Laminar flow diffusion of power-law fluids in a tube with arbitrary order heterogeneous and homogeneous reactions

Solutions for isothermal laminar flow diffusion with simultaneous heterogeneous and homogeneous reactions in a tube are extended to the case of non-Newtonian power-law fluids with arbitrary order reactions. Finite-difference methods are employed to yield the solutions. Special emphases are placed on the role of the reaction product characterized by two unique parameters, the diffusivity ratio and the stoichiometric coefficient ratio. Effects of reaction rate kparameters on the unique parameters, the diffusivity ratio and the stoichiometric coefficient ratio. Effects of reaction rate parameters on the system performance are also presented, showing a crossover behavior of the Sherwood number. The results are in good agreement with known solutions for systems of Newtonian fluids with first-order reactions.     

Absorption of carbon dioxide into laminar falling films of aqueous kaolin slurries containing sodium hydroxide

To confirm the theory for gas absorption accompanied by an instantaneous irreversible reaction in laminar falling films of power-law liquids which was presented in a previous paper, experiments were carried out on the absorption of pure carbon dioxide into aqueous kaolin slurries containing sodium hydroxide by using a long wetted-wall column. The experimental data were in fairly good agreement with the theoretical predictions, the average deviation being 3.0%. The discussion on the effect of the power-law index of the liquid upon the reaction factor suggested an approximate method of estimating the reaction factors for power-law liquids.     

Non-Newtonian power-law flow across a confined triangular bluff body in a channel

Wall effects on the flow of incompressible non-Newtonian power-law fluids across an equilateral triangular cylinder confined in a horizontal plane channel have been investigated for the range of conditions: Reynolds number, Re=1–40, power-law index, n=0.4–1.8 (covering shear-thinning, Newtonian and shear-thickening behaviors) and blockage ratio=0.125–0.5. Extensive numerical results on flow pattern, wake/recirculation length, individual and overall drag coefficients, variation of pressure coefficient on the surface of the triangular cylinder and so forth are reported to elucidate the combined effect of power-law index, blockage ratio and Reynolds number. The size of vortices decreases with an increase in the value of the blockage ratio and/or power-law index. For a fixed value of the Reynolds number, individual and overall drags decrease with decrease in power-law index and/or blockage ratio in steady confined flow regime. Simple correlations of wake length and drag are also obtained for the range of settings considered.     

Deactivation disguised kinetics in high-velocity dilute-phase transport reactors

For a chemical reaction carried out with a fast-decaying catalyst in an isothermal high-velocity dilute-phase transport reactor, the apparent kinetics of the primary chemical reaction may be disguised by the presence of the catalyst deactivation. With a given reaction system of power-law type expressions for both the chemical reaction and catalyst deactivation rates, investigated are the existence conditions of its disguised kinetic system which is also of power-law type formulations.     

Ni/ZnO吸附剂上汽油反应吸附脱硫本征动力学

采用小型固定床反应器,对制备的Ni/ZnO吸附剂的动力学进行测定,动力学实验基本条件为:以噻吩和正辛烷混合物作为模拟汽油,反应压力(0.4~0.8)MPa,反应温度(330~370)℃,氢油体积比70∶1,空速5h-1。在消除吸附剂内、外扩散影响的条件下,通过设计正交实验,得到固定床反应条件下的动力学实验数据。根据幂函数型速率方程,对实验数据进行多元非线性拟合,得到动力学方程为:r=0.0229×e-22528.51/RTp0.0013Hp0.053Sc0.95ZnO,并对模型进行统计检验。结果表明,该模型对表面反应控制阶段具有较好的适用性。     

幂律流体在Kenics型静态混合器中流动特性分析

为了探究Kenics型静态混合器内扭旋叶片剪切作用对幂律流体流动的影响,利用旋转流变仪测量了浓度为0.5wt%, 0.7wt%, 0.9wt%的羧甲基纤维素(CMC)水溶液的流变参数,采用数值模拟与实验研究了扭旋叶片作用下幂律流体流动阻力和剪切稀化特性。对流场研究表明,扭旋叶片诱导产生了内流涡旋、绕流涡旋和近壁面涡旋,有效强化了静态混合器内流体流动的剪切作用。受多个纵向涡旋分布的影响,扭旋叶片局域流场中周向45°位置速度最高,周向30°位置涡量与剪切应力最高而黏度最低。径向0.4倍半径位置速度最高,0.7倍半径位置黏度最高。静态混合器有效提高了流体的二次流流动速度和剪切应力,降低了幂律流体的黏度和流动阻力系数。     

Critical extent of reaction of a polydimethylsiloxane polymer network

A direct rheological technique was used to measure the critical time for gelation, t_c, of a well characterized polydimethylsiloxane (PDMS) polymer network. This technique is based on the observation that the gel point of crosslinking systems occurs at the instant at which the viscoelastic behaviour reduces to power-law relaxation (critical state described by the gel equation). The extent of reaction, p(t), was measured by a Fourier-transform infra-red method. The measured value of the critical extent of reaction, p_c = p(t_c) = 0.57 ± 0.01, agrees extremely well with the value predicted by mean-field theory. This agreement is an independent confirmation of the observation that power-law relaxation is a property of the polymer at the gel point.     

MOMENTUM INTEGRAL METHOD FOR FORCED CONVECTION IN THERMAL NONEQUILIBRIUM POWER-LAW FLUID-SATURATED POROUS MEDIA

Forced convection heat transfer for power-law fluid flow in porous media was studied analytically. The analytical solutions were obtained based on the Brinkman-extended Darcy model for fluid flow and the two-equation model for forced convection heat transfer. As a closed-form exact velocity profile is unobtainable for the general power-law index, an approximate velocity profile based on the parabolic model is proposed by subscribing to the momentum boundary layer integral method. Heat transfer analysis is based on the two-equation model by considering local thermal nonequilibrium between fluid and solid phases and constant heat flux boundary conditions. The velocity and temperature distributions obtained based on the parabolic model were verified to be reasonably accurate and improvement is justified compared to the linear model. The expression for the overall Nusselt number was derived based on the proposed parabolic model. The effects of the governing parameters of engineering importance such as Darcy number, power-law index, nondimensional interfacial heat transfer coefficient, and effective thermal conductivity ratio on the convective heat transfer characteristics of non-Newtonian fluids in porous media are analyzed and discussed.     

USING POWER-LAW RATE EXPRESSION PARAMETERS FOR DISCRIMINATION AMONG MECHANISTIC MODELS IN RATE DATA REGRESSION

Langmuir-Hinshelwood (or Hougen-Watson) type rate expressions are most often used in modeling reaction rate data. In cases when there are tens of possible rival models, effective discrimination between them requires that most of the inadequate models be discarded as early as possible in the discrimination process.

In this paper, the relationship between power-law and Hougen and Watson type rate expressions was studied. It was found that there is a clear mathematical connection between the two types of rate expressions. This connection can be utilized in order to discriminate between feasible and infeasible models, using only the numerical values of the power-law rate expression parameters. This way most of the inadequate mechanisms can be discarded after fitting the data to a single (power-law) model.

The 95% confidence intervals of the parameters have proven to be key statistical variables in determining the adequacy of both power-law and mechanistic models. Using the data and results of Hougen and Watson (1947), it is shown that they rejected valid mechanisms and accepted invalid ones because they did not take into account the confidence intervals on the parameters.     

CoMo/Al2O3-TiO2催化剂上加氢深度脱硫反应及其宏观动力学

采用气液固三相滴流床反应器,在反应温度(493~558) K,氢压(1.5~3.0) MPa和氢油体积比为200~800条件下,研究了苯并噻吩和二苯并噻吩模型化合物在钴钼基催化剂上加氢脱硫反应及其宏观动力学。根据幂函数型动力学方程,以全局通用算法结合马夸特算法对动力学参数进行估值,建立了与实验数据相吻合的柴油中含硫模型化合物的深度加氢脱硫反应动力学模型。其中,苯并噻吩的一级方程活化能为3.985×104 J·mol^-1,二苯并噻吩的二级方程的活化能为3.130×104 J·mol^-1。残差检验和统计学考察表明,模型计算结果和实验数据吻合良好。     

Optimization of the active component distribution through the catalyst bed

A variational problem was formulated to determine the optimal axially non-uniform catalyst activity distribution along the fixed catalyst bed. It was observed that the mass transport limitations or non-isothermal temperature profile are necessary conditions for potential optimization of the catalyst distribution along the bed length. Under isothermal conditions with linear dependence of the reaction rate on concentration at a constant mass transfer coefficient, the uniform distribution is optimal. Analytical solution for the first-order reaction and numerical solutions for power-law kinetics were found.     

Kinetics of asphaltenes conversion during hydrotreating of Maya crude

The kinetics of asphaltene conversion was studied during the hydrotreating of Maya heavy crude oil. Experimental tests were conducted in a pilot plant at the following reaction conditions: total pressure of 70–100 kg/cm², liquid hourly space-velocity (LHSV) of 0.33–1.5 h⁻¹, and reaction temperature of 380–420 °C at a constant hydrogen-to-oil ratio of 5000 ft³/bbl. A commercial NiMo/Al₂O₃ catalyst was used in all experiments. Asphaltenes were precipitated from Maya crude and from hydrotreated products in a Parr Batch Reactor at 25 kg/cm² and 60 °C with n-heptane as solvent. Asphaltene hydrocracking data were used to estimate reaction orders and activation energy using a power-law model, and the average absolute error between experimental and calculated concentrations of asphaltenes was found to be less than 5%.     

Numerical simulation of entry and exit flows in slit dies

A general-purpose finite element program has been used to simulate the flow of Newtonian, power-law, and viscoelastic fluids in the entry and exit regions of a slit die. It was found that shear-thinning increases the entrance correction while it decreases the exit correction. Shear-thinning reduces the size of the small corner vortex that forms in the entry flow of a Newtonian fluid. The swelling ratio had a value of 1.196 for Newtonian fluids and decreased as the value of the power-law index decreased. Viscoelastic calculations were performed using the Criminale-Ericksen-Filbey (CEF) constitutive equation. Convergence of the iterative scheme was unattainable for Deborah numbers above 1.0. The results showed a decrease of the entrance correction and an increase of the exit correction with elasticity. Extrudate swell first decreased slightly and further increased with the Deborah number.     

MOTION OF A CIRCULATING POWER-LAW DROP TRANSLATING THROUGH NEWTONIAN FLUIDS AT INTERMEDIATE REYNOLDS NUMBERS

The equations of motion for the flow of a power-law fluid sphere in a Newtonian continuous phase have been approximately satisfied by Galerkin's method: External and internal stream functions have been obtained for the following ranges of variables: 10-50 for Re₀, 0.1-1000 for the viscosity ratio parameters, X, and 0.6-1.0 for the dispersed phase power-law index, n_i,. It is predicted that pseudoplasticity in the dispersed phase causes a reduction in the circulation within the drop and that it has a minor effect on the drag coefficients and the rates of mass transfer in the continuous phase     

LB型节能催化剂上高温变换反应本征动力学及工业化测定

运用正交实验设计安排了LB型节能催化剂高温变换反应本征动力学实验,测得不同温度、不同流量、不同水碳比、不同反应气体摩尔分数下LB型节能催化剂上CO高温变换反应本征动力学数据。用甲酸盐机理模型和幂函数模型拟合实验数据,确定了本征动力学模型参数。进行了本征动力学模型统计检验,表明所建模型无论局部还是整体都是显著和可信的。在此基础上,进行了大型合成氨装置上LB型节能催化剂高变反应工业化测定,按多组分单一反应等温球形催化剂一维非均相反应-扩散模型,利用配置法结合解非线性方程组的Merson法求解模型,得到了工业反应器中催化剂床层温度、内扩散有效因子、CO转化率和摩尔分数随床层相对高度的分布,模拟结果与工业化测定结果吻合。     

Stability of fiber spinning of power-law fluids

A stability analysis of fiber spinning of isothermal power-law fluids has been carried out. The analysis for purely viscous fluids indicates that the critical extension ratio increases with an increase in power-law constant q above 1. For q greater than approximately 1.5, very high values of critical extension ratio are obtained. A stability analysis in the presence of viscous and inertial forces indicates that for q > 1 critical extension ratio can be correlated to a quantity Rq = q ? 1 + 3Re, wherein Re is the Reynolds number. For the values of Rq greather than approximately 0.5, very high values of critical extension ratios are obtained.     

UNSTEADY MHD BOUNDARY LAYER FLOW WITH DIFFUSION AND FIRST-ORDER CHEMICAL REACTION OVER A PERMEABLE STRETCHING SHEET WITH SUCTION OR BLOWING

In this study, unsteady MHD boundary layer flow with diffusion of chemically reactive species undergoing first-order chemical reaction over a permeable stretching sheet with suction or blowing and also with power-law variation in wall concentration is investigated. Using similarity transformation, the governing partial differential equations are converted into nonlinear self-similar ordinary differential equations. The transformed equations are then solved by the finite difference method using the quasi-linearization technique. Due to the increase in the unsteadiness parameter, the velocity initially decreases, but after a certain point it increases. A similar effect is also observed in case of concentration distribution. The increase in magnetic parameter causes a decrease in velocity and an increase in concentration. For increasing strength of applied suction both momentum and concentration boundary layer thicknesses decrease. On the other hand, applied blowing has reverse effects. Moreover, the mass transfer from the sheet is enhanced with increasing values of Schmidt number, reaction rate parameter, and also power-law exponent (related to wall concentration distribution). For high negative values of the power-law exponent, mass absorption at the sheet occurs. Moreover, due to increase of unsteadiness, this mass absorption is prevented.     

Kinetic Effects on Hydroxyapatite Whiskers Synthesized by the Chelate Decomposition Method

Hydroxyapatite (HA) whiskers have been synthesized using a number of chemical solution methods, including the chelate decomposition method. Numerous previous studies have investigated the effects of the reagents, reagent concentrations, solution pH, and reaction temperature on HA whisker morphology and composition. However, purely kinetic effects, such as the reaction heating and stirring rates, have not been rigorously investigated and are rarely reported in the literature. Therefore, the objective of this study was to investigate kinetic effects on the morphology of HA whiskers synthesized using the chelate decomposition method. In order to study the kinetic effects on the morphology of HA whiskers, three experimental parameters were varied independently: the reaction heating rate (0.36°–3.0°C/min), stirring rate (0–250 rpm), and temperature (80°–200°C). At all heating and stirring rates, precipitated whiskers were confirmed by XRD and FT-IR to comprise phase-pure, calcium-deficient HA (Ca/P=1.57–1.62). The length and aspect ratio of HA whiskers increased with decreased heating rate, decreased stirring rate, and increased reaction temperature. The mean length and aspect ratio of HA whiskers increased approximately twofold with decreased heating rate over the range studied, following a power-law relationship. Therefore, the reaction heating rate is a key variable that can be used to tailor the morphology of HA whiskers and ought to be reported in the literature. The reaction heating rate and temperature had relatively little effect on the width of HA whiskers. However, the precipitate morphology was altered significantly from micro-scale whiskers to nano-scale plates with increased stirring rate. These results offered new insights and provided clarification regarding the reaction mechanism, which is discussed in detail.     

Laminar mixing of shear thinning fluids in a SMX static mixer

Flow and mixing of power-law fluids in a standard SMX static mixer were simulated using computational fluid dynamics (CFD). Results showed that shear thinning reduces the ratio of pressure drop in the static mixer to pressure drop in empty tube as compared to Newtonian fluids. The correlations for pressure drop and friction factor were obtained at Re_MR?100. The friction factor is a function of both Reynolds number and power-law index. A proper apparent strain rate, area-weighted average strain rate on the solid surface in mixing section, was proposed to calculate pressure drop for a non-Newtonian fluid. Particle tracking showed that shear thinning fluids exhibit better mixing quality, lower pressure drop and higher mixing efficiency as compared to a Newtonian fluid in the SMX static mixer.     

Relative Young’s modulus and thermal conductivity of isotropic porous ceramics with randomly oriented spheroidal pores – Model-based relations,cross-property predictions and numerical calculations

Based on computer-generated digital microstructures with spherical or spheroidal pores (isolated or overlapping) of aspect ratio 1 (spherical), 10 (prolate) and 0.1 (oblate), the relative thermal conductivity and Young’s modulus is numerically calculated and compared to predictions based on generalized effective medium approximations (EMAs) and a recently proposed generalized cross-property relation (CPR). It is shown that, when the aspect ratio is known, generalized power-law and exponential relations provide satisfactory predictions of these two properties without the use of empirical fit parameters. The maximum deviation of these two types of EMA predictions from the true values ranges from ?0.04 to +0.06 relative property units (RPU) for the power-law relation and from ?0.02 to ?0.10 RPU for the exponential relation. However, the generalized CPR results in an even higher accuracy of the predictions, with maximum deviations smaller than 0.01 RPU for the Young’s modulus when the thermal conductivity is known.