Diffusion Controlled Effective Reaction Rate for a Surface Reaction with Orientational Selectivity

1978 ◽  
Vol 33 (11) ◽  
pp. 1243-1250
Author(s):  
Siegfried Hess
Keyword(s):  
Continued Fraction ◽  
Reaction Rate ◽  
Surface Reaction ◽  
Reaction Plane ◽  
Special Choice ◽  
Continued Fraction Expansion ◽  
Diffusion Controlled ◽  
Nonspherical Molecules ◽  
Effective Reaction ◽  
Effective Reaction Rate

The influence of the orientational selectivity of a chemical reaction on the diffusion controlled effective reaction rate is investigated theoretically for the following situation: Nonspherical molecules with random orientation are put into a chemically inert solution at a plane which is a certain distance away from the parallel reaction plane. The reaction frequency at the surface shall depend on the orientation of the figure axis of a molecule relative to the normal of the reaction plane. With a special choice for the orientational dependence of the surface reaction, a continued fraction expansion is derived for the diffusion controlled effective reaction rate. This quantity is discussed and displayed graphically as function of the relevant parameters.

scholarly journals Electrochemical Behavior of Malachite Green in Aqueous Solutions of Ionic Surfactants

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammad Mijanur Rahman ◽  
M. Yousuf A. Mollah ◽  
M. Muhibur Rahman ◽  
Md. Abu Bin Hasan Susan
Keyword(s):  
Malachite Green ◽  
Electrochemical Behavior ◽  
Cetyltrimethylammonium Bromide ◽  
Reaction Rate ◽  
Surface Reaction ◽  
Sodium Dodecyl ◽  
Reaction Rate Constant ◽  
Carbon Electrode ◽  
Diffusion Controlled ◽  
Apparent Diffusion

Electrochemical behavior of malachite green (MG) oxalate in aqueous solution was studied in the presence of a cationic surfactant, cetyltrimethylammonium bromide (CTAB), and an anionic surfactant, sodium dodecyl sulfate (SDS) at a glassy carbon electrode using cyclic voltammetry. The electrochemical oxidation of MG has been characterized as an electrochemically irreversible diffusion-controlled process. Oxidative peak current sharply decreased with increasing SDS concentration, while a slight increase with increasing [CTAB] was apparent. The apparent diffusion coefficient, the surface reaction rate constant, and the electron transfer coefficient of MG clearly show correlation of the electrochemical behavior with the dissolved states of the surfactants. Electrochemical observations together with spectrophotometric results at varying surfactant concentrations provide evidence of interaction of MG with the surfactants to varying extent depending on the type of the surfactant and the concentration.

Influence of the formation of short-chain olefins by manganese/cobalt-catalyzed Fischer–Tropsch synthesis on the selectivity and effective reaction rate

2020 ◽  
Vol 10 (2) ◽  
pp. 475-483
Author(s):  
Dominik Schröder ◽  
Johannes Thiessen ◽  
Andreas Jess ◽  
Judith Scholz
Keyword(s):  
Low Temperature ◽  
Reaction Rate ◽  
High Selectivity ◽  
Cobalt Catalysts ◽  
Short Chain ◽  
Industrial Scale ◽  
Fischer Tropsch ◽  
Fischer Tropsch Synthesis ◽  
Effective Reaction ◽  
Effective Reaction Rate

For cobalt catalysts with manganese as promoter, a high selectivity to olefins is found in low-temperature FTS over small catalyst particles. With industrial scale particles severe changes in selectivity and an increase of reaction rate is found.

scholarly journals Analysis and modelling of the effective reaction rate in a developing mixing layer

2011 ◽  
Vol 318 (9) ◽  
pp. 092026
Author(s):  
Karol Wędołowski ◽  
Konrad Bajer ◽  
Kamil Kwiatkowski
Keyword(s):  
Reaction Rate ◽  
Mixing Layer ◽  
Effective Reaction ◽  
Effective Reaction Rate

THERMAL, STABILITY OF W/C MULTILAYER FILMS

1985 ◽  
Vol 56 ◽  
Author(s):  
Yasuo Takagi ◽  
David A. Pawlik ◽  
Alan M. Kadin ◽  
Steven A. Flessa ◽  
Keith L. Hart ◽  
...  
Keyword(s):  
Reaction Rate ◽  
Beta Phase ◽  
X Ray Diffraction ◽  
X Ray ◽  
Tentative Model ◽  
C 50 ◽  
Initial Crystal ◽  
Thermal Stability Of ◽  
Effective Reaction ◽  
Effective Reaction Rate

Arstract:W(15 Å)/C(15 Å), W(50 Å)/C(50 Å) and W(100 Å)/C(100 Å) periodic multilaver films were prepared by magnetron sputtering and suhsequently annealed at 980, 730 and 500°C. The changes of layered and crystal structures were studied by x-ray diffraction. The results depended largely on the thickness of W layers and their initial crystal struictures of W. The kinds of transformations are classified into two types: one is the non-reacting type in the case of multilayers having the thinner W layers like W(15 Å)/C(15 Å), in which the crystallization of W layers prevails over the reactions between W and C layers; the other, the reacting type in the multilayers having thicker W layers like W(50 Å)/C(50 Å) and W(100 Å)/C(100 Å), in which reactions Prevail over crystallization. A tentative model in which the effective reaction rate between amorphous–W and amornhous–C is much smaller than that of crystalline-W(beta phase) and amorphous-C is proposed to explain the origin of the phenomena.

scholarly journals Diffusion and Heterogeneous Reaction in Porous Media: The Macroscale Model Revisited

2017 ◽  
Vol 15 (6) ◽  
Author(s):  
Francisco J. Valdés-Parada ◽  
Didier Lasseux ◽  
Stephen Whitaker
Keyword(s):  
Porous Media ◽  
Reaction Rate ◽  
Rate Coefficient ◽  
Heterogeneous Reaction ◽  
Volume Averaging ◽  
Effective Medium ◽  
Reaction Rate Coefficient ◽  
Wide Range ◽  
Effective Reaction ◽  
Effective Reaction Rate

Abstract Diffusion and reaction in porous media have been studied extensively due to the wide range of applications in which this transport phenomenon is involved. In particular, in chemical reactor engineering, reactive mass transfer is crucial to understand the performance of porous catalyst particles immersed in chemical reactors. Due to the disparity of characteristic lengths between the pores and the porous particles, this type of process is usually modeled by means of effective-medium equations, in which the solid and fluid phases are conceived as a pseudo-continuum. For conditions in which the pore-scale Thiele modulus (or Kinetic number) is much smaller than unity, it is reasonable to assume that the effective diffusivity involved in the effective-medium model is only a function of the porous medium geometry. However, a long debate has existed in the literature concerning the extensive use of this assumption for situations in which the Kinetic Number does not satisfy the above mentioned constraint. In addition, the functionality of the effective reaction rate coefficient with the Kinetic number has not been sufficiently studied. In this work we address these issues by means of the volume averaging method. Our analysis is focused on cases in which the Kinetic number can reach values up to 1. Interestingly, for this particular condition, the use of the intrinsic diffusivity tensor is justified. In addition, by means of Maclaurin series expansions, the effective reaction rate coefficient is shown to be acceptably approximated as a first-order function. These two conclusions for the effective medium coefficients constitute the major contributions from this work. In addition, the predictions from the upscaled model are validated by comparison with direct numerical simulations under steady and transient conditions.

scholarly journals Improvement of acid treatment with the sintanol preparation after hydro-sand blasting of wells in the conditions of ANK «Bashneft»

2021 ◽  
pp. 76-83
Author(s):  
M. Ya. Khabibullin ◽  
◽  
G. G. Gilaev ◽  
R. U. Rabaev ◽  
◽  
...  
Keyword(s):  
Acid Solution ◽  
Acid Treatment ◽  
Reaction Rate ◽  
Ionic Surfactant ◽  
Annular Space ◽  
Sand Blasting ◽  
Selective Processing ◽  
Effective Reaction ◽  
Effective Reaction Rate

A sandblasting hammer is lowered into the well, setting against the selected processing interval, and hydraulic clamps are necessary for the rig to be held firmly. The displacement of the latter eliminates the possibility of selective processing. After the usual sandblasting and flushing the well from sand, without changing the position of the perforator, an acid solution is pumped into the pipes, which, entering the channel formed, is filtered through its walls into the treated section of the formation. The part of the acid that, after the end of the treatment, has accumulated in the wellbore, is forced into the reservoir by the squeezing fluid through the annular space. Increase the acid depletion time, i.e. slow down the reaction rate by adding special reagents to the solution. So, a syntanol DS-10 TU 2483-016-71150986-2012 (a non-ionic surfactant and is intended for use as an effective surfactant) is a very effective reaction rate reducer. Adding it in an amount of 0.5% (by weight of the volume of the solution) can reduce the reaction rate by 2.7 times. Keywords: speed; reaction; syntanol; processing; pressure.

The Solvability of Polynomial Pell’s Equation

2020 ◽  
Vol 25 (2) ◽  
pp. 125-132
Author(s):  
Bal Bahadur Tamang ◽  
Ajay Singh
Keyword(s):  
Trivial Solution ◽  
Continued Fraction ◽  
Laurent Series ◽  
Quadratic Polynomial ◽  
Continued Fraction Expansion ◽  
Pell’S Equation ◽  
Integer Polynomials

This article attempts to describe the continued fraction expansion of ÖD viewed as a Laurent series x-1. As the behavior of the continued fraction expansion of ÖD is related to the solvability of the polynomial Pell’s equation p2-Dq2=1  where D=f2+2g  is monic quadratic polynomial with deg g<deg f  and the solutions p, q  must be integer polynomials. It gives a non-trivial solution if and only if the continued fraction expansion of ÖD  is periodic.

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