Large-amplitude behavior of the Grinfeld instability: a variational approach

In previous work, we have performed amplitude expansions of the continuum equations for the Grinfeld instability and carried them to high orders. Nevertheless, the approach turned out to be restricted to relatively small amplitudes. In this article, we use a variational approach in terms of multi-cycloid curves instead. Besides its higher precision at given order, the method has the advantages of giving a transparent physical meaning to the appearance of cusp singularities and of not being restricted to interfaces representable as single-valued functions. Using a single cycloid as ansatz function, the entire calculation can be performed analytically, which gives a good qualitative overview of the system. Taking into account several but few cycloid modes, we obtain remarkably good quantitative agreement with previous numerical calculations. With a few more modes taken into consideration, we improve on the accuracy of those calculations. Our approach extends them to situations involving gravity effects. Results on the shape of steady-state solutions are presented at both large stresses and amplitudes. In addition, their stability is investigated.Received: 3 September 2003, Published online: 24 October 2003PACS: 47.20.Hw Morphological instability; phase changes - 05.70.Ln Nonequilibrium and irreversible thermodynamics - 46.25.-y Static elasticity - 81.10.Aj Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation     

Synthesis of 1‐(p‐Sulphophenyl)‐3‐methyl‐5‐pyrazolone Based Acid Dyes and Their Applications on Leather

A new series of pyrazolone based azo acid dyes (3a–g) has been synthesized starting from 1‐(p‐sul‐phophenyl)‐3‐methyl‐5‐pyrazolone (1). The synthetic methodology included the nitrosation of p‐sulphophenyl methyl pyrazolone followed by reduction, diazotization and coupling with Naphthol AS derivatives (2a–f), in alkaline medium to yield different acid dyes. Multichromic metal complexes of these dyes (5a–f, 6a–f and 7a–f) with 3d transition metals Chromium, Iron and Copper were also synthesized. The structures of all of newly synthesized compounds were confirmed by analytical data and spectroscopic techniques. The synthesized dyes were applied on leather to assess their light fastness, wash fastness and rubbing fastness and were shown to exhibit high values of 4–5 for majority of dyes.     

Thermodynamic aspect: kinetics of the reduction of dicyanobis(phen)iron(III) by acetylferrocene and methylferrocenemethanol

Protonation plays an important role in the redox reactions. We observed this leading role during the reduction of [Fe^III(phen)₂(CN)₂]⁺ by FcCOMe and FcCHOHMe. The kinetic data showed that the reaction(s) followed a complex kinetics due to the formation of protonated acetylferrocene (FcC⁺OHMe), and or, protonated α-methylferrocenemethanol (FcCHO⁺H₂Me) in aqueous dioxane (80% v/v). Our results helped us to conclude that the reactions were completed in three phases. An overall zeroth order was observed in the first phase of the reactions. In the second phase, the kinetic data showed an overall second order reaction. The third phase was a complex phase where the rate of redox reactions and the insolubility of the neutral product ([Fe^II(phen)₂(CN)₂]) competed with each other. We studied the effect of different factors to identify the reacting entities, which take part in the rate-determining step of each reaction in the second phase. Consequently, we determined the effects of selected factors upon the observed pseudo-first order rate constant(s) (k′ _obs) of each reaction. The value of k′ _obs increased upon addition of protons in the reaction mixture in case of FcCOMe, and it decreased during the oxidation of FcCHOHMe. Meanwhile, upon enhancing the ionic strength, we observed an increase in k′ _obs for FcCOMe, and no change in the value of k′ _obs during the reaction of FcCHOHMe. However, a decrease in k′ _obs was noticed upon increasing the dielectric constant of the reaction mixture when the reductant was FcCOMe, and no effect was observed in case of FcCHOHMe. Together, these results suggested oxidation of FcC⁺OHMe and FcCHOHMe in the slow-step, and FcCOMe and FcCHO⁺H₂Me during the fast-step. We refined our results by estimating the thermodynamic parameters of activation. The low values of activation energy and enthalpy of activation confirmed that the reduction of [Fe^III(phen)₂(CN)₂]⁺ hardly depends upon temperature when the reducing agent is FcCOMe. The outcomes justified that the rate of reaction depends upon the unsaturated FcC⁺OHMe. This intermediate species contain a ‘carbonium ion’, which is very reactive and energetic. We obtained comparatively high values of the activation energy and enthalpy of activation for the reaction between [Fe^III(phen)₂(CN)₂]⁺ and FcCHOHMe. The results show that FcCHOHMe is a saturated and stable compound that leads the slow-step and controls the rate of reaction.     

Reduction of water-soluble colloidal manganese dioxide by thiourea: a kinetic and mechanistic study

Kinetic data for the colloidal MnO₂–thiourea redox system are reported for the first time. The reduction of water-soluble colloidal MnO₂ by thiourea (sulfur containing reductant) in aqueous perchloric acid medium has shown that it proceeds in two stages, i.e., a fast stage followed by a relatively slow second stage. The log (absorbance) versus time plot deviates from linearity. The kinetics of both the stages was investigated spectrophotometrically. The first-order kinetics with respect to [thiourea] at low concentration shifts to zero-order at higher concentration. The reaction rate increases with [HClO₄] and the kinetics reveals complex order dependence in [HClO₄]. Addition of P₂O ₇ ⁴⁻ and F⁻ in the form of Na₄P₂O₇ and NaF, respectively, has inhibitory effect on the reaction rate. The reaction proceeds through the fast adsorption of thiourea on the surface of the colloidal MnO₂. A mechanism involving the protonated thiourea as the reactive reductant species is proposed. The observed results are discussed in terms of Michaelis–Menten/Langmuir–Hinshelwood model. From the observed kinetic data, colloidal MnO₂–thiourea adsorption constant (K _ad1) and rate constant (k ₁) were calculated to be 1.25×10¹⁰ mol⁻¹ dm³ and 3.1×10⁻⁴ s⁻¹, respectively. The variation of temperature does not have any effect on the reaction rate.     

Formulation and Evaluation of a Clove Oil-Encapsulated Nanofiber Formulation for Effective Wound-Healing

Wound-healing is complicated process that is affected by many factors, especially bacterial infiltration at the site and not only the need for the regeneration of damaged tissues but also the requirement for antibacterial, anti-inflammatory, and analgesic activity at the injured site. The objective of the present study was to develop and evaluate the natural essential oil-containing nanofiber (NF) mat with enhanced antibacterial activity, regenerative, non-cytotoxic, and wound-healing potential. Clove essential oil (CEO) encapsulated in chitosan and poly-ethylene oxide (PEO) polymers to form NFs and their morphology was analyzed using scanning electron microscopy (SEM) that confirmed the finest NFs prepared with a diameter of 154 ± 35 nm. The successful incorporation of CEO was characterized by Fourier transform infra-red spectroscopy (FTIR) and X-ray diffractometry (XRD). The 87.6 ± 13.1% encapsulation efficiency and 8.9 ± 0.98% loading of CEO was observed. A total of 79% release of CEO was observed in acidic pH 5.5 with 117% high degree of swelling. The prepared NF mat showed good antibacterial activity against Staphylococcus aureus and Escherichia coli and non-cytotoxic behavior against human fibroblast cell lines and showed good wound-healing potential.     

Improving the mass conservation of the level set method in a finite element context

In this Note, a new algorithm is proposed for improving the mass conservation of the level set method in the finite element context. Two kinds of Lagrange multipliers are introduced, associated respectively to the redistancing and advection equations. The first one, is located at the vicinity of the interface, while the second one is associated to a correction that is global to the domain. The performances of the proposed method are tested on the Zalesak test case, and the convergence rate versus the element mesh size are founded to be improved.     

Thermal study of date kernels via TG and DTA

Thermal analyses was performed on Egyptian date kernels to assess the value of the products as possible sources of valuable compounds. It also furnished technical data necessary for determination of the optimum degree of temperature for the design and operation of units for the pyrolytic processing of date kernels.Two different sets of experiments were carried out, involving thermogravimetry (TG) and differential thermal analysis (DTA).The TG results revealed a purely kinetically controlled, first-order reaction. The activation energy and the Arrhenius constant were 8.17 kJ/mol and 0.0115 min^–1, respectively.The DTA results indicated the nature of the reactions involved in the pyrolysis and the corresponding products.

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Zusammenfassung Ägyptische Dattelkerne wurden thermisch untersucht, um die Möglickkeit einer Verwendung als Quellen für wertvolle Verbindungen zu ergründen. Außerdem wurden technische Daten ermittelt, die zur Festlegung der Optimumtemperatur für die Gestaltung und den Betrieb der Geräte zur pyrolytischen Behandlung von Dattelkernen benötigt werden. Es wurden zwei Versuchsreihen durchgeführt, bei denen einerseits Thermogravimetrie (TG) und andererseits Differentialthermoanalyse (DTA) Anwendung fand. Die TG Ergebnisse eröffnen eine rein kinetisch kontrollierte Reaktion erster Ordnung. Die Aktivierungsenergie und die Arrheniuskonstante betrugen 8,17 kJ/mol bzw. 0,0115 min^–1. DTA Resultate gaben Auskunft über den Charakter und Reaktionsprodukte der Reaktionen bei der Pyrolyse.

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The authors wish to express their sincere appreciation to Prof. Dr. S. G. Serag El-Din, Professor of the Chemical Engineering Department, Cairo University, and Dr. H. H. Abou El-Naga, Manager of Analytical and Research Centre, Misr Petroleum Company, for their sincere and helpful co-operation.