Housam Binous

Dynamic simulation of one and two particles sedimenting in viscoelastic suspensions of FENE dumbbells

Abstract A new method is introduced for simulating the motion of particles in a viscoelastic fluid. The viscoelastic fluid is represented as a suspension of finite-extension-non-linear-elastic (FENE) dumbbells in Newtonian solvent. Instead of using an averaging technique to derive a continuum constitutive model, such as that of Chilcott and Rallison, we calculate directly the particle–particle and particle–bead interactions by using a modified version of the Stokesian dynamics method. This method is applied to a series of sedimentation problems, including the sedimentation of a single sphere, a non-spherical particle, and two spheres. It is found that the drag of a single sphere can be increased significantly by the presence of the dumbbells, and at high Deborah numbers (De) the sphere velocity becomes time-periodic. Non-spherical particles rotate as they fall such that their long axis is ultimately pointed in the direction of gravity. Two sedimenting spheres are in most cases attracted to each other, and they turn such that their line-of-centers is in the direction of gravity. The rotational velocity of the spheres in a side-by-side configuration is in the same direction as it would be in Newtonian fluid, in keeping with experimental observations found in the literature.

The effect of sphere-wall interactions on particle motion in a viscoelastic suspension of FENE dumbbells

Abstract A new method for simulating the motion of particles in viscoelastic Boger fluids is extended to problems with bounded geometries. Viscoelasticity is incorporated into the Stokesian dynamics method by modeling a viscoelastic fluid as a suspension of finite-extension nonlinear-elastic (FENE) dumbbells. Wall–particle and wall–bead interactions are included by using the image system method of Blake; particle–particle and particle–bead interactions are also modified by the presence of the wall. The method of incorporating sphere–wall interactions is verified by doing calculations for several problems involving particle–wall interactions in Newtonian fluids. The method is then used to study particle–wall interactions in viscoelastic dumbbell suspensions by examining several problems of interest: the sedimentation of a spherical particle near vertical and tilted walls; the sedimentation of a nonspherical particle between two flat plates; and the migration of a neutrally buoyant sphere in plane Poiseuille flow. We find that a single sphere falling near a wall moves toward the wall and exhibits anomalous rotation. When the wall is tilted by an amount less than a few degrees, the sphere still moves toward the wall, but tilting the wall greater than an angle of approximately 1.5° results in the sphere falling away from the wall. A nonspherical particle settling in a channel exhibits an oscillatory motion, but ultimately becomes centered in the channel with its long axis parallel to gravity. Finally, it is shown that a neutrally buoyant sphere in plane Poiseuille flow migrates to the channel center in wide channels, but migrates to the walls when the sphere is sufficiently large relative to the channel width.

Oxidative dehydrogenation of propane to propylene over VOx/CaO–γ-Al2O3 using lattice oxygen

Oxidative dehydrogenation (ODH) of propane to propylene is studied using a new vanadium catalyst supported on CaO–γ-Al2O3 under a gas phase oxygen free atmosphere. The catalysts are synthesized with different CaO/γ-Al2O3 ratios, keeping the vanadium loading at 10 percent. The prepared catalysts are characterized using various physicochemical techniques. Raman spectroscopy reveals that the catalysts have monovanadate and polyvanadate surface species (VOx) with minute crystal particles of V2O5. FTIR spectroscopy and XRD analysis confirm the presence of V2O5, CaO and γ-Al2O3 in the catalyst. The catalysts show stable reduction and re-oxidation behavior in repeated TPR and TPO cycles, respectively. NH3-TPD shows that catalyst acidity decreases with increasing CaO content. The NH3-TPD kinetics analysis reveals that the activation energy of desorption increases with higher CaO, indicating stronger active site–support interactions. The ODH of propane experiments are conducted in a fluidized CREC Riser Simulator under gas phase oxygen free conditions. Among the studied catalysts, VOx/CaO–γ-Al2O3 (1 : 1) displays the highest propane conversion (65%) and propylene selectivity (85%) and a low COx due to its excellent oxygen carrying capacity, balanced acidity and moderate active site–support interactions.

Chromatographic reactions of three components: application to separations

Consider three chemical components in a chromatographic system that interact according to A1 ⇌ A2 ⇌ A3 or the cyclic reaction A1 ⇌ A2 ⇌ A3 ⇌ A1 and move with different velocities . This problem has application in a variety of chromatographic reaction systems, including the case of three interacting isomers undergoing separation by electrophoresis or sedimentation. A particular example is the separation of proteins that fold and unfold. A mathematical model consisting of three partial differential equations, accounting for convection, longitudinal dispersion and chemical reaction, describes these chromatographic reactions. For the unsteady-state case, Fourier transformation with symbolic and numeric manipulations by computer allow the determination of the spatial moments and their asymptotic behavior, which provide the shape characteristics of the pulse responses. The concentration profiles are constructed using the moment expressions in a polynomial expansion. In addition, generalization to any number of components interacting according to a first-order reaction mechanism is discussed for large and small time asymptotes. At short times (relative to the reaction time), the components move independently; at long times, the interacting components move as a group. For the steady-state reactor with adsorption, similar computer techniques provide concentration distributions and show entrance and exit discontinuities (in the absence of diffusion and longitudinal dispersion).

Introduction of the arc-length continuation technique in the chemical engineering graduate program at KFUPM

The present paper describes the arc‐length continuation method; a mathematical technique that can solve a wide variety of chemical engineering problems. Several case studies involving distillation, reaction engineering, and thermodynamics are treated with the help of this method. The approach is powerful enough to elucidate situations when several turning points occur. Finally, the authors conclude with their experience teaching this technique. Indeed, this methodology was introduced to the graduate students of the nonlinear dynamics course at King Fahd University of Petroleum & Minerals (KFUPM).

Chebyshev orthogonal collocation technique to solve transport phenomena problems with Matlab® and Mathematica

We present in this pedagogical paper an alternative numerical method for the resolution of transport phenomena problems encountered in the teaching of the required course on transport phenomena in the graduate chemical engineering curricula. Based on the Chebyshev orthogonal collocation technique implemented in Matlab® and Mathematica©, we show how different rather complicated transport phenomena problems involving partial differential equations and split boundary value problems can now readily be mastered. A description of several sample problems and the resolution methodology is discussed in this paper. The objective of the incorporation of this approach is to develop the numerical skills of the graduate students at King Fahd University of Petroleum & Minerals (KFUPM) and to broaden the extent of transport‐phenomena problems that can be addressed in the course. We noted with satisfaction that the students successfully adopted this numerical technique for the resolution of problems assigned as term projects.

Study of the separation of simple binary and ternary mixtures of aromatic compounds

Consider binary and ternary mixtures of aromatic compounds composed of benzene/toluene and benzene/toluene/p‐xylene, respectively. The present study shows how one can apply both mass and energy balance equations in order to understand the separation of such ideal mixtures by distillation. An adiabatic flash distillation problem is solved graphically for a mixture composed of benzene/toluene. Rigorous resolution of a steady‐state binary distillation problem, using Mathematica® and the same benzene/toluene mixture, shows perfect agreement with results obtained using HYSYS. Results of a dynamic simulation involving the solution of a relatively large system of differential algebraic equations are presented and discussed for the benzene/toluene mixture. SIMULINK© and Mathematica® are used to perform control of this binary distillation column. Finally, a steady‐state simulation of a simple multicomponent mixture, composed of benzene/toluene/p‐xylene, is studied and some qualitative results are drawn from both the temperature and composition profiles.

Simple batch distillation of a binary mixture

A simple experiment such as the batch distillation of an ethanol–water binary mixture can be performed in a 3‐h laboratory session using a very rudimentary apparatus consisting of a still pot and two thermocouples. Yet, the results can lead to very interesting insights to distillation and chemical engineering thermodynamics. The present article describes how one can exploit this simple laboratory experiment to teach these various aspects of chemical engineering. In addition, several simple calculations using computer software such as Mathematica® are performed to explain, interpret and reproduce theoretically all the gathered experimental data during the laboratory session.© 2012 Wiley Periodicals, Inc. Comput Appl Eng Educ 22:649–657, 2014; View this article online at wileyonlinelibrary.com/journal/cae; DOI 10.1002/cae.21556

Solving two-dimensional chemical engineering problems using the chebyshev orthogonal collocation technique

The present paper describes how to apply the Chebyshev orthogonal collocation technique to solve steady‐state and unsteady‐steady two‐dimensional problems. All problems are solved using one single computer algebra, Mathematica©. The problems include: (1) steady‐state heat transfer in a rectangular bar, (2) steady‐state flow in a rectangular duct, (2) steady‐state heat transfer in a cooling cylindrical pin fin, (4) steady‐state heat conduction in an annulus, (5) unsteady‐state heat transfer in a rectangular bar, and finally (6) unsteady‐state diffusion reaction system. Whenever possible the results obtained with orthogonal collocation are compared to the analytical solution in order to validate the applied numerical technique.

Residue curve map for homogeneous reactive quaternary mixtures

We show how one can compute residue curve maps (RCMs) for the methyl acetate and isopropyl acetate chemistries at atmospheric pressure. These computations involve solving a complex system of differential algebraic equations (DAEs). This can be readily achieved using the built‐in functions of Mathematica and MATLAB. The governing equations, which depend on transformed compositions, are provided. Equations to compute vapor–liquid equilibrium when there is dimerization in the gas phase are given because of the presence of acetic acid in both quaternary mixtures. The occurrence of a chemical reaction leads to the disappearance of an azeotrope in the methyl acetate chemistry. On the other hand, a reactive azeotrope appears in the isopropyl acetate chemistry. Transformed compositions of these azeotropes are provided. The MATLAB programs and Mathematica notebooks are available from the author upon request or via http://library.wolfram.com/infocenter/search/?search_results=1;search_person_id=1536 or http://www.mathworks.com/matlabcentral/fileexchange/loadAuthor.do?objectType=author&objectId=1093893.