nash equilibria in integer programming games, a class of simultaneous and noncooperative games in which each player solves a parameterized integer program. We introduce zero regrets, a general and efficient cutting-plane algorithm to compute, enumerate, and select Nash equilibria. Our framework leverages the concept of equilibrium inequality, an inequality valid for any Nash equilibrium, and the associated equilibrium separation oracle. We evaluate our algorithmic framework on a wide range of practical and methodological problems from the literature, providing a solid benchmark against the existing approaches. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.0282 .

Electromigration separation of lithium isotopes: The effect of electrolytes

The high-abundance lithium isotopes are key materials for the development of the nuclear industry. Lithium amalgamation is currently the only industrial method used to produce lithium isotopes, but it involves serious environmental pollution. Electromigration separation is one of the green and promising alternatives. Here, a “lithium salt aqueous solution │ organic solution │ aqueous solution” electromigration system was fabricated for lithium isotope separation. At a higher or lower voltage, the effects of species and initial pH of catholyte on the separation effects of lithium isotopes during electromigration were studied with different migrate time, and the origin of isotope separation was discussed. It was found that the initial pH values of the catholyte had an effect on the pH values of the anolyte. While the dramatic variation of pH in the electrolyte during electromigration was averse to the migration of Li+ and isotope separation. Furthermore, an extremely high isotope separation coefficient (1.6) was obtained at a very low Li+ migration ratio that is based on the dynamic separation. While the separation coefficient decreases with the increase of Li+ migration ratio rapidly and finally levels off, that is based on the equilibrium separation. This work provides important guidance for understanding the electromigration process and the origin of isotope separation in this system.