Steady-state process convection rates

If the activity of the immobilised catalyst is sufficiently high, the reaction which it mediates occurs essentially at the interface between the catalyst and the substrate solution. In the case of the surface immobilised enzyme or a thin microbial film this will, of course, occur irrespective of the level of activity. Under these conditions the limiting process for transporting substrate from the bulk of the solution to the immobilised enzyme is molecular or convective diffusion through the layer of solution immediate to the carrier. Under steady-state conditions, the rate of reaction at the active sites is equal to the rate at which substrate arrives at the site. This... 

Transport of a species in solution to and from an electrode/solution interface may occur by migration, diffusion and convection although in any specific system they will not necessarily be of equal importance. However, at the steady state all steps involved in the electrode reaction must proceed at the same rate, irrespective of whether the rate is controlled by a slow step in the charge transfer process or by the rate of transport to or from the electrode surface. It follows that the rate of transport must equal the rate of charge transfer ... 

For the analysis, a steady-state fire was assumed. A series of equations was thus used to calculate various temperatures and/or heat release rates per unit surface, based on assigned input values. This series of equations involves four convective heat transfer and two conductive heat transfer processes. These are ... 

Diffusion. The transport process may consist of two parts, diffusion and convection. When the liquid is stagnant and resting relative to the particle the transport is done by diffusion only. A steady state is quickly established in the solution around the particle (4 ). (Strictly it is a quasi-steady state since the particle is growing ( 5)). At the particle surface the concentration gradient becomes equal to (c-cs)/r, which leads to the growth rate... 

Diffusion time (diffusion time constant) — This parameter appears in numerous problems of - diffusion, diffusion-migration, or convective diffusion (- diffusion, subentry -> convective diffusion) of an electroactive species inside solution or a solid phase and means a characteristic time interval for the process to approach an equilibrium or a steady state after a perturbation, e.g., a stepwise change of the electrode potential. For onedimensional transport across a uniform layer of thickness L the diffusion time constant, iq, is of the order of L2/D (D, -> diffusion coefficient of the rate-determining species). For spherical diffusion (inside a spherical volume or in the solution to the surface of a spherical electrode) r spherical diffusion). The same expression is valid for hemispherical diffusion in a half-space (occupied by a solution or another conducting medium) to the surface of a disk electrode, R being the disk radius (-> diffusion, subentry -> hemispherical diffusion). For the relaxation of the concentration profile after an electrical perturbation (e.g., a potential step) Tj = L /D LD being - diffusion layer thickness in steady-state conditions. All these expressions can be derived from the qualitative estimate of the thickness of the nonstationary layer... 

The potential profile associated with hydrodynamic techniques usually takes the form of a linear sweep between two potentials in which the oxidation or reduction processes of interest occur. As for cyclic voltammetry, the gradient of the ramp represents the scan rate. However, for steady-state techniques, the scan rate used must be sufficiently slow to ensure that the steady state is attained at every potential during the course of the voltammetric scan. The upper value of the scan rate that may be used under the steady-state regime is therefore restricted by the rate of convective mass transport of material to the electrode surface. The faster the rate of convective mass transport the faster the scan rate that may be used consistent with the existence of steady-state conditions. 

In the actual situation, both convective transfer of A to the film surface and diffusion of A through the film occur serially. At steady state these processes take place at equal rates, so that... 

The gas phase balance includes a convective flow term for the mass flow of species i into the system. The pressure would rise were it not for the rate of adsorption, that is, the process that removes i from the gas phase and locates it in the second phase, the adsorbent. Now we can make progress in the analysis even before we substitute in the rate expression. The reason is this in the experiment the rate of adsorption must be equal to the rate of delivery. Therefore we have a pseudo-steady state in that the gas phase concentration remains constant all the while the surface concentration is changing ... 

Under steady-state conditions in a plug-flow tubular reactor, the onedimensional mass transfer equation for reactant A can be integrated rather easily to predict reactor performance. Equation (22-1) was derived for a control volume that is differentially thick in all coordinate directions. Consequently, mass transfer rate processes due to convection and diffusion occur, at most, in three coordinate directions and the mass balance is described by a partial differential equation. Current research in computational fluid dynamics applied to fixed-bed reactors seeks a better understanding of the flow phenomena by modeling the catalytic pellets where they are, instead of averaging or homogenizing... 

Additionally, phenomena such as catalysis, ion-pair interactions, chemi- or bioluminescence, redox changes, etc., may be employed in the chemical transduction process. In catalysis type of system, for example, the immobilized reagent catalyzes the conversion of analyte to form a product whose optical property is then measured. Several examples of such reactions include those which utilize immobilized enzymes acting as a catalyst. The response of the sensor in such a system, involves a steady state, in which the rate of product formation is equal to the rate at which it is removed from the transducer by processes such as diffusion and convection. The concentration of the steady-state product increases with... 

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