Alternative solution for diffusion to two spheres with first-order surface reaction

2000 ◽  
Vol 113 (23) ◽  
pp. 10818-10819 ◽  
Author(s):  
William Strieder ◽  
Salma Saddawi
Keyword(s):  
Surface Reaction ◽  
Alternative Solution ◽  
First Order ◽  
Order Surface

Mass Transport Effects In Selectively Deposited Diamond Thin Films

1995 ◽  
Vol 416 ◽  
Author(s):  
Michael C. Kwan ◽  
Karen K. Gleason
Keyword(s):  
Growth Rate ◽  
Gas Phase ◽  
Surface Reaction ◽  
Three Dimensional ◽  
Chemical Vapor ◽  
Scanning Electron Micrographs ◽  
First Order ◽  
Reaction Coefficient ◽  
Hot Filament ◽  
Order Surface

ABSTRACTIn order to study the effects of gas phase transport on the growth of hot-filament chemical vapor deposited (HFCVD) diamond, crystallites were selectively grown on a pre-nucleated, oxygen plasma patterned silicon wafer. Growth rate differences across the substrate were observed from scanning electron micrographs. The deposition system was then modeled with a three dimensional finite difference scheme that employed gas phase diffusion of a single growth limiting species from the hot filament to the surface coupled with a first order surface reaction. The variations in the predicted gas phase concentration directly above the surface were adjusted to match the observed growth rate differences through the Dahmk6hler number which was then used to calculate a first order surface reaction coefficient. This value was compared to published reaction coefficients for the abstraction of a surface H-atom by a gas-phase H-atom.

Biodegradation rates of aromatic contaminants in biofilm reactors

1995 ◽  
Vol 31 (1) ◽  
pp. 117-128 ◽  
Author(s):  
Jean-Pierre Arcangeli ◽  
Erik Arvin
Keyword(s):  
Aromatic Hydrocarbons ◽  
Competitive Inhibition ◽  
Removal Rate ◽  
First Order ◽  
Biofilm Reactors ◽  
First Order Kinetics ◽  
Reducing Conditions ◽  
Low Concentrations ◽  
Degradation Rates ◽  
Order Surface

This study has shown that microorganisms can adapt to degrade mixtures of aromatic pollutants at relatively high rates in the μg/l concentration range. The biodegradation rates of the following compounds were investigated in biofilm systems: aromatic hydrocarbons, phenol, methylphenols, chlorophenols, nitrophenol, chlorobenzenes and aromatic nitrogen-, sulphur- or oxygen-containing heterocyclic compounds (NSO-compounds). Furthermore, a comparison with degradation rates observed for easily degradable organics is also presented. At concentrations below 20-100 μg/l the degradation of the aromatic compounds was typically controlled by first order kinetics. The first-order surface removal rate constants were surprisingly similar, ranging from 2 to 4 m/d. It appears that NSO-compounds inhibit the degradation of aromatic hydrocarbons, even at very low concentrations of NSO-compounds. Under nitrate-reducing conditions, toluene was easily biodegraded. The xylenes and ethylbenzene were degraded cometabolically if toluene was used as a primary carbon source; their removal was influenced by competitive inhibition with toluene. These interaction phenomena are discussed in this paper and a kinetic model taking into account cometabolism and competitive inhibition is proposed.

Heat/mass transport in shear flow over a heterogeneous surface with first-order surface-reactive domains

2015 ◽  
Vol 782 ◽  
pp. 260-299 ◽  
Author(s):  
Preyas N. Shah ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Mass Transfer ◽  
Shear Rate ◽  
Shear Flow ◽  
Reaction Rate ◽  
Patch Size ◽  
Patch Area ◽  
First Order ◽  
Effective Boundary ◽  
Order Surface ◽  
Slip Distance

Surfaces that include heterogeneous mass transfer at the microscale are ubiquitous in nature and engineering. Many such media are modelled via an effective surface reaction rate or mass transfer coefficient employing the conventional ansatz of kinetically limited transport at the microscale. However, this assumption is not always valid, particularly when there is strong flow. We are interested in modelling reactive and/or porous surfaces that occur in systems where the effective Damköhler number at the microscale can be $O(1)$ and the local Péclet number may be large. In order to expand the range of the effective mass transfer surface coefficient, we study transport from a uniform bath of species in an unbounded shear flow over a flat surface. This surface has a heterogeneous distribution of first-order surface-reactive circular patches (or pores). To understand the physics at the length scale of the patch size, we first analyse the flux to a single reactive patch. We use both analytic and boundary element simulations for this purpose. The shear flow induces a 3-D concentration wake structure downstream of the patch. When two patches are aligned in the shear direction, the wakes interact to reduce the per patch flux compared with the single-patch case. Having determined the length scale of the interaction between two patches, we study the transport to a periodic and disordered distribution of patches again using analytic and boundary integral techniques. We obtain, up to non-dilute patch area fraction, an effective boundary condition for the transport to the patches that depends on the local mass transfer coefficient (or reaction rate) and shear rate. We demonstrate that this boundary condition replaces the details of the heterogeneous surfaces at a wall-normal effective slip distance also determined for non-dilute patch area fractions. The slip distance again depends on the shear rate, and weakly on the reaction rate, and scales with the patch size. These effective boundary conditions can be used directly in large-scale physics simulations as long as the local shear rate, reaction rate and patch area fraction are known.

scholarly journals Imaging of first-order surface-related multiples by reverse-time migration

2016 ◽  
Vol 208 (2) ◽  
pp. 1077-1087 ◽  
Author(s):  
Xuejian Liu ◽  
Yike Liu ◽  
Hao Hu ◽  
Peng Li ◽  
Majid Khan
Keyword(s):  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Order Surface

The thermal decomposition of cyclobutane-1,2-dione

1985 ◽  
Vol 63 (11) ◽  
pp. 2945-2948 ◽  
Author(s):  
J.-R. Cao ◽  
R. A. Back
Keyword(s):  
Activation Energy ◽  
Thermal Decomposition ◽  
Vapor Pressure ◽  
Gas Phase ◽  
Rate Constant ◽  
Surface Reaction ◽  
Order Rate Constant ◽  
Reaction Vessel ◽  
Arrhenius Parameters ◽  
First Order

The thermal decomposition of cyclobutane-1,2-dione has been studied in the gas phase at temperatures from 120 to 250 °C and pressures from 0.2 to 1.5 Torr. Products were C2H4 + 2CO, apparently formed in a simple unimolecular process. The first-order rate constant was strongly pressure dependent, and values of k∞ were obtained by extrapolation of plots of 1/k vs. 1/p to1/p = 0. Experiments in a packed reaction vessel showed that the reaction was enhanced by surface at the lower temperatures. Arrhenius parameters for k∞, corrected for surface reaction, were log A (s−1) = 15.07(±0.3) and E = 39.3(±2) kcal/mol. This activation energy seems too low for a biradical mechanism, and it is suggested that the decomposition is probably a concerted process. The vapor pressure of solid cyclobutane-1,2-dione was measured at temperatures from 22 to 62 °C and a heat of sublimation of 13.1 kcal/mol was estimated.

The thermal decomposition of nitrous oxide I. Secondary catalytic and surface effects

1955 ◽  
Vol 231 (1185) ◽  
pp. 162-178 ◽  
Keyword(s):  
Nitric Oxide ◽  
Thermal Decomposition ◽  
Nitrous Oxide ◽  
Surface Reaction ◽  
Order Rate Constant ◽  
Side Reactions ◽  
Chain Reactions ◽  
First Order ◽  
Reaction Vessels ◽  
Decomposition Of Nitrous Oxide

In the region of pressure 0 to 500 mrn approximately to the equation the thermal decomposition of nitrous oxide conforms approximately to the equation k = an /1 + a'n + bn , where k is the form al first-order rate constant, — (1/n) d n /d t , n the initial concentration and a, a' and b are nearly constant. Above about 100 m m this expression approximates to k = A + bn , which holds up to several atmospheres. Fresh and more detailed experiments have once again disproved the suggestion that the first term in these expressions is due to a surface reaction. (In certain states of reaction vessels, made of a particular brand of silica, a surface reaction may appear but is immediately recognizable by special criteria, and can be eliminated.) Detailed study of the formation of nitric oxide in the course of the decomposition, and of the effect of inert gas upon this process, shows that side reactions involving oxygen atoms, chain reactions and catalysis by nitric oxide play only minor parts in determining the shape of the k-n curve. The form of this curve, which is an inherent character of the reaction N 2 O = N 2 + O, raises theoretical questions of considerable interest.

First order surface roughness correction of active microwave observations for estimating soil moisture

1997 ◽  
Vol 35 (4) ◽  
pp. 1065-1069 ◽  
Author(s):  
T.J. Jackson ◽  
H. McNairn ◽  
M.A. Weltz ◽  
B. Brisco ◽  
R. Brown
Keyword(s):  
Surface Roughness ◽  
Soil Moisture ◽  
First Order ◽  
Order Surface
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