Chemical reactions diffusion

Fluorescence correlation spectroscopy (FCS) measures rates of diffusion, chemical reaction, and other dynamic processes of fluorescent molecules. These rates are deduced from measurements of fluorescence fluctuations that arise as molecules with specific fluorescence properties enter or leave an open sample volume by diffusion, by undergoing a chemical reaction, or by other transport or reaction processes. Studies of unfolded proteins benefit from the fact that FCS can provide information about rates of protein conformational change both by a direct readout from conformation-dependent fluorescence changes and by changes in diffusion coefficient. 

A chronomal is a dimensionless parameter [symbohzed by I or /(a)] that is proportional to time. Chronomals are especially useful in deahng with diffusion, chemical reactions, and other related processes. One can chose to express the properties of such systems as t equal to Kb Ib, where Kb contains all the physical constants and has overall units of time, whereas Ib is a chronomal expressed in terms of the extent of reaction C In many respects, the chronomal can be regarded as dimensionless time. 

In our laboratory we perform experiments adapted to the study of diffusion chemical reaction phenomena under maintained nonequilibrium conditions. 

Nielsen, P. H. and Villadsen, J. (1984) An analysis of the multiplicity pattern of models for simultaneous diffusion, chemical reaction and adsorption. Chem. Engng Sci. 40, 571-587. 

The overpotential 77 is required to overcome hindrance of the overall electrode reaction, which is usually composed of the sequence of partial reactions. There are four possible partial reactions and thus four types of rate control charge transfer, diffusion, chemical reaction, and crystallization. Charge-transfer reaction involves transfer of charge carriers, ions or electrons, across the double layer. This transfer occurs between the electrode and an ion, or molecule. The charge-transfer reaction is the only partial reaction directly affected by the electrode potential. Thus, the rate of charge-transfer reaction is determined by the electrode potential. 

Heterogeneous photochemical processes are concerned with the effect of light on interacting molecules and solid surfaces. The concept of photoinduced surface chemistry is commonly used to integrate these processes. As cited earlier, they involve surface phenomena such as adsorption, diffusion, chemical reaction and desorption [3]. Experiments and theoretical calculations make clear that the photochemical behavior of an adsorbed molecule can be very different from that of a molecule in the gas or liquid phase [4]. Photochemical reactions of this type involve molecules and systems of quite different complexity, from species composed of a few atoms in the stratosphere to large chiral organic molecules that presumably were formed in prebiotic systems. 

Hollow fiber contactors use membranes to separate two phases and transport is due to diffusion, chemical reaction, or chemical potential rather than pressure. The main examples of hollow fiber contactors are found in dialysis, gas adsorption/deadsorption, and solvent extraction. Use of hydrophilic and hydrophobic fiber materials controls the wetting of the pores. Typically, the phase that has higher mass transfer is allowed to wet the pores in order to minimize overall mass transfer resistance. 

Modeling of the molecular diffusion-chemical reaction processes to predict the local reaction rate. 

Let us consider the diffusion-chemical reactions stages of the LM transport from the most complex BLM systems to simpler ones. As can be seen in Fig. 2.1 A transport of solutes or their complexes through the BLM with hydrophobic membrane supports consists of the fohowing discrete steps ... 

Reactions taking place on the surface of solid or liquid particles and inside liquid droplets play an important role in the middle atmosphere, especially in the lower stratosphere where sulfate aerosol particles and polar stratospheric clouds (PSCs) are observed. The nature, properties and chemical composition of these particles are described in Chapters 5 and 6. Several parameters are commonly used to describe the uptake of gas-phase molecules into these particles (1) the sticking coefficient s which is the fraction of collisions of a gaseous molecule with a solid or liquid particle that results in the uptake of this molecule on the surface of the particle (2) the accommodation coefficient a which is the fraction of collisions that leads to incorporation into the bulk condensed phase, and (3) the reaction probability 7 (also called the reactive uptake coefficient) which is the fraction of collisions that results in reactive loss of the molecule (chemical reaction). Thus, the accommodation coefficient a represents the probability of reversible physical uptake of a gaseous species colliding with a surface, while the reaction probability 7 accounts for reactive (irreversible) uptake of trace gas species on condensed surfaces. This latter coefficient represents the transfer of a gas into the condensed phase and takes into account processes such as liquid phase solubility, interfacial transport or aqueous phase diffusion, chemical reaction on the surface or inside the condensed phase, etc. 

M. Chertkov and V. Lebedev. Boundary effects on chaotic advection-diffusion chemical reactions. Phys. Rev. Lett., 90 134501, 2003. 

The condensed phase density p, specific heat C, thermal conductivity A c, and radiation absorption coefficient Ka are assumed to be constant. The species-A equation includes only advective transport and depletion of species-A (generation of species-B) by chemical reaction. The species-B balance equation is redundant in this binary system since the total mass equation, m = constant, has been included the mass fraction of B is 1-T. The energy equation includes advective transport, thermal diffusion, chemical reaction, and in-depth absorption of radiation. Species diffusion d Y/cbfl term) and mass/energy transport by turbulence or multi-phase advection (bubbling) which might potentially be important in a sufficiently thick liquid layer are neglected. The radiant flux term qr... 

More complicated reactions can be easily treated by the methods outlined in the preceeding sections, that is (a) determine the coupled diffusion-chemical reaction equations, (b) linearize the equations in the concentration fluctuations, (c) solve the linearized rate equations by Fourier-Laplace transforms, (d) solve the dispersion equation... 

To this point the equations of change have been set down for pure fluids under both isothermal and nonisothermal conditions, and for multicomponent fluids and charged species. The boundary and initial conditions have, however, been considered only to a limited extent. They will be discussed in the context of the specific subject areas for example, diffusion, chemical reaction, surface tension, and heat transfer. Here, the form of the equations of change will be analyzed so that some of the more important characteristic similarity parameters can be brought out and the stage set for subsequent analyses over restricted ranges of these parameters. 

Reactor performance is established by calculating the molar density of reactant A from a steady-state mass balance that accounts for axial convection and transverse diffusion. Chemical reaction only occurs on the well-defined catalytic surface which bounds fluid flow in the regular polygon channel. Hence, depletion of reactant A due to chemical reaction appears in the boundary conditions, but not in the mass balance which applies volumetrically throughout the homogeneous flow channel. The mass transfer equation for duct reactors is written in vector form ... 

Since electrode reactions commonly involve the transfer of several electrons, the complications (a)—(c) can occur sandwiched between as well as preceding or following electron transfer. Moreover very complex situations do arise. Thus, for example, reaction (1.5) is likely to involve electron transfer, diffusion, chemical reactions (protonation and hydration equilibria as well as sulphation), phase transformation and adsorbed intermediates In this chapter, however, we shall take the approach of considering each fundamental type of process in turn. The equations that will arise must be regarded as idealistic and simplistic but will generally be sufficient for us to understand most cells in industrial practice provided we can recognize which of the fundamental steps in the overall electrode processes predominantly determine the cell characteristics. 

Since electrode reactions commonly involve the transfer of several electrons, the complications (a)-(c) can occur sandwiched between, as well as preceding or following, electron transfer. Thus, for example. Reaction (1.9) is likely to involve electron transfer, diffusion, chemical reactions (protonation and hydration... 

Consider the situation of catalytic particles dispersed in a reasonably thin polymeric film, where the substrate/product reaction occurs via Michaelis-Menten kinetics. This problem is directly relevant to the associated problems of immobilized enzyme catalysis and diffusion/chemical reaction processes in chemical engineering. Aspects of the theory presented in here have recently been described by Albery and coworkers for enzyme electrodes. 

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