Molecular Kinetic Model Research Articles

Molecular kinetic modelling of non-equilibrium evaporative flows

Recent years have seen the emergence of new technologies that exploit nanoscale evaporation, ranging from nanoporous membranes for distillation to evaporative cooling in electronics. Despite the increasing depth of fundamental knowledge, there is still a lack of simulation tools capable of capturing the underlying non-equilibrium liquid–vapour phase changes that are critical to these and other such technologies. This work presents a molecular kinetic theory model capable of describing the entire flow field, i.e. the liquid and vapour phases and their interface, while striking a balance between accuracy and computational efficiency. In particular, unlike previous kinetic models based on the isothermal assumption, the proposed model can capture the temperature variations that occur during the evaporation process, yet does not require the computational resources of more complicated mean-field kinetic approaches. We assess the present kinetic model in three test cases: liquid–vapour equilibrium, evaporation into near-vacuum condition, and evaporation into vapour. The results agree well with benchmark solutions, while reducing the simulation time by almost two orders of magnitude on average in the cases studied. The results therefore suggest that this work is a stepping stone towards the development of an accurate and efficient computational approach to optimising the next generation of nanotechnologies based on nanoscale evaporation.

Effect of the dynamic contact angle on electromagnetically driven flows in free liquid films

We study the effect of a dynamic contact angle on an electromagnetically driven flow in a horizontal free electrolyte film stretched between two coaxial cylindrical electrodes and placed in a uniform magnetic field. The flow dynamics and film deformation are described using the reduced hydrodynamic model derived in the lubrication approximation in [A. Pototsky and S. A. Suslov, J. Fluid Mech., 984, A75 (2024)]. The linearized molecular kinetic model is used to relate the dynamic and static contact angles to the wetting-line friction coefficient. Steady azimuthal flow is found for arbitrary static contact angles. Linear stability of the base azimuthal flow with respect to azimuthally invariant perturbations is studied using the numerical continuation method. We find that the flow stability is highly sensitive to variations of the wetting-line friction coefficient and the static contact angle. The least stable azimuthal flow is found for the frictionless contact line corresponding to a free film that remains perpendicular to the surface of the electrodes. The azimuthal flows are found to experience a supercritical Hopf bifurcation upon which they transition to a stable oscillatory dynamic regime characterized by alternating squeezing and swelling of the film near the inner and outer electrodes.

A molecular-level kinetic model for the primary and secondary reactions of polypropylene pyrolysis

The environmental pollution caused by waste plastics and their potential of resource recovery are receiving increasing attention. In this study, a molecular level kinetic model was established to simulate the polypropylene pyrolysis based on the SOL method, Poisson distribution model and genetic algorithm, which was simplified and effective without the introduction of extensive chemical databases and stiff differential equations. The automatic generation of complex reaction network was based on the representation of species and reactions at molecular level and the design of 14 reaction rules consistent with the mechanism. The model prediction achieved good agreement with experimental data affected by the primary and secondary reactions, verifying the generalizability of the models. The model prediction according to the kinetic parameters provided guidance for the pyrolysis experiments. In general, the molecular-level model behaves exquisite in the evaluation, validation, and prediction, and can gain an insight into the pyrolysis of polymers.

Deformation diagrams of amorphous polyimide (kapton H) in the state of moderate and deep cooling: Experiment and theory

A comprehensive experimental and theoretical study of the regularities of active deformation at a constant rate of an amorphous polymer at room temperature and the influence of moderate and deep cooling on them was performed. The samples of amorphous aromatic polyimide (an analogue of kapton H) that are randomly cut fragments of the industrially produced thermoplastic film with a thickness of 25 μm were the object of the experimental study. The σ–ε diagrams of the tensile test, where σ and ε=ε˙t are the tensile stress and the relative strain, respectively, were recorded for 32 samples at three rates ε˙ = 7⋅10–5, 7⋅10–4, 6⋅10–3 s–1 under three temperatures T = 293, 77, and 4.2 K. In the state of deep cooling at T = 4.2 K, several samples were deformed as brittle glassy bodies – rupture after short elastic deformation. But the majority of the samples at all values of the experimental parameters (T,ε˙) had the rheological properties of rubber-like highly elastic materials (elastomers) with traditional tensile test diagrams: initial stage I of linear elastic deformation σI=Meε with Young’s modulus Me=Me(T); stage III of linear highly elastic deformation σIII=σfe+Mheε with modulus Mhe=Mhe(T) and conditional limit of elasticity σfe=σfe(T,ε˙); intermediate stage II of the relaxation type σII(ε;T,ε˙) with a nonlinear stress-strain dependence. The σ–ɛ diagrams of the individual samples with sufficiently high accuracy coincide with the graph of the function σ(ε;T,ε˙) which is the solution of the previously derived nonlinear rheological equation (V. D. Natsik and H. V. Rusakova, Fiz. Nizk. Temp.48, 281 (2022) [Low Temp. Phys.48, 253 (2022)]; Fiz. Nyzk. Temp.49, 246 (2023) [Low Temp. Phys.49, 228 (2023)]). In its derivation, a molecular-kinetic model was used: an amorphous polymer is considered as a set of statistically independent kinetic units, namely, molecular segments, and the elementary act of deformation is caused by thermomechanical activation of nonlinear excitations of these segments called elastons. The elaston mechanism of transformation of the deformation diagrams of amorphous polyimide samples under their moderate and deep cooling is discussed in detail: the transition between deformation states of warm and frozen elastomer, low-temperature effects of structural-deformation glass transition and deformation melting. Comparing the results of experiments and theory made it possible to obtain the empirical estimates for the macromechanical characteristics of the studied samples and the microparameters of elaston excitations. A significant and unsystematic (random) scatter of the macro- and micromechanical characteristics of the samples was revealed, which indicates a significant and random heterogeneity of the macro- and microstructure of the polyimide film from which they were made.

A molecular kinetic model for heavy gas oil catalytic pyrolysis to light olefins

AbstractPetroleum catalytic pyrolysis to light olefin technology has received wide‐ranging research interest in the refining industry. This work built a molecular kinetic model for the catalytic pyrolysis of a heavy gas oil from bitumen synthetic crude oil (SCO) to light olefins. A feedstock compositional model was constructed containing 1311 molecules using bulk properties information. A variety of reaction rules was summarized and digitized, and from which, a reaction network involving 2631 substances and 6793 reactions was generated via a reaction network autogeneration algorithm. The reaction network for the catalytic pyrolysis was transformed into reaction rate equations. Systematical pilot‐scale catalytic pyrolysis experiments were carried out, which were used to regress the molecular kinetic model parameters. The tuned model is able to predict the product yield and molecular distribution. Moreover, a range of sensitivity analysis was performed, revealing the dependence of light olefins yields on the reaction conditions.

A molecular kinetic model incorporating catalyst acidity for hydrocarbon catalytic cracking

AbstractThis work built a molecular‐level kinetic model for hydrocarbon catalytic cracking, incorporating the catalyst acidity as the parameter to estimate reaction rates. The n‐decane and 1‐hexene co‐conversion catalytic cracking process was chosen as the studying case. The molecular reaction network was automatically generated using a computer‐aided algorithm. A modified linear free energy relationship was proposed to estimate the activation energy in a complex reaction system. The kinetic parameters were initially regressed from the experimental data under several reaction conditions. On this basis, the product composition was evaluated for three catalytic cracking catalysts with different Si/Al. The Bronsted acid and Lewis acid as the key catalyst properties were correlated with kinetic parameters. The built model can calculate the product distribution, gasoline composition, and molecular distribution at different reaction conditions for different catalysts. This sensitive study shows that it will facilitate the model‐based optimization of catalysts and reaction conditions according to product demands.

Theory of low-temperature elasticity of amorphous polymers: Deformation at a constant rate and relaxation of deforming stress

The effect of temperature variations over a wide range on the rheological properties of amorphous polymers with high rubber-like elasticity (elastomers) is discussed. A theoretical study of the transition from the deformation state of a warm elastomer to the state of a frozen one, the effects of structural-strain glass transition and forced elasticity was done. Two types of mechanical testing of polymer samples are considered in detail: slow tensile deformation at a constant rate and relaxation of the deforming stress after deformation stops. The study was carried out on the basis of the previously proposed molecular-kinetic model of the processes of highly elastic deformation of amorphous polymers and the corresponding nonlinear rheological equation (V. D. Natsik and H. V. Rusakova, Fiz. Nizk. Temp. 48, 281 (2022) [Low Temp. Phys. 48, 253 (2022)]).

High-Temperature Wetting and Dewetting Dynamics of Silver Droplets on Molybdenum Surfaces.

The wetting and dewetting behaviors of Ag droplets on Mo(100), Mo(110), and Mo(111) surfaces were investigated over 1200-2000 K via molecular dynamics simulations. We used the diffusion energy barriers of Ag droplets on the three surfaces to analyze the phenomenon of different precursor films and adsorption layers on the different surfaces. Alloying enabled the Mo(111) surface better wettability in both Mo(110) and Mo(111) surfaces, where there were significant precursor films. We observed that the dewetting rate was the fastest on the surface with the densest adsorption layer. Simulations proved that the same molecular kinetic theory model was applicable to not only the wetting process but also the dewetting process on the same surface. We also provided evidence to support the fact that an increased temperature could reduce the time to reach equilibrium for the wetting and dewetting processes.

Laboratory hydrogenation of the photo-fragments of PAH cations: Co-evolution interstellar chemistry

To investigate co-evolution interstellar chemistry, we studied the gas-phase hydrogenation processes of possible photo-fragments of large polycyclic aromatic hydrocarbon (PAH) cations. Our experimental results show that hydrogenated photo-fragments of hexa-peri-hexabenzocoronene (HBC, C42H18) cations are efficiently formed. The predominance of even-mass fragments (C42H2n+, n = [0–9]) is observed in the photo-fragmentation experiments, while no even-odd hydrogenated mass patterns are observed in the hydrogenation experiments. We investigated the structure of these newly formed hydrogenated photo-fragments and the bonding energies for the reaction pathways with quantum chemistry calculations. We used a molecular kinetic reaction model to simulate the hydrogenation processes of the photo-fragments (e.g. C42H12+) as a function of the reaction time under the experimental conditions. We obtain the possible structure distribution of the newly formed hydrogenated fragments of C42H18+ and the infrared (IR) spectra of these possible molecules. We infer that the hydrogenation and photo-dehydrogenation channels are not reversible reaction channels. Hydrogenation tends to be more random and disorderly, with no restrictions or requirements for the carbon reaction sites of PAH species. As a result, under the co-evolution interstellar chemistry network, there is little chance that PAH compounds return to their initial state through hydrogenation processes after photo-dehydrogenation. Consequently, the hydrogenation states and forms of PAH compounds are intricate and complex in the interstellar medium (ISM).

Erythrocyte lysis and angle-resolved light scattering measured by scanning flow cytometry result to 48 indices quantifying a gas exchange function of the human organism.

Molecular/cell level of gas exchange function assumes the accurate measurement of erythrocyte characteristics and rate constants concerning to molecules involved into the CO2 /O2 transport. Unfortunately, common hematology analyzers provide the measurement of eight indices of erythrocytes only and say little about erythrocyte morphology and nothing about rate constants of cellular function. The aim of this study is to demonstrate the ability of the Scanning Flow Cytometer (SFC) in the complete morphological analysis of mature erythrocytes and characterization of erythrocyte function via measurement of lysing kinetics. With this study we are introducing 48 erythrocyte indices. To provide the usability of application of the SFC in clinical diagnosis, we formed four categories of indices which are as follows: content/concentration (9 indices), morphology (26 indices), age (5 indices), and function (8 indices). The erythrocytes of 39 healthy volunteers were analyzed with the SFC to fix the first-ever reference intervals for the new indices introduced. The essential measurable reliability of the presented method is expressed in terms of errors of characteristics of single erythrocytes retrieved from the solution of the inverse light-scattering problem and errors of parameters retrieved from the fitting of the experimental kinetics by molecular-kinetics model of erythrocyte lysis.

Low-temperature elasticity of amorphous polymers: Molecular model and rheological equation

A molecular-kinetic model of the processes of highly elastic deformation of amorphous polymers is proposed and, on its basis, nonlinear rheological equations are obtained; these latter make it possible to describe these processes under changes of deformation conditions in a wide range: temperature, deforming stress, and strain rate. A connection of the nonlinear micromechanical model of a polymer with the classical macromechanical model of a standard linear body is established. The transitions between the structural-deformation states of a warm and frozen elastomer, as well as the effects of low-temperature deformation melting and quantum elasticity of an amorphous polymer, are discussed.

Spreading behavior of dodecane-oleic acid collector mixture in low-rank coal flotation

Spreading of water-insoluble collectors on the mineral surface is important in flotation. In this study, the spreading behavior of dodecane (D), oleic acid (OA), and dodecane-oleic acid (D-OA) mixture in low-rank coal flotation was investigated. The viscosity and oil/water interfacial tension was measured to calculate the spreading coefficient and speed. The relaxation of coal-oil–water contact angle and the movement of three- phase contact line during the collector droplet spreading process were interpreted using the molecular kinetic (MK) model. It was found that the order of absolute values of spreading coefficient were D-OA < OA < D, and the spreading speeds were in the order of OA < D-OA < D. D-OA had the smallest coal-oil–water contact angle and the longest contact line length. The addition of OA can enhance the interaction between D and the low-rank coal surface, but at the same time reduce the spreading speed. This was mainly because OA not only increased the spreading force of the droplet but also increased the spreading resistance. MK model fitting results showed that the length of molecular displacement increased in the order of D < D-OA < OA, indicating that the hydrophobic sites were more dense than hydrophilic ones on the coal surface and D-OA interacted with both sites simultaneously. The molecular substitution frequency and the free energy of wetting activation had an opposite order. High molecular substitution frequency meant fast-spreading velocity, and thus the MK model fitting parameters were consistent with the contact angle relaxation results.

Improving Cracking Severity in an Ethane Thermal Cracker Based on Dynamic Optimization Considering Process Limitations

The main goal of this research is to improve cracking severity in an industrial ethane thermal cracker in a domestic plant. In the first step, the considered cracker is modeled based on the mass and energy balance equations considering a molecular kinetic model. To develop an accurate model, a detailed thermal model is adopted to predict the tube skin temperature. To prove the accuracy of the developed model and considered assumptions, the simulation results are compared with the available plant data. In the next step, a sensitivity analysis is performed to investigate the effects of coil outlet temperature and steam to ethane ratio on the cracking severity factors including ethane conversion and production rate. Based on the results of sensitivity analysis although increasing steam to ethane ratio decreases ethane conversion, it improves ethylene yield. Then, a dynamic optimization problem is formulated to maximize ethylene production and minimize production decay during the process run time considering feed temperature, furnace temperature, and steam to ethane ratio as decision variables. The results show that applying the optimal condition to the system improves ethylene production by about 9.44%.

Fischer-Tropsch wax catalytic cracking for the production of low olefin and high octane number gasoline: Experiment and molecular level kinetic modeling study

A molecular level kinetic model of Fischer–Tropsch wax catalytic cracking based on the structural unit and bond-electron matrix framework was developed. A molecular compositional model was built according to the detail molecular characterization data, containing 225 representative molecules. The reaction law was studied and then transformed to 17 reaction rules based on experimental data under different reaction conditions. All molecules traversed reaction rules, and a reaction network, including 700 molecules and 2029 reactions, was formed. The model parameters were reduced based on linear free energy relationship and tuned by experimental data. The predicted values of the model were in good agreement with the experimental data, with a maximum absolute error of 2.89 wt% and a minimum absolute error of 0.02 wt%. The model predicted that gasoline olefin content will achieve less than 25 wt% and RON > 90 under the reaction conditions of 510 °C, CTO 12 g/g and WHSV 6 h−1. The modelling also demonstrated that the feedstock was consumed rapidly, and multiple reactions could occur immediately. Thus, secondary reactions play an important role in the production of low olefin and high octane number gasoline.

Three dimensional modeling of liquid droplet spreading on solid surface: An enriched finite element/level-set approach

A physically consistent approach is introduced to simulate dynamics of droplets in contact with solid substrates. The numerical method is developed by introducing the molecular–kinetic model within the framework of the level-set/enriched finite element method and including the theoretically resolved sub-elemental hydrodynamics. The level-set method is customized to comply fully with the model acquired for the moving contact-line. The consistency of the proposed method is verified by comparing the simulation results with the theoretical predictions. In order to further validate the method, the spreading of a droplet is numerically modeled and compared rigorously with the experimental data reported in the literature. The proposed method is also employed to capture the evolution of a droplet trapped in a conical pore. All test-cases are simulated on three-dimensional computational domains.

Kinetics of bubble interaction with low rank coal surface in the presence of adsorbed dodecane-oleic acid collector mixture

ABSTRACT Bubble–particle interactions are crucial in the flotation process, and the influence of adsorbed chemicals on bubble-surface collisions/attachment is important to fully understand the role of mixed collector in low-rank coal (LRC) flotation. In this paper, the process of rising bubble attachment to LRC surface in the presence of adsorbed dodecane (D)-oleic acid (OA) collector mixture was studied using high-speed video camera and molecular-kinetic (MK) model. The results showed that collector adsorbed on LRC surface reduced the collision times, the time for stopping collision and reaching standstill. Mixed collector showed more obvious advantages than single collectors in accelerating bubble-surface collisions/attachment and increasing contact line length. Only when OA and OA-D were adsorbed, the wetting film between bubble and LRC surface broke and a stable three-phase contact was formed. The molecular displacement length of D-OA was smaller than that of single collectors, indicating the adsorption sites of bubbles on LRC surface treated with D-OA were more dense, and the higher displacement frequency of D-OA meant that the molecular displacement rate and TPCL expansion velocity was faster. D-OA enhanced the hydrophobicity of LRC surface through the synergistic effect between OA and D, which promoted the kinetics of bubble interaction with LRC surface.

Spreading and receding of oil droplets on silanized glass surfaces in water: Role of three-phase contact line flow direction in spontaneous displacement

HypothesisThe spontaneous displacement of both spreading and receding droplets on surfaces are extensively involved in numerous technical applications. We hypothesize that the spreading and receding displacement behaviors could be interpreted differently due to opposite flow directions at the three-phase contact line. ExperimentsWe performed two groups of displacement experiments using different initial setups of oil droplets on silanized glass surfaces in aqueous surroundings. FindingsThe different initial configurations mostly resulted in oil displacement in opposite directions: either spreading or receding of the oil droplet. Different static states were observed at the end of the spreading and receding processes on surfaces with the same wettability due to the contact angle hysteresis. The dynamic displacement was analyzed using the hydrodynamic and molecular kinetic models, which showed distinct applicabilities for the data description of the spreading and receding possesses. The model analysis further indicated the different nature of these possesses, in particular, the resistance to displacement dynamics, which was illustrated by the interpretation of the microscopic slip length and contact line friction in the respective models. This study can shed light on the fundamental role of the displacement direction in the spontaneous liquid–liquid displacement.

A molecular, elemental, and multiphase kinetic model for the hydrothermal liquefaction of microalgae

This work presents a molecular, elemental, and multiphase kinetic model for the hydrothermal liquefaction (HTL) of microalgae that leverages previously published experimental data. We propose a reaction network comprising 16 reaction pathways based on known classes of reactions that occur during HTL, including hydrolysis, repolymerization, cyclodehydration, retro-aldol condensation, Maillard reactions, deamination, and decarboxylation. We utilize these pathways with 22 unique lumped-product components to construct a system of coupled, first-order ordinary differential equations governing the rate of evolution of the carbon, nitrogen, and mass yields of each component. We evaluate the accuracy of model solutions over the entire range of experimental conditions, including over specific subsets therein, highlighting their relative strengths and areas to expand upon for future iterations. The model describes many empirical trends that were documented previously, including the effects of slurry concentration and Maillard reactions, which until now have never been modeled for this system. The model captures the biocrude and ammonia quantities most accurately, substantiating the utility of the model for optimizing important HTL process metrics, such as biocrude C recovery and aqueous ammonium recovery, that could help enhance overall process sustainability and energy return on investment.

Numerical approaches for moist air condensing flows modelling in the transonic regime

The paper presents mathematical modelling of water vapour condensation process in the moist air transonic internal flows. The condensation model based on the classical theory of nucleation and molecular-kinetic droplet growth model is implemented into a commercial software ANSYS Fluent. Two approaches are shown in the paper, one in which the air with water droplets is treated as a fluid mixture and second where the water droplets and humid air are computed as separate phases. Both models are validated against in-house and literature experimental studies of internal flow in nozzles. The impact of air humidity and contamination on the condensation process in internal flows for different conditions is examined. The latent heat release in the condensation process influences the flow structure, thus the analysis of condensation wave and shock wave position change with the change of relative air humidity is presented. Moreover, the importance of inertia force and the resulting velocity difference between phases is highlighted. The paper shows that the impact of the condensation in transonic flow is non-negligible and should be taken under consideration in high-velocity flow simulations.

Effect of Sodium Citrate and Calcium Ions on the Spontaneous Displacement of Heavy Oil from Quartz Surfaces

The dynamic displacement of heavy oil from solid surfaces by water plays a significant role in the oil recovery process. In this work, a bitumen-water-quartz system was applied to study the effect of sodium citrate and calcium ions on the dynamic displacement of bitumen from quartz surfaces. It was found that the addition of calcium ions slowed down the bitumen displacement rate and generated daughter droplets during the receding process. In contrast, the presence of sodium citrate not only accelerated the displacement of bitumen from quartz surfaces, but also led to a smaller contact angle at the end of the experiments. Moreover, calcium ions were chelated by the added sodium citrate, which counterbalanced the detrimental effect of calcium ions on the bitumen displacement. The reduced interfacial tension of bitumen-water interface and the increased negative charges on both bitumen and silica surfaces by sodium citrate were considered the reasons of the improved bitumen displacement process. To better understand the underlying physics, both the hydrodynamic model and molecular kinetic model were employed to analyze the dewetting dynamics of heavy oil from quartz surfaces under the effect of calcium ions and sodium citrate.