Rebound Process Research Articles

Rebound and attachment involving single bubble and particle in the separation of plastics by froth flotation

Bubble–particle interaction is critical to the separation of particles by flotation which can be used in plastic recycling. The two particular processes of the interaction (rebound and attachment) are examined visually using high-speed photography in a laboratory scale flotation column. The effects of surfactant (concentration and type) and plastic material on these two stages are also studied quantitatively. The considered surfactants are Tea Saponin, SDBS and CTMAB, while the plastic materials are polyethylene, polypropylene and Teflon. A simple model of bubble attachment time is developed to analyse and interpret the experimental data. The results show that the presence of surfactant significantly affects the rebound process of a gas bubble, while the type of surfactant and plastic material seem to have slight effect. The bubble attachment process is a strong function of the surfactant and plastic material, which can be associated with the changing of bubble size and its hydrodynamic fluid resistance, contact angle on solid surface, as well as surface tension and viscosity of the solution. Such results are helpful for evaluation and analysis of the plastic flotation process, especially for the selection of reagents and objects at an early stage of design.

1104 水中衝撃波を用いた指向性マイクロジェットの生成

Cavitation bubbles generated by an underwater shock wave formed microjets during the collapse and rebound process and they were visualized by a high-speed camera. The directions of the microjets showed the same direction of the initial shock wave propagation. These results imply that the direction of the microjets were affected by the compression wave not expansion wave which was generated by reflection at an interface between water and air.

Resilience and Deformability of Fused Textile Systems

*Department of Electrical Power Systems, Faculty of Electrical and Electronics Engineering, Kaunas University of Technology, Studentu str. 50, LT-51424, Kaunas, Lithuania, E-mail: loreta.krusinskiene@ktu.lt Abstract The aim of this research was to investigate the resilience properties of textile systems fused with different interlinings by applying the method of pendulum impact loading. For the investigations, four worsted outer fabrics and four interlinings were chosen. For testing, a pendulum impact device was used, the operation of which is based on cyclical strikes of the spherical indentor upon the specimen, taking into account the resilience and deformability of the material. It was defined that resilience properties could be characterised not only by the values of impact bn and angles rebound αn but also by the duration of vibration periods Tn. It was defined that the decay of pendulum impact bn and rebound angles αn in the period of t = 20 s can be described by power function y = a + bxc with a high accuracy (R2 = 0.995 0.999). For the rebound process, better resilience of fabrics and their fused systems is characterized by higher values of power function coefficients a and b and lower values of its coefficient c. For the impact process, lower deformability of the samples tested is characterised by lower values of power function coefficients a and b, but with a more intensive decrease in deformability – by higher values of coefficient c. The degree of the fused system’s deformability directly depends upon the thickness and mass per unit area of the interlinings used, i.e. less deformable and more stable systems were obtained with thicker interlinings, the mass per unit area of which was higher.

A Review of Mine Water Rebound Predictions from the VSS–NET Model

Mine water rebound predictions made in the late 1990s and early 2000s were critically reviewed in light of subsequent monitoring data and available literature. The VSS–NET physically-based groundwater model simulates the rebound process by representing both laminar and turbulent flow; the latter is observed in mined out voids, including shafts, adits, and underground roadways. We found good agreement between modelled and predicted rebound rates at a coal mine (Whittle Colliery) in NE England. The rebound from an abandoned tin mine in Cornwall, England (South Crofty), which closed in 1998, took place more rapidly than initially predicted by the VSS–NET model; however, by back-fitting the storage coefficient, the observed rate was matched by the model. In a third case study from a coal mine in South Wales, we managed to reproduce the flow rate from an adit reasonably closely following rebound. However, at a fourth site, a better fit to the rebound curve was obtained using a simpler, lumped model. These studies show the value of using models to predict rebound and discharge from flooded mines, which is important since these mines can produce a long-term legacy of pollution and can cause serious environmental impacts downstream.

Visualized study on the interaction between single bubbles and curved solid surface in flotation separation process.

The present study has been devoted to bubble-curved solid surface interaction in water, which is critical to the separation of suspended particles by air flotation. For this purpose, two particular stages of the interaction (collision and attachment) have been examined visually using high-speed photography in a laboratory-scale flotation column. The effects of the surface material and surfactant concentration on these two stages have been also studied quantitatively. The considered solid materials are the cleaned glass as hydrophilic surface and Teflon as hydrophobic surface. The experimental results show that the presence of surfactant significantly affects the collision and rebound process of a gas bubble, while there is no obvious effect of the surface material on the rebound process. An increase in surfactant concentration has been observed to suppress the rebound number and maximal distance of the bubble from the surface. Moreover, the three-phase contact time of the bubble is a strong function of the surfactant concentration and surface hydrophobicity as well as of the bubble diameter. Another important finding is that the bubble attachment is only observed at the hydrophobic Teflon surface below the surfactant CMC (critical micelle concentration). Results of this study are relevant for deep understanding of the attachment mechanism and to determine the proper conditions for a selective flotation process.

Prediction of the Groundwater Rebound Process in a Backfilled Open Cut Mine Using an Artificial Neural Network

A neural network model was used to predict the groundwater rebound process after cessation of dewatering at a restored open cut coal site in the East Midlands area of the UK. Time (days after dewatering), water table levels in the aquifer and the backfilled site, hydraulic conductivity of the aquifer and backfilled site, and precipitation were used as input. The output of the network was the water table height, until the water table reached its equilibrium position. A feed-forward artificial neural network that uses batch gradient descent with a momentum-learning algorithm and 6-1-6-1 arrangement was found capable of predicting the groundwater rebound process. Predicted values were very close to the monitored results. The correlation coefficient values were 0.98221 for the training set, and 0.99329, 0.99499, 0.98667, 0.98289, and 0.97141 during the testing stage for the five monitoring points, showing that the model prediction was satisfactory.

On the implementation of faults in finite-element glacial isostatic adjustment models

Stresses induced in the crust and mantle by continental-scale ice sheets during glaciation have triggered earthquakes along pre-existing faults, commencing near the end of the deglaciation. In order to get a better understanding of the relationship between glacial loading/unloading and fault movement due to the spatio-temporal evolution of stresses, a commonly used model for glacial isostatic adjustment (GIA) is extended by including a fault structure. Solving this problem is enabled by development of a workflow involving three cascaded finite-element simulations. Each step has identical lithospheric and mantle structure and properties, but evolving stress conditions along the fault.The purpose of the first simulation is to compute the spatio-temporal evolution of rebound stress when the fault is tied together. An ice load with a parabolic profile and simple ice history is applied to represent glacial loading of the Laurentide Ice Sheet. The results of the first step describe the evolution of the stress and displacement induced by the rebound process. The second step in the procedure augments the results of the first, by computing the spatio-temporal evolution of total stress (i.e. rebound stress plus tectonic background stress and overburden pressure) and displacement with reaction forces that can hold the model in equilibrium. The background stress is estimated by assuming that the fault is in frictional equilibrium before glaciation. The third step simulates fault movement induced by the spatio-temporal evolution of total stress by evaluating fault stability in a subroutine. If the fault remains stable, no movement occurs; in case of fault instability, the fault displacement is computed.We show an example of fault motion along a 45°-dipping fault at the ice-sheet centre for a two-dimensional model. Stable conditions along the fault are found during glaciation and the initial part of deglaciation. Before deglaciation ends, the fault starts to move, and fault offsets of up to 22m are obtained. A fault scarp at the surface of 19.74m is determined. The fault is stable in the following time steps with a high stress accumulation at the fault tip. Along the upper part of the fault, GIA stresses are released in one earthquake.

Episodic orogeny deduced from coeval sedimentary sequences in the foreland basin and its implication for uplift process of Longmen Mountain, China

Longmen Mountain located at the boundary between the Sichuan Basin and Tibetan Plateau, representing the steepest gradient of any edges of the plateau. Three endmember models of uplift process and mechanism have been proposed, including crustal thickening, crustal flow, and crustal isostatic rebound. Here we use coeval sedimentary sequences in the foreland basin to restraint uplift process and mechanism in the Longmen Mountain. The more than 10,000 m thick Late Triassic-Quaternary strata filled in this foreland basin and can be divided into six megasequences that are distinguished as two distinct types. The first type is the wedge-shaped megasequences which are sedimentary response of strong active thrust loading events, characterized by a high rate of subsidence and sediment accumulation, coarsening-upward succession and a dual-sourced sediment supply. This type includes Late Triassic, Late Jurassic to Early Cretaceous and Late Cretaceous to Paleogene megasequences. The second type is the tabular megasequences, characterized by the low rate of subsidence and sediment accumulation, fining-upward succession, and a single-sourced sediment supply, which is sedimentary response of isostatic rebound and erosion unloading. This type includes the Early to Middle Jurassic, Middle Cretaceous and Neogene to Quaternary megasequences. Basing on sedimentary, active tectonic, geomorphic evidence, we infer that the direction has been reversed from SSW-directed sinistral strike-slip to NNE-directed dextral strike-slip during 40-3.6 Ma, and since 3.6 Ma, the Longmen Mountain thrust belt belong to times of isostatic rebound and erosional unloading with NNE-directed dextral strike-slip. This suggests that crustal isostatic rebound is a primary driver for uplift and topography of the present Longmen Mountain. The Wenchuan (Ms8.0) earthquake, which ruptured a large thrust fault with NNE-directed dextral strike-slip along the range front, is an active manifestation of this crustal isostatic rebound process with dextral strike-slipping and shortening. This process may be the cause for the Wenchuan Earthquake and the apparent paradox of high relief, little shortening, the relative dearth of historical seismicity in the region.

Is Isostatic Rebound in Slow Spreading Gakkel Ridge of Arctic Region Due to the Climate Change? A Case Study

Ny-Alesund, Swalbard region which is located in the mid-ocean ridge of the Arctic Ocean, and named Gakkel ridge, is the slowest spreading ridge of the global system. In the present study an attempt has been made to associate isostatic rebound using GPS campaign data collected at Ny-Alesund area. The Artic Region Campaign GPS network was established in 2009. The network consists of three campaign mode station. The distance between GPS point is about ~30 km. The preliminary results of our investigation appear broadly consistent with the recent tectonic activity in western Svalbard. The resultant velocity vector is 14.84 mm·yr–1 with an azimuth of 27.67°N and a vertical displacement of 7.62 ± 3.0 mm·yr–1 is estimated in Swalbard, in which we presume Glacial Isostatic Rebound (5.1 mm·yr–1) and post glacial geological process (Present Day Ice Melting, erosion, and shore line deposits) of 2.52 mm per year in the study area.

Tracking methods for free surface and simulation of a liquid droplet impacting on a solid surface based on SPH

With some popular tracking methods for free surface, simulations of several typical examples are carried out under various flow field conditions. The results show that the Smoothed Particle Hydrodynamics (SPH) method is very suitable in simulating the flow problems with a free surface. A viscous liquid droplet with an initial velocity impacting on a solid surface is simulated based on the SPH method, and the surface tension is considered by searching the free surface particles, the initial impact effect is considered by using the artificial viscosity method, boundary virtual particles and image virtual particles are introduced to deal with the boundary problem, and the boundary defect can be identified quite well. The comparisons of simulated results and experimental photographs show that the SPH method can not only exactly simulate the spreading process and the rebound process of a liquid droplet impacting on a solid surface but also accurately track the free surface particles, simulate the free-surface flow and determine the shape of the free surface due to its particle nature.

THE REBOUND CONDITION OF DUST AGGREGATES REVEALED BY NUMERICAL SIMULATION OF THEIR COLLISIONS

Collisional growth of dust aggregates is a plausible root of planetesimals forming in protoplanetary disks. However, a rebound of colliding dust aggregates prevents dust from growing into planetesimals. In fact, rebounding aggregates are observed in laboratory experiments but not in previous numerical simulations. Therefore, the condition of rebound between dust aggregates should be clarified to better understand the processes of dust growth and planetesimal formation. We have carried out numerical simulations of aggregate collisions for various types of aggregates and succeeded in reproducing a rebound of colliding aggregates under specific conditions. Our finding is that in the rebound process, the key factor of the aggregate structure is the coordination number, namely, the number of particles in contact with a particle. A rebound is governed by the energy dissipation along with restructuring of the aggregates and a large coordination number inhibits the restructuring at collisions. Results of our numerical simulation for various aggregates indicate that they stick to each other when the mean coordination number is less than 6, regardless of their materials and structures, as long as their collision velocity is less than the critical velocity for fragmentation. This criterion of the coordination number would correspond to a filling factor of ∼0.3, which is somewhat larger than that reported in laboratory experiments. In protoplanetary disks, dust aggregates are expected to have low bulk densities (<0. 1gc m −3 ) during their growth, which would prevent dust aggregates from rebounding. This result supports the formation of planetesimals with direct dust growth in protoplanetary disks.

Theory of chemical bonds in metalloenzymes. XIV. Correspondence between magnetic coupling mode and radical coupling mechanism in hydroxylations with methane monooxygenase and related species

AbstractBroken‐symmetry (BS) and approximate spin‐projected (AP) BS hybrid density functional theory (DFT) calculations were performed to elucidate possible mechanisms of hydroxylation reactions of methane and alkanes with soluble methane monooxygenase (sMMO) and related metalloenzymes. The BS HDFT (UB3LYP) method was employed to elucidate electronic and spin structures of the key intermediate “Q” and to locate transition structures for hydroxylation reactions in the lowest‐spin (LS) singlet and the highest‐spin (HS) states of sMMO. The spin density populations and chemical indices obtained by the BS B3LYP calculations were found to be consistent with orbital interaction models for hydroxylation with MMO. However these indices in turn indicated significant spin contamination errors in the BS LS solution. The elimination of the errors with the AP procedure indeed reduced the barrier height for the recombination step of alkyl and hydroxyl radicals in the pure LS singlet state, leading to a rebound process. Then present computational results indicated that hydroxylation reactions proceed through the continuous diradical (diradicaloid) mechanism without discreet free radical fragments in the pure LS singlet state. The computational results are, respectively, compatible with local singlet (SD) and local triplet (TD) diradical mechanisms for hydroxylation in the LS and HS states; those were already applied to P450 successfully. Thus magnetic (exchange) coupling modes (LS and HS) in MMO, P450 and related metalloenzymes are directly related to local SD and TD mechanisms for hydroxylation, indicating the correspondence between the magnetic coupling mode and the radical reaction mechanism. These theoretical results enable us to examine recent BS hybrid DFT computational results for hydroxylation reactions with sMMO by several groups. Implications of the present theoretical and computational results are also discussed in relation to several experimental aspects of hydroxylation reactions. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Are artificial satellites orbits influenced by an expanding Earth?

Albeit in the past great theoretical and experimental efforts were made in proposing and searching for G time-decreasing, a major role could be played by an increase of M. A recent analysis (Scalera, 2003a) converges toward an upper limit of the Earth’s mass variation in the order of magnitude of M/M=10-9 /yr. It is here discussed the possible role that can be played by parameters linked to the expanding Earth in the effects we observe in the orbital motion of the artificial satellites. The important result in this short note is the discrimination between the reality of the glacial rebound process and/or the relaxation of the 100m excess of equatorial bulge testified by the high rate of j2 , and the improbable role that glacial rebound can have in driving PM and TPW. It is recommended that the new technology of drag-free satellites be used (Gravity-Probe B is the first step) to reveal possible residual orbital parameter variations ascribable to formerly unrecognized fictitious drag terms due to Earth radial increase.

A note on the modelling of the bouncing of spherical drops or solid spheres on a wall in viscous fluid

A generalized description of the rebound of spherical drops or solid spheres over a wall is proposed using two parameters: a coefficient of restitution that compares the velocity of restitution to the velocity before impact and the contact time with the wall. During the bouncing, the incident kinetic energy is transferred into deformation energy (stored on the surface for the case of liquid drops or in the bulk for the case of solid particles) and then restored into kinetic energy allowing the particle to leave or not the wall. The corresponding criteria is given by the Stokes number that compares the inertia of the particle (added mass included) and the viscous force exerted on the particle during the drainage of the film formed between the particle and the wall. The general behavior of the coefficient of restitution observed in many experiments can be modelled for solid spheres as well as spherical drops by the use of a unique simple correlation depending on this Stokes number. For solid particles, the contact time with the wall in viscous flows is found to be of the same order as that predicted by the Hertzian theory; hence, the contact with the wall can be described as a discontinuity in the particle motion. On the other hand, for liquid drops, the contact time is significant and of the same order as other characteristic time scales of the particle motion. Therefore, to properly describe the rebound process, both a restitution coefficient and a contact time must be considered. Finally, a simple model is proposed and its predictions are compared with experiments performed for millimetric toluene drops in water.

Experimental Identification of Elastic, Damping and Adhesion Forces in Collision of Spherical Sliders With Stationary Magnetic Disks

This paper deals with the experimental identification of elastic, damping and adhesion forces in the dynamic collision of a spherical slider with a stationary magnetic disk. We used rough Al2O3TiC and smooth glass spherical sliders with a radius of 1 mm, and magnetic disks with four different lubricant film thicknesses of 0, 1, 2, and 3 nm. We found that the Al2O3TiC slider shows ordinary approach and rebound processes, whereas the glass slider showed a velocity drop at the end of the rebound process when the lubricant thickness was 1, 2, and 3 nm. We identified the elastic force factors in the approach and rebound processes, based on Herztian contact theory, and the damping force factors based on a damping force model that is proportional to slider velocity and penetration depth (contact area). From the drop in velocity when the slider and disk separated, we found that the dynamic adhesion force is almost equal to the static pull-off force except for with a 3 nm lubricant thickness. The dynamic adhesion force with a 3 nm lubricant thickness is significantly higher, probably because of squeeze damping effect.

Prediction of turbulent separation over a backward-facing smooth ramp

Large eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) calculations have been performed of the turbulent flow over a smoothly contoured ramp. The upstream conditions are obtained from a separate pre-computation of a flat-plate turbulent boundary layer. The flow in the primary calculation develops downstream, first experiencing an increase in the surface skin friction due to ramp curvature, then exhibiting a shallow separation with subsequent reattachment on a flat section downstream. The LES results provide a baseline for investigation of the flow and enable assessment of the RANS models, the specific closures applied being the Spalart–Allmaras one-equation model v 2−f, and a modified version of v 2−f. The wall layer is resolved in all of the calculations, the Reynolds number based on the boundary layer thickness at the inlet plane is 10 400. LES results show that the separation process is intermittent and exhibits a transition of turbulence structures, features that are challenging for the turbulence closures to model adequately. LES mean velocities return to the log law at about four ramp lengths downstream of the beginning of the curved section, whereas the turbulence quantities recover more slowly. The effect of separation is to increase the turbulence intensity away from the wall and decrease it in the vicinity of the wall. The recovery of the inner layer takes place through a rapid rebound process while that of the outer layer through a slow decay process. Both occur in a monotonic fashion. The steady RANS predictions upstream of separation for all the models are similar, with differences observed within and downstream of the separated region. RANS predictions of the skin friction following separation show a relatively slower recovery to the LES results. Spalart–Allmaras gives the closest agreement to LES on the size of the separation bubble. Downstream of separation, v 2−f yields a better agreement with LES than does its modified version, which exhibits a delayed reattachment and slower recovery. For the turbulence quantities, v 2−f yields a better agreement with LES than the other models. All the RANS models, however, fail to completely follow the dynamics of the inner layer in the rebound process revealed by LES.

A Finite Element Model to: 2. Simulate Groundwater Rebound Problems in Backfilled Open Cut Mines

A two-dimensional finite element softwate called SEEP/W can be easily modified to simulate the groundwater rebound process within the spoil of an open cut mine taking into account saturated and unsaturated flow, hydraulic conductivity, and water content (as a function of pore-water pressure). Flexibility in the model is achieved by assigning different boundary conditions. In this paper, the results of the numerical model of the ground water rebound are presented and compared with those obtained from analytical solutions, another numerical model, and with data measured at the Horsley backfilled site in the UK. This model calculates realistic results that can be used by mine operators and environmental engineers to control the quality of mine drainage in a backfilled open cut operation.

Collision and rebound of small droplets in an incompressible continuum gas

We study the head-on collision between two weakly deformable droplets, each of radius a (in the range 10–150 μm), moving towards one another with characteristic impact speeds ±U′c. The liquid comprising the drop has density ρd and viscosity μd. The collision takes place in an incompressible continuum gas with ambient density ρg [Lt ] ρd, ambient pressure p′∞ and viscosity μg [Lt ] μd The gas–liquid interface is surfactant free with interfacial tension σ. The Weber number based on the drop density, Wed ≡ ρdU′2ca/σ [Lt ] 1 and the capillary number based on the gas viscosity, Cagg ≡ μgU′cσ [Lt ] 1. The Reynolds number characterizing flow inside the drops satisfies Red ≡ aU′cρd/μd [Gt ] We1/2d and the Stokes number characterizing the drop inertia, St ≡ 2Wed(9Cag)−1 ≡ 2(ρdU′caμ−1g)/9 is O(1) or larger.We first analyse a simple model for the rebound process which is valid when St [Gt ] 1 and viscous dissipation in both the gas and in the drop can be neglected. We assume that the film separating the drops only serves to keep the interfaces from touching by supplying a constant excess pressure 2σ/a. A singular perturbation analysis reveals that when ln(We−1/4d) [Gt ] 1, rebound occurs on a time scale t′b = &amp;23frac;1/2πaWe1/2dln1/2 (We−1/4d)U′−1c. Numerical results for Weber numbers in the range O(10−6) − O(10−1) compare very well to existing experimental and simulation results, indicating that the approximate treatment of the bounce process is applicable for Wed &lt; 0:3.In the second part of the paper we formulate a general theory that not only models the flow inside the drop but also takes into account the evolution of the gap width separating the drops. The drop deformation in the near-contact inner region is determined by solving the lubrication equations and matching to an outer solution. The resulting equations are solved numerically using a direct, semi-implicit, matrix inversion technique for capillary numbers in the range 10−8 to 10−4 and Stokes numbers from 2 to 200. Trajectories are mapped out in terms of Cag and the parameter χ = (Wed/Cag)1/2 so that St ≡ 2/9χ2. For small Stokes numbers, the drops behave as nearly rigid spheres and come to rest without any significant rebound. For O(1) Stokes numbers, the surfaces deform noticeably and a dimple forms when the gap thickness is approximately O(aCa1/2). The dimple extent increases, reaches a maximum and then decreases to zero. Meanwhile, the centroids of the two drops come to rest momentarily and then the drops rebound, executing oscillatory motions before finally coming to rest. As the Stokes number increases with Cag held fixed, more energy is stored as deformation energy and the maximum radial extent of the dimple increases accordingly. For St [Gt ] 1, no oscillations in the centroid positions are observed, but the temporal evolution of the minimum gap thickness exhibits two minima. One minimum occurs during the dimple evolution process and corresponds to the minimum attained by the dimple rim. The second minimum occurs along the axis of symmetry when the dimple relaxes, a tail forms and then retracts. A detailed analysis of the interface shapes, pressure profiles and the force acting on the drops allows us to obtain a complete picture of the collision and rebound process.

Dynamics of droplet rebound from a weakly deformable gas–liquid interface

A droplet of radius a moves with kinetic energy 2πρdUc′2a3/3 in an incompressible, continuum ambient gas and rebounds from an initially planar, weakly deformable interface bounding a half-space of liquid. We study the rebound process in the limit Wed≡ρdUc′2a/σ≪1, where σ is the surface tension of the two liquid–gas interfaces and ρd is the density of the fluid comprising the drop and the planar half-space. When viscous dissipation in both the ambient gas and in the drop is negligible, the flow inside the drop is inviscid and driven by the deformation of the near contact dimple region. The dimple region is approximated as a section of a sphere of radius 2a. Analysis of the motion induced in the liquid phase, coupled with a physically appropriate description of the interfaces, provides a theoretical description of the deformation and flow modes that ensue. Analytical predictions based on a singular perturbation analysis valid in the limit ln(Wed−1/4)≫1 indicate that the time taken by the drop to complete a bounce is aWed1/2Uc′−1π(4/3)1/2 ln1/2(Wed−1/4) and the angular extent of the near contact region which undergoes strong deformation is (4Wedln−1(Wed−1/4)/3)1/4. The asymptotes are compared to numerical solutions to the full governing equations.

A theoretical study of the dynamic behavior of alkane hydroxylation by a compound I model of cytochrome P450.

Dynamic aspects of alkane hydroxylation mediated by Compound I of cytochrome P450 are discussed from classical trajectory calculations at the B3LYP level of density functional theory. The nuclei of the reacting system are propagated from a transition state to a reactant or product direction according to classical dynamics on a Born-Oppenheimer potential energy surface. Geometric and energetic changes in both low-spin doublet and high-spin quartet states are followed along the ethane to ethanol reaction pathway, which is partitioned into two chemical steps: the first is the H-atom abstraction from ethane by the iron-oxo species of Compound I and the second is the rebound step in which the resultant iron-hydroxo complex and the ethyl radical intermediate react to form the ethanol complex. Molecular vibrations of the C-H bond being dissociated and the O-H bond being formed are significantly activated before and after the transition state, respectively, in the H-atom abstraction. The principal reaction coordinate that can represent the first chemical step is the C-H distance or the O-H distance while other geometric parameters remain almost unchanged. The rebound process begins with the iron-hydroxo complex and the ethyl radical intermediate and ends with the formation of the ethanol complex, the essential process in this reaction being the formation of the C-O bond. The H-O-Fe-C dihedral angle corresponds to the principal reaction coordinate for the rebound step. When sufficient kinetic energy is supplied to this rotational mode, the rebound process should efficiently take place. Trajectory calculations suggest that about 200 fs is required for the rebound process under specific initial conditions, in which a small amount of kinetic energy (0.1 kcal/mol) is supplied to the transition state exactly along the reaction coordinate. An important issue about which normal mode of vibration is activated during the hydroxylation reaction is investigated in detail from trajectory calculations. A large part of the kinetic energy is distributed to the C-H and O-H stretching modes before and after the transition state for the H-atom abstraction, respectively, and a small part of the kinetic energy is distributed to the Fe-O and Fe-S stretching modes and some characteristic modes of the porphyrin ring. The porphyrin marker modes of nu(3) and nu(4) that explicitly involve Fe-N stretching motion are effectively enhanced in the hydroxylation reaction. These vibrational modes of the porphyrin ring can play an important role in the energy transfer during the enzymatic process.