Mathematical modelling of hydrothermal performance for Kenics type static mixer using power law obeying fluids

In this study, analytical, numerical, and experimental works are presented to demonstrate hydrothermal characteristics of a flow choosing non-Newtonian behaviour through a Kenics type static mixer. Experiments are conducted by varying the superficial fluid velocities of the heterogeneous mixture oil with Sudan dye and water, as well as for the homogeneous aqueous system, consisting of CMC (2 wt%) in water. Six static mixing elements are placed in series, and the corresponding wall temperatures of the inline pipe are varied over a range of 293–363 K. In the context of hydrodynamic study, analytical models are solved using the Bessel function and Laguerre function and validated with the in-house experimental results and numerical results. In the thermal performance study, mathematical models are formulated based on differential transformation method (DTM) and homotopy perturbation method (HPM), and have been validated with the numerical results. The deviation among the experimentally measured average pressure drops estimated from our experiment and that predicted by analytical models is found to be as low as ±8.1%. The deviation between the analytical results obtained from the HPM and DTM method and numerical results based on the finite volume method solution of the same equation is observed as low as ±4%. Additionally, both proposed analytical methods used are compared with each other to evaluate the dimensionless swirl flow velocity and temperature gradient of the inline Kenics Static mixer. In the thermal performance study, we observe that the DTM is in good agreement with the numerical method as compared to HPM.     

Novel solution for acceleration motion of a vertically falling non-spherical particle by VIM–Padé approximant

In this paper, the acceleration motion of a vertically falling non-spherical particle in incompressible Newtonian media was investigated. The velocity and acceleration were carried out using analytical solution techniques i.e., the variational iteration method (VIM) and a Padé approximant. The results were also compared with VIM and the established fourth order Runge–Kutta method in order to verify the accuracy of the proposed method. It was shown that this method can lead into more accurate results compared with VIM.     

A phosphorus‐containing phenolic derivative and its application in benzoxazine resins: Curing behavior,thermal, and flammability properties

In this work, flame‐retardant benzoxazine resins were prepared by copolymerization of bisphenol A based benzoxazine (BA‐a) and a phosphorous‐containing phenolic derivative (DOPO‐HPM). The curing behavior, thermal stability, and flame resistance of BA‐a/DOPO‐HPM composites were studied by differential scanning calorimeter (DSC), thermogravimetric analysis (TGA), limited oxygen index (LOI) measurement, UL94 test, and cone calorimeter. The DSC results indicated that DOPO‐HPM catalyzed the curing reaction because of its acidity. The TGA results revealed that the BA‐a/DOPO‐HPM thermosets possessed higher decomposition temperatures (T_5%) and char yields than that of BA‐a. The combustion tests indicated that the flame retardant properties of BA‐a/DOPO‐HPM thermosets were enhanced. The BA‐a/DOPO‐HPM‐20 sample acquired the highest LOI value of 32.6% and UL94 V‐0 rating. Moreover, the average of heat release rate (av‐HRR), peak of heat release rate (pk‐HRR), average of effective heat of combustion (av‐EHC) and total heat release (THR) of BA‐a/DOPO‐HPM‐20 were decreased by 24.6%, 53.1%, 14.9%, and 22.1%, respectively, compared with BA‐a. The attractive performance of BA‐a/DOPO‐HPM blends was attributed to the molecular structure of DOPO‐HPM composed of DOPO group with excellent flame‐retardant effect and phenolic hydroxyl group with catalysis. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43403.     

Nickel electroless deposition process on chemically pretreated Si(100) wafers in aqueous alkaline solution

Pretreating Si wafer surfaces with hydrochloric acid and hydrogen peroxide mixture (HPM) or ethanol was found to enhance the reactivity of chemical Ni deposition on Si(100) wafers in a simple bath of NiSO₄-(NH₄)₂SO₄ at pH 9.0. This phenomenon was identified as the acceleration of anodic reaction involved in chemical Ni deposition reaction on Si wafer surfaces, namely oxidation process of surface Si. Just after immersing into the alkaline bath, a reactive surface where oxidation reaction of Si was accelerated was formed on Si wafer surface with HPM or ethanol pretreatment. On the reactive surface, uniform and glossy Ni deposition film was obtained. In order to clarify the effects of HPM- or ethanol-pretreatment on anodic reaction, the pretreated Si(100) wafers were immersed into aqueous alkaline solution excluding NiSO₄, resulting acceleration of Si oxidation compared to the unpretreated Si(100) surface. The progress of surface reactivity was also clarified by open circuit potentials (OCP), XPS, and ex-situ ATR FTIR. Moreover, by using this pretreatment, selective deposition onto nano-patterned Si substrate was performed. A two-dimensional array of fine Ni dots (diameter ca. 80 nm) was successfully fabricated.     

Two Analytical Approaches for Solution of Population Balance Equations: Particle Breakage Process

Various particulate systems were modeled by the population balance equation (PBE). However, only few cases of analytical solutions for the breakage process do exist, with most solutions being valid for the batch stirred vessel. The analytical solutions of the PBE for particulate processes under the influence of particle breakage in batch and continuous processes were investigated. Such solutions are obtained from the integro‐differential PBE governing the particle size distribution density function by two analytical approaches: the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM). ADM generates an infinite series which converges uniformly to the exact solution of the problem, while HPM transforms a difficult problem into a simple one which can be easily handled. The results indicate that the two methods can avoid numerical stability problems which often characterize general numerical techniques in this area.     

Probability density function simulation of turbulent reactive gas‐solid flow in a FCC riser

A newly developed hybrid solution algorithm applicable on turbulent multiphase, gas‐solid, reactive flows is presented. A finite volume (FV) and a probability density function (PDF) method are combined. The FV technique is used to solve the total mass and momentum conservation equations together with the k‐ε turbulence equation for the gas phase and the granular temperature equation for the solid phase. The PDF method is applied to solve the species continuity equations and avoids the need to model the chemical source terms in the latter. Stochastic differential equations (SDEs) are introduced as replicas of the transported composition PDF equations. The notional‐particle‐based Monte‐Carlo technique is used to solve the PDF model equations. The hybrid FV/PDF solution algorithm is applied to simulate a fluid catalytic cracking (FCC) riser using a 12‐lump kinetic model. A good agreement between simulated results and available plant data is obtained. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Mathematical modeling of diffusion and kinetics in amperometric immobilized enzyme electrodes

An analysis of the diffusion and kinetics in amperometric immobilized enzyme electrodes is presented for reactions of the enzyme and substrate. This analysis contains a non-linear term related to Michaelis-Menten kinetics. In this paper, we obtain approximate analytical solutions for the non-linear equations that describe diffusion and the reaction within the film by employing the homotopy perturbation method (HPM). The obtained analytical results are compared with the available limiting case results and found to be in satisfactory agreement.     

Moving ion fronts in mixed ionic‐electronic conducting polymer films

The aim of this paper is to analyze moving front dynamics of ions and holes in a planar, mixed ionic‐electronic conducting polymer film. As cations invade the film, holes evacuate; thus, an ionic current is converted to an electronic signal. Recent experiments show that the location of the advancing ion front increases as the square‐root of time, a scaling typically associated with diffusive transport, which is surprising given the large driving voltages utilized. Ionic and electronic transport is modeled via the drift‐diffusion equations. A similarity transformation reduces the governing partial differential equations to ordinary differential equations that are solved numerically. The similarity transformation elucidates the origin of the square‐root‐of‐time front scaling. The similarity solution is then compared to the numerical solution of the full drift‐diffusion equations, finding excellent agreement. When compared with experimental data, our model captures the front location; however, qualitative differences between the ion profiles are observed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1447–1454, 2015     

On the numerical solution of differential algebraic equations

A method is proposed to transform a system of differential algebraic equations (D.A.E.) to a system of ordinary differential equations (O.D.E.) which can be solved relatively easily by standard numerical techniques. Two examples, including a model of an absorption tower, are given to illustrate the utility of the method. The example problems reveal that this easily implemented technique offers significant savings in CPU time compared to the numerical solution of the untransformed D.A.E.s particularly when the algebraic equations are nonlinear. Furthermore, it appears to be faster and/or more reliable than other numerical schemes which have been recently developed for equations of this type.     

Automatic differentiation‐based quadrature method of moments for solving population balance equations

The quadrature method of moments (QMOM) is a promising tool for the solution of population balance equations. QMOM requires solving differential algebraic equations (DAEs) consisting of ordinary differential equations related to the evolution of moments and nonlinear algebraic equations resulting from the quadrature approximation of moments. The available techniques for QMOM are computationally expensive and are able to solve for only a few moments due to numerical robustness deficiencies. In this article, the use of automatic differentiation (AD) is proposed for solution of DAEs arising in QMOM. In the proposed method, the variables of interest are approximated using high‐order Taylor series. The use of AD and Taylor series gives rise to algebraic equations, which can be solved sequentially to obtain high‐fidelity solution of the DAEs. Benchmark examples involving different mechanisms are used to demonstrate the superior accuracy, computational advantage, and robustness of AD‐QMOM over the existing state‐of‐the‐art technique, that is, DAE‐QMOM. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Strontium(II) ion uptake on poly(N‐vinyl imidazole)‐based hydrogels

In this article, we report on the extraction of Sr(II) ions from aqueous solution with a series of poly(N‐vinyl imidazole)‐based hydrogels. The hydrogels were synthesized by the crosslinking of N‐vinyl imidazole with four different crosslinkers with γ rays as initiators. The well‐characterized hydrogels were used as Sr(II) sorbents. Sr(II) uptake was determined with a colorimetric method with Rose Bengal anionic dye. Scanning electron microscopy–energy‐dispersive spectroscopy analysis of the Sr(II)‐loaded polymers was recorded to ascertain the uptake of Sr(II) ions. The experimental adsorption values were analyzed with the Freundlich and Temkin equations, and the kinetics of adsorption were investigated with a pseudo‐second‐order sorption kinetic model. The results show that the equilibrium data fit well in the Freundlich isotherm and followed a pseudo‐second‐order kinetic model. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Adsorption of cadmium (II) and copper (II) ions from aqueous solution using chitosan composite

The binary chitosan/silk fibroin composite synthesized by reinforcement of silk fibroin fiber into the homogenous solution of chitosan in formic acid was used to investigate the adsorption of two metals of Cu(II) and Cd(II) ions in an aqueous solution. The binary composite was characterized by Fourier transform infrared and scanning electron microscopy. The optimum conditions for adsorption by using a batch method were evaluated by changing various parameters such as contact time, adsorbent dose, and pH of the solution. The experimental isotherm data were analyzed using the Freundlich and Langmuir equations, indicated to be well fitted to the Langmuir isotherm equation under the concentration range studied, by comparing the correlation co‐efficient. Adsorption kinetics data were tested using pseudo‐first‐order and pseudo‐second‐order models. Kinetics studies showed that the adsorption followed a pseudo‐second‐order reaction. Due to good performance and low cost, this binary chitosan/silk fibroin composite can be used as an adsorbent for removal of Cu(II) and Cd(II) from aqueous solutions. POLYM. COMPOS., 2013. © 2013 Society of Plastics Engineers     

Accelerated successive substitution schemes for bubble-point and dew-point calculations

The accelerated successive substitution (SS) algorithms developed by Mehra et al. for flash calculations have been extended to the prediction of saturation points. A transformation matrix which is used to calculate the acceleration parameter has been rewritten in a form that is applicable at the saturation conditions. Simple equations for estimating the initial values and recursive formulae according to which the iterates can be updated are presented. The proposed schemes were compared with the conventional SS method and a multivariate Newton's method. The comparison suggests that the accelerated SS schemes are more tolerant of poor initial values and sometimes more efficient than Newton's method.     

Determination of the crystalline phases of poly(vinylidene fluoride) under different preparation conditions using differential scanning calorimetry and infrared spectroscopy

A method with good precision has been developed to quantitatively measure the degree of α‐, β‐, and γ crystallinity in poly(vinylidene fluoride) (PVDF) by means of infrared spectroscopy. The phase composition of solution‐deposited PVDF films was found to be strongly influenced by the presence of hydrophilic residues on the silicon substrate, the relative humidity present at film deposition, the spatial position on the substrate, and the thermal treatment of the deposited film. Films produced on pristine surfaces gave predominantly α‐phase PVDF, but when a layer of polar solvent (acetone or methanol) remained on the surface, the films produced were predominantly γ phase. Higher humidity promoted a higher fraction of γ crystallinity in the solution‐deposited PVDF films. Solution‐cast films had highly variable composition across the substrate, whereas spin‐cast films were uniform. High‐temperature annealing of PVDF films normally converts the polymer to the γ phase, but annealing the film while still attached to the silicon substrate inhibited this phase transformation. Low‐temperature annealing of freestanding films led to a previously unreported thermal event in the DSC, a premelting process that is a kinetic event, assigned to a crystalline relaxation. Higher‐temperature annealing gave a double endotherm, assigned to melting of different‐sized crystalline domains. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 1093–1100, 2003     

A parallel function evaluation approach for solution to large-scale equation-oriented models

The equation-oriented (EO) approach is widely used for process simulation and optimization. Nevertheless, large-scale EO models consist of a huge number of nonlinear equations and make the solution procedure a challenging and time-consuming task. For most gradient-based numerical algorithms, function evaluations are the dominant step during the solution procedure. Here, a parallel computation method is developed for function evaluations within EO optimization strategies. After dividing the equations into several groups, function evaluations are calculated by using multiple threads on a parallel hardware platform simultaneously. Theoretical analysis for the speedup ratio is conducted. The implementation of the proposed method on a multi-core processor platform as well as a graphics processing unit (GPU) platform is then presented with several case studies. Numerical results are compared and discussed to show that the multi-core processor implementation has good computational performance, whereas the GPU implementation only achieves computational acceleration under relatively specific conditions.     

A comparative study on optimised and non‐optimised axial flow,spherical reactors in naphtha reforming process

In this study, the operating conditions of an axial flow spherical reactor have been optimised using a reliable optimisation technique and the results are compared with the results of non‐optimised conditions. The dynamic behaviour of the reactor has been considered in the optimisation process and orthogonal collocation method has been used in order to solve the obtained equations from mathematical modelling of the process. The goal of this study is to maximise the aromatics and hydrogen production rate. Therefore, the objective function is the combination of two terms which include the production rate of the mentioned components. The catalyst distribution for each reactor, the inlet pressure of the system, Length per radius for each reactor, the naphtha feed molar flow rate and the hydrogen mole fraction in the recycle stream as well as the inlet temperature of each reactor have been optimised in this study. © 2011 Canadian Society for Chemical Engineering     

General rate equations and their applications for cyclic reaction networks: pyramidal systems

The King-Altman-Hill graphic method has been widely used to derive the rate laws of enzymatic reactions, but the compilation of all the possible pathways is very time-consuming and the reaction rates are not given explicitly. In this study, the network reduction and Y-to-delta transformation techniques were systematically used to derive the general rate equations for pyramidal reaction networks in homogeneous catalysis. The enzymatic reaction of 7,8-dihydrofolate and NADPH to form 5,6,6,8-tetrahydrofolate and NADP, catalyzed by dihydrofolate reductase was taken as an example to illustrate the application of the general reaction rate equations. The calculated overall reaction rate was compared with that obtained from the exact solution by matrix algebra and those obtained from the King-Altman-Hill graphic method.     

A GENERALIZED DIFFERENTIAL TRANSFORM METHOD FOR COMBINED FREE AND FORCED CONVECTION FLOW ABOUT INCLINED SURFACES IN POROUS MEDIA

In this article, we apply the differential transform method (DTM) to obtain approximate analytical solutions of combined free and forced (mixed) convection about inclined surfaces (or wedges) in a saturated porous medium. Both aiding and opposing flows are considered. It is found that the parameter mixed convection from inclined surfaces in porous media is Gr/Re, where Gr is the local Grashof number and Re is the local Reynolds number. DTM solutions are obtained for mixed convection from an isothermal vertical flat plate as well as an inclined plate with constant heat flux having an inclination of 45°. Temperature and velocity profiles for these two cases at different values of Gr/Re are presented. The similarity transformations are applied to reduce the governing partial differential equations (PDEs) to a set of nonlinear coupled ordinary differential equations (ODEs) in dimensionless form. DTM is used to solve the nonlinear differential equations governing the problem in the form of series with easily computable terms. Thereafter a Padé approximant is applied to the solutions to increase the convergence of the given series. Excellent correlation between DTM-Padé and numerical quadrature (shooting) solutions is achieved. The DTM-Padé simulation is shown to be a robust benchmarking tool providing an excellent means of validation of numerical methods. The study has applications in geothermal energy systems, chemical engineering filtration systems, and packed beds.     

Fabrication of mPEGylated graphene oxide/poly(2‐dimethyl aminoethyl methacrylate) nanohybrids and their primary application for small interfering RNA delivery

Graphene oxide (GO)‐based nanohybrids were designed for small interfering RNA (siRNA) delivery for their high water dispensability, good biocompatibility, easily tunable surface functionalization, and particular optical properties. In this study, novel nanohybrids based on GO were fabricated. Methoxypoly(ethylene glycol) (mPEG) was covalently conjugated to GO via amide bonds. Then, poly(2‐dimethyl aminoethyl methacrylate) (PDMAEMA), which was synthesized via reversible addition–fragmentation chain transfer polymerization (RAFT) with 2‐(dodecyl thiocarbonothioyl thio)‐2‐methyl propionic acid (DTM) as the RAFT agent, was attached onto GO via physical interaction between DTM and GO. Compared with Lipofectamine 2000, the novel mPEG–GO/PDMAEMA nanohybrids showed comparable gene transfection efficiency and a low cytotoxicity. Moreover, the mPEG–GO/PDMAEMA nanohybrids showed enhanced optical properties compared to the original GO because of the presence of mPEG and PDMAEMA. Our work encouraged further exploration of the novel nanovector for combined photothermal and siRNA delivery. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43303.