Homogeneous First-order Reaction Research Articles

Kinetics of free fatty acids esterification in waste frying oil using novel carbon-based acid heterogeneous catalyst derived from Amazonian Açaí seeds – Role of experimental conditions on a simpler pseudo first-order reaction mechanism

This study reports the kinetics of free fatty acids esterification in waste frying oil, based on a simpler non-conventional pseudo first-order homogeneous reaction mechanism using a highly-efficient acid heterogeneous catalyst derived from seeds of Açaí (Euterpe oleracea Mart.), subjected to changes in temperature, catalyst dosage, MeOH:Oil ratio, and stirring speed. Statistical analyses revealed significant effects all four conditions (p < .05) on the reaction's apparent rate constant (k1) over their different pre-defined levels. Reaction mechanism was inferred to be fundamentally acid ionic exchanges with the oil/water film on catalyst's surface, neglecting kinetically controlled liquid-to-liquid splitting and autocatalyzed esterification.

CFD-based geometrical shape optimization of a packed-bed reactor combining multi-objective and adjoint system methods

This paper presents the development of a geometric shape optimization methodology based on the so-called ”Hadamard boundary variation” method for performing very general domain deformations, and the related concept of domain differentiation. The resulting method is used to determine the optimal configuration of a two-dimensional packed-bed reactor that simultaneously optimizes its conversion rate and fluid energy dissipation, and where a homogeneous first-order reaction or a catalytic surface reaction takes place. The considered multi-objective optimization problem is subjected to four constraints: the process model constraints consisting of the Navier–Stokes, continuity and mass balance equations, an iso-volume and two manufacturing constraints. The approach to solve the problem is based on the linear scalarization method which converts the multi-objective problem into a single objective problem. The adjoint system method is used to compute the gradient of the performance indices and constraints. Since the indices are conflicting, the solution of the problem is a set of solutions, called Pareto front. Each optimal solution is evaluated using multi-attribute utility theory (MAUT) to determine the best optimal shape of the reactor. Finally, the resulting shape is fabricated using a 3D printing technique and will be experimentally validated.

Heterogeneous Reaction Model for Evaluating the Kinetics of Levulinic Acid Synthesis from Pretreated Sugarcane Bagasse

The abundance of sugarcane bagasse, a by-product of sugarcane juice extraction in sugar factories, serves as an advantage of its potential for producing chemicals such as levulinic acid (LA). Levulinic acid contains carbonyl and carboxyl groups that can be utilized for many applications, such as pharmacies, cosmetics, and solvents. Bagasse hydrolysis into LA was preceded by alkaline-acid pretreatment to separate cellulose from hemicellulose and lignin. This treatment could minimize the disturbance of these unwanted components, so that LA synthesis would be more optimal. Pretreated bagasse contained 82.64% cellulose, about two-fold from the non-pretreated one. It was hydrolyzed with hydrochloric acid (HCl), which acts as a catalyst (a Bronsted acid), at 150-170 oC, 0.1-1 M catalyst concentration, 1-10% solid-to-liquid (cellulose:catalyst-solution) ratio, and 0-200 minutes reaction time. The range of LA yield values obtained in the study were between 15-64.05%. The maximum LA yield was obtained at a temperature of 160 oC, 1 M catalyst concentration, and 1% solid-to-liquid ratio. The high LA yield indicates the importance of pretreatment supported by optimal conditions of synthetic reaction. The reaction route involved in hydrolysis was cellulose-glucose-levoglucosan (LG)-hydroxymethylfurfural (HMF)-LA. The result exhibits that temperature and catalyst concentration do not significantly affect the maximum potential LA yield. However, higher temperatures and catalyst concentration can accelerate the time to achieve the maximum potential LA yield. Meanwhile, the LA yield increases with a lower solid-to-liquid ratio. In contrast to previous studies, this study evaluated the reaction model in a more precise way using combination of models, considering that the reaction occurs between solid and liquid. The heterogeneous reaction model, namely the shrinking core model (SCM) for cellulose conversion to glucose and the first-order homogeneous reaction model for glucose to LA reaction, give good fitting results. The more appropriate reaction model is expected to be the basis of scale-up process carried out for industry one day. The results of this research have the potential to be applied for various other biomass raw materials with some improvements based on their characteristics which can be studied in the future.

In English

The goal of this study is unraveling the specific features of non-stationary surface concentration distribution of electroactive and inactive species in a model electrochemical process with a preceding homogeneous first-order chemical reaction (CE mechanism). For this purpose, the exact analytical expressions for the non-stationary concentration distributions of electroactive and inactive species in the thin layer attached to a planar electrode are analyzed. The both cases of equal and unequal diffusion coefficients of species taking part in the preceding chemical reaction are considered. In the former case, the exact analytical expressions for the concentration distributions of electroactive and inactive species on a planar electrode are obtained. The peculiarities of the limiting cases of zero and infinite frequency of an applied alternating current for the both cases of equal and unequal diffusion coefficients of species are discussed. It is shown that there is a phase shift between AC and the surface concentration of species that changes under the action of this current. At low frequencies, the phase angle tends to p/2, whereas at high frequencies it decreases to p/4. The phase angle is the function of the two important measures, namely, the ratio of the Nernst diffusion layer thickness to the oscillation diffusion layer thickness, and the ratio of the Nernst diffusion layer thickness to the reaction layer one. It is shown that the phase angle depends on the diffusion coefficient of species in different manner for low and high values of the rate constants of the chemical reaction. At low values of these parameters, the phase angle shifts slightly to the range of high frequencies with an increase of diffusion coefficient. At the high rate constants, the phase angle decreases with frequency more slowly, and its dependence on diffusion coefficient is observed only at middle frequencies. The surface concentration of electroactive and inactive species decreases with an increase of frequency, but for the inactive species this process is faster than that for the electroactive species. The influence of the inactive species on the surface concentration of electroactive species decreases at high frequencies and at low rate constants of the preceding chemical reaction. The results obtained shed the light on complex dynamics at an electrode/electrolyte interface under non-stationary conditions.

Numerical Investigation of Radiation Effects on MHD Convective Heat and Mass Transfer Flow Past a Semi-Infinite Vertical Moving Porous Plate in the Presence of Chemical Reaction

Abstract: The numerical solutions for heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting and heat generation/absorbing fluid on a continuously vertical permeable surface in the presence of a radiation, a first-order homogeneous chemical reaction and the mass flux are considered. The plate is assumed to move with a constant velocity in the direction of fluid flow. A uniform magnetic field acts perpendicular to the porous surface, which absorbs the fluid with a suction velocity varying with time. The Equations of continuity, linear momentum, energy and diffusion, which govern the flow field, are solved by using a Finite Element Method. The results of the velocity, temperature, concentration, skin- friction, Nusselt number and Sherwood number has been discussed for variations in the governing parameters. Keywords: MHD, Radiation, Heat and Mass Transfer, Porous Medium, Unsteady flow, Finite Element Method.

Dispersion of a Solute in Blood Flowing Through Narrow Arteries with Homogeneous First-order Chemical Reaction

Dispersion of a Solute in Blood Flowing Through Narrow Arteries with Homogeneous First-order Chemical Reaction

Nickel recovery from precipitate of NCA lithium-ion battery leach liquor by using disodium ethylene diamine tetraacetate

The nickel cobalt aluminium oxides (NCA) type Li-ion battery is a type of battery currently used in electric vehicles. The UGM battery team has recycled this type of battery to obtain high purity lithium metal. Aside from lithium, the NCA battery contains high-value metals, nickel is one of them. This experiment aims to test the ease of nickel to chelate with disodium ethylene diamine tetraacetate (EDTA). The experiment was carried out by means of a triple neck flask for 4 hours. The samples were taken at certain minutes and then fitted using a pseudo homogeneous first-order reaction equation. The chelate formed was further processed through multilevel precipitation or electrodialysis to separate nickel. Based on the experiment, nickel formed chelates optimally at 60°C using 0.086 M EDTA with the reaction constant for nickel being 1.4819 min−1. The Arrhenius constant and activation energy for nickel were 3.48×1011min−1 and 76,907 J/mole, respectively.

Mass transport and dynamical instabilities in a model electrocatalytic process with a preceding chemical reaction

The influence of mass transport on the occurrence of periodic current oscillations and bistability in a model electrocatalytic process with a preceding homogeneous first-order chemical reaction in the Nernst diffusion layer for different diffusion coefficients of species involved in the chemical reaction is shown. The impacts of the diffusion coefficients of electrochemically active and inactive species, as well as the preceding chemical reaction rate constants on the emergence of these dynamical instabilities are uncovered. The effect of the aforementioned parameters on frequency of oscillations is determined. The peculiarities of the system behavior at the bifurcation points are demonstrated in the Nyquist and Bode plots. For the first time, the role of diffusion coefficient of inactive species in these nonlinear processes is presented theoretically.

Hall and ion slip current’s impact on magneto-sodium alginate hybrid nanoliquid past a moving vertical plate with ramped heating, velocity slip and Darcy effects

PurposeThe purpose of this study is to analyze an unsteady MHD Darcy flow of nonNewtonian hybrid nanoliquid past an exponentially accelerated vertical plate under the influence of velocity slip, Hall and ion slip effects in a rotating frame of reference. The fluids in the flow domain are assumed to be viscously incompressible electrically conducting. Sodium alginate (SA) has been taken as a base Casson liquid. A strong uniform magnetic field is applied under the assumption of low magnetic Reynolds number. Effect of Hall and ion-slip currents on the flow field is examined. The ramped heating and time-varying concentration at the plate are taken into consideration. First-order homogeneous chemical reaction and heat absorption are also considered. Copper and alumina nanoparticles are dispersed in base fluid sodium alginate to be formed as hybrid nanoliquid.Design/methodology/approachThe model problem is first formulated in terms of partial differential equations (PDEs) with physical conditions. Laplace transform method (LTM) is used on the nondimensional governing equations for their closed-form solution. Based on these results, expressions for nondimensional shear stresses, rate of heat and mass transfer are also determined. Graphical presentations are chalked out to inspect the impacts of physical parameters on the pertinent physical flow characteristics. Numerical values of the shear stresses, rate of heat and mass transfer at the plate are tabulated for various physical parameters.FindingsNumerical exploration reveals that a significant increase in the secondary flow (i.e. crossflow) near the plate is guaranteed with an augmenting in Hall parameter or ion slip parameter. MHD and porosity have an opposite effect on velocity component profiles for both types of nanoliquids. Result addresses that both shear stresses are strongly enhanced by the Casson effect. Also, hybrid nanosuspension in Casson fluid (sodium alginate) exhibits a lower rate of heat transfer than usual nanoliquid.Social implicationsThis model may be pertinent in cooling processes of metallic infinite plate in bath and hybrid magnetohydrodynamic (MHD) generators, metallurgical process, manufacturing dynamics of nanopolymers, magnetic field control of material processing, synthesis of smart polymers, making of paper and polyethylene, casting of metals, etc.Originality/valueThe originality of this study is to obtain an analytical solution of the modeled problem by using the Laplace transform method (LTM). Such an exact solution of nonNewtonian fluid flow, heat and mass transfer is rare in the literature. It is also worth remarking that the influence of Hall and ion slip effects on the flow of nonNewtonian hybrid nanoliquid is still an open question.

The Gerischer finite length impedance: A case of unequal diffusion coefficients

This work is devoted to the theoretical study of the impedance response associated with coupled homogeneous first-order chemical reaction in diffusion layer and reversible heterogeneous electrochemical reaction (CE mechanism). For the first time, the exact analytical expression for the Gerischer finite length impedance is obtained for different diffusion coefficients of the species involved in the homogeneous first-order chemical reaction. In a general case, the Gerischer finite length impedance has two capacitive loops, one associated with the diffusion of the inactive species and the other with the homogeneous chemical reaction. The effect of the diffusion coefficients difference is observed at low frequencies. At high frequencies, the impedance behavior is determined by the diffusion coefficient of the active species. At low chemical reaction rate constants, the classic behavior of the Gerischer impedance is observed in the complex plane. The position of the zero-frequency point in the Nyquist plot is determined by the thickness of the kinetic (reaction) layer. The obtained results can be applied for a better understanding of reaction-diffusion impedance, especially during analysis of the parameters extracted from low frequency range of impedance.

Transport of a reactive solute in a pulsatile non-Newtonian liquid flowing through an annular pipe

The impact of heterogeneous (kinetic reversible phase exchange and irreversible absorption) chemical reactions along with a homogeneous first-order reaction is considered for the dispersion of a solute in a solvent flowing through an annular pipe under a periodic pressure gradient. A Casson model is used to describe the non-Newtonian viscosity of the liquid. The Aris–Barton method of moments is employed to study the behavior of the dispersion coefficient. The axial distribution of the mean concentration is determined using the Hermite polynomial representation of central moments. This study focuses on the transport phenomena in terms of the dispersion coefficient due to multiple kinds of reaction, yield stress, radius ratio, etc., which could be useful for analysis of flow of physiological blood-like liquids.

Exploration of Chemical Reaction Effects on Entropy Generation in Heat and Mass Transfer of Magneto-Jeffery Liquid

Abstract In many chemical engineering processes, a chemical reaction between a foreign mass and the fluid does occur. These processes find relevance in polymer production, oxidation of solid materials, ceramics or glassware manufacturing, tubular reactors, food processing, and synthesis of ceramic materials. Therefore, an exploration of homogeneous first-order chemical reaction effects on heat and mass transfer along with entropy analysis of Jeffrey liquid flow towards a stretched isothermal porous sheet is performed. Fluid is conducting electrically in the company of transverse magnetic field. Variations in heat and mass transfer mechanisms are accounted in the presence of viscous dissipation, heat source/sink and cross-diffusion aspects. The partial differential equations system governing the heat transfer of Jeffery liquid is reformed to the ordinary differential system through relevant transformations. Numerical solutions based on Runge-Kutta shooting method are obtained for the subsequent nonlinear problem. A parametric exploration is conducted to reveal the tendency of the solutions. The present study reveals that the Lorentz force due to magnetism can be used as a key parameter to control the flow fields. Entropy number is larger for higher values of Deborah and Brinkman numbers. It is also established that the concentration species field and its layer thickness of the Jeffery liquid decreases for a stronger chemical reaction aspect. To comprehend the legitimacy of numerical results a comparison with the existing results is made in this exploration and alleged an admirable agreement.

Improving enzymatic saccharification of eucalyptus with a pretreatment process using MgCl2

Pretreatment using an acid salt is a novel technology for biomass conversion, which not only improves the following enzymatic efficiency but also decreases the equipment corrosion. In the present work, MgCl2 was used as a pretreatment for enzymatic saccharification. After pretreatment, the solid substrate (SS) and pretreatment liquor (PL) were characterized, and the SS was enzymatically hydrolyzed to evaluate the conversion yield of cellulose (CYC). The results showed that the pretreatment using MgCl2 had a strong degradation effect on hemicellulose, whose removal rate was nearly 100% in certain cases. After pretreatment, the efficiency of the enzymatic SS saccharification increased, such that the CYC was as high as 99.5%. The degradation kinetics of hemicellulose and cellulose both followed first-order homogeneous reactions, and the reaction activation energies Ea were 46.63 kJ/mol and 82.26 kJ/mol, respectively. The suitable pretreatment conditions were as follows: 0.2 mol/L MgCl2 at 210 °C for 20 min.

Mathematical modeling of the dynamics of homogeneous reactions in the cascade of perfect mixing reactors

Present study tackles theoretical analysis and mathematical modeling of the process of homogeneous first-order reaction in the cascade of perfect mixing reactors of continuous action (PMR-C). The modeling of chemical reactors is based on the thermal and material balances in combination with chemical kinetics. The mathematical model of the dynamics of the process of homogeneous first-order reaction in the PMR-C cascade is represented in the form of equations of change in the molar fraction of substance over time and a change in the inner energy of the ideal flow of substance. In the present work, we calculated, by the mathematical model, the process of acetic anhydride hydrolysis in 5 sequentially connected PMR-C. Calculation by the model is performed by the Runge-Kutta method of third order. We obtained temperature profiles for the dynamics of the process of acetic anhydride hydrolysis for a cascade of PMR-C. The temperature gradient in reactor grows over time; consequently, it takes on a constant value. We analyzed the impact of the volume of reaction mixture on the depth of the course of the process both for the separate perfect mixing reactors and for the cascade of perfect mixing reactors. With an increase in the volume of mixture, the reaction rate increases, while the speed of reaching the necessary degree of conversion decreases. The speed of reaching the maximum degree of conversion for the cascade of reactors compared with one perfect mixing reactor of the same volume is considerably higher. Recommendations regarding the course of the process are formulated. We calculated the value of cost for conducting the process of acetic anhydride hydrolysis depending on the change in temperature. Minimum cost is attained at temperature 341 K and amounts to UAH 1.70 million per year.

Free Convection Heat and Mass Transfer Flow for Magnetohydrodynamic Chemically Reacting and Radiating Elastico-Viscous Fluid Past a Vertical Permeable Plate with Gravity Modulation

An analysis of a two-dimensional unsteady magnetohydrodynamic free convective heat and mass transfer flow of an electrically conducting, optically thin, incompressible, and radiating elastico-viscous fluid (characterised by Walters’ liquid $${B}'$$ ) past a vertical permeable infinite plate embedded in a uniform porous medium with gravity modulation is considered. It is assumed that there exists a homogeneous first-order chemical reaction. Analytical solutions for velocity, temperature and concentration field have been derived. The effects of gravity modulation, radiation, and chemical reaction on velocity profile and shear stress for both Newtonian and elastico-viscous fluid have been studied and presented graphically. It was observed that velocity distribution increases with an increase in gravity modulation parameter and radiation parameter for both Newtonian and elastico-viscous fluid, where as it shows reverse effects in the case of magnetic field parameter and viscoelastic parameter. It is seen that viscous drag on the plate is reduced under the effect of chemical reaction parameter, where as it shows reverse effect in the case of gravity modulation parameter and radiation parameter.

MHD Mixed Convection Oscillatory Flow over a Vertical Surface in a Porous Medium with Chemical Reaction and Thermal Radiation

The present paper concerns with the study of thermal radiation and magnetohydrodynamic effects on mixed convection flow of a viscous incompressible electrically-conducting fluid through a porous medium with variable permeability in the presence of oscillatory suction. The influence of a first-order homogeneous chemical reaction, heat source and Soret effects are analyzed. The resultant governing boundary layer equations are highly nonlinear and coupled form of partial differential equations which are solved analytically using two-term harmonic and non-harmonic functions. The effects of different physical parameters on the velocity, temperature and concentration fields are discussed in detail. The results are presented graphically and discussed qualitatively.

Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder

The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.

Chemically reactive species and radiation effects on MHD convective flow past a moving vertical cylinder

The numerical solution of transient natural convection flow of radiation effects on MHD heat and mass transfer past a moving vertical cylinder with chemical reaction is presented. The governing boundary layer equations for the above flow problem of first-order homogeneous chemical reaction are setup and non-dimensionalized. An implicit finite difference method is used to solve the unsteady, non-linear, and coupled governing equations. Numerical results are presented for various parameters. The unsteady velocity, temperature, concentration profiles, local and average skin-friction, Nusselt number, and Sherwood number are shown graphically and are discussed for both generative and destructive reaction.

EFFECTS OF HALL CURRENT AND CHEMICAL REACTION ON OSCILLATORY MIXED CONVECTION-RADIATION OF A MICROPOLAR FLUID IN A ROTATING SYSTEM

This article is concerned with the analysis of the effects of thermal radiation on oscillatory mixed convection flow of a micropolar fluid in a rotating frame of reference in the presence of transverse magnetic field and Hall current. The influence of a first-order homogeneous chemical reaction and heat source effects is also analyzed. The governing partial differential equations with the appropriate boundary conditions are reduced to a set of ordinary differential equations using similarity transformations. The dimensionless governing equations for this investigation are solved analytically after using small perturbation approximation. The effects of various parameters on the velocity, temperature, and concentration fields as well as on skin-friction coefficient, Nusselt number, and Sherwood number with their amplitude and phase are discussed in detail. Numerical results are discussed with the help of graphs and tables. Present results are also compared with previously published work.

Thermal heating regimes during first-order homogeneous reactions

Qualitative features of self-heating regimes for first-order homogeneous reactions are considered by analyzing the structure of the phase trajectories. Consideration of the temperature dependence of the heating rate makes it possible to extend the main results of Semenov’s theory of thermal explosion and pass to a two-dimensional parameter diagram, which allows the determination of the critical ignition conditions taking into account kinetic inhibition. It is found that the diagram of the Todes criterion versus the reciprocal of the Semenov criterion has four characteristic regions with different kinetics, two of which are limiting and two transitional ones. The boundaries of the regions are calculated, and the classical theory of thermal explosion is shown to be a special case of the projections of these boundaries on the range of the Semenov criterion.