Areal speed

The volumetric speed (areal speed) is thus expressed in moles per second and m (moles per second and m ). This magnitude is a priori based on the extent of the reaction (among others like temperature, concentration of the reactants, etc.) and therefore time, but is independent of the volume (or the surface) of the zone. 

Expression of the volumetric speed (areal) from variations in the amount of a component... 

This complex subsequently reacts with other reagents in the solution to produce either an insoluble dimer product, which also adsorbs on the AW device surface, or a massive ion (l3 was used) that inserts into an ionic binding site in the surface film. Thus, the areal mass increase per bound analyte is significantly amplified. While these and other immunosensor detection schemes can involve rather complex reagent and/or buffer systems, the relative advantages of piezoelectric sensors in terms of cost, speed, and safety make them attractive alternatives to radioimmunoassay and other standard assay techniques. 

The deviation ofthe work performed in areal expansion of a gas from that of reversible expansion can be shown to be of order dlKu). Here (u) is the average molecular speed and the is the speed of the piston. What piston speed is required f or a 10 % deviation from the reversible work formula ... 

Slow sand filtration invdves removing material in suspension and/or dissolved in water by percolation at slow speed. In principle, a slow filter comprises a certain volume of areal surfiice, with or without construction of artificial containment, in which filtration sand is placed at a sufficient depth to allow free flow of water through the bed. When the available head loss reaches a limit of approximately 1 m, the filter must be pulled out of service, drained, and cleaned. The thickness of the usual sand layer is approximately of 1 - 1.50 m, but the formation of biochemically active deposits and clogging of the filter beds takes place in the few topmost centimeters of the bed. 

We see that all the preceding reactions are surface or interface reactions, taking place in zones with two dimensions. The volume of this zone is thus the product of its area and the thickness of the interface zone, that is, roughly the cell parameter of the solid. Thus, we can define an areal speed of such interface reaction as follows ... 

Now examine the case of diffusion of a species i in a three-dimensional zone. We can define the speed of diffusion by the flow of molecules of / that cross a surface (fictitious) perpendicular to the direction of diffusion. Then the flux of diffusion/, will be an areal speed because we have the following expression ... 

A zone of diffusion is a three-dimensional one, but taking into account the preceding expression of the voluminal speed, we will distinguish the diffusion length parallel with the flux, which is included in the expression of this flux, from the surface perpendicular to the direction of displacement. Thus, the areal speed of diffusion, that is, the flux, also depends on the geometry of the zone through the diffusion length. 

The product vo is called the surface reactivity or the reactivity of the reaction (this is its areal speed), that is. 

We choose to express flux at the internal interface. But this flux, which plays the role of an areal speed, not oidy depends on intensive variables, but also contains a geometrical term as shown in the second colunm of Tables 7.1 and 7.2 for various geometries. In order to separate the two contributions, we introduce Go, the space number of diffusion and we can write flux in the form ... 

When we identify the areal speed or a flux in a rate-determining step mode, we know (see section 7.5.2) that the eoneentrations of the intermediate species are connected to those of the reactants and products via the equihbrium constants of the steps with infinite rate constants. However, in ease of coalescence, the effects of the radii of curvatures are completely prevalent since there is no total chemical conversion. We saw (see section 3.11.1) that the eqnilibrinm constants depend on the radii of curvatures and in particular, as we will further show, on the smallest of them - the radius of the neck. 

As we did for the diffusion in the chemical conversions, we will introduce a factor G without dimension into the space function and we will define the reactivity starting from areal speed as follows ... 

To calculate the reactivities, we calculate areal speeds or flux of diffusions in case of the modes with a rate-determining step. However, it is to be noticed that steps [12.Et.a] and [12.Et.c] are exactly reverse of each other and that we will not be able to consider that only one of them is with infinite rate constant and not the other. Then, it will be necessary to consider the case of the pseudo-steady state mixed modes [12.Et.a] and [12.Et.c] as we did in the cases studied above (see section 12.6.1.3). 

The volumetric speed of a single-zone reaction is the speed of the reaction per unit of volume (the areal speed will be used for 2D zones). We emphasize that this notion is only defined for reactions with a single reaction zone, which includes all homogeneous reactions, in other words that occur entirely in one phase ... 

This flow, which acts as an areal speed, not only depends on intensive variables but also contains factor G, which is a geometric term. In order to separate both contributions, the flux can be written as ... 

The speed of a heterogeneous reaction (or its rate) is usually an extremely complex function that depends on physico-chemical and textural variables (shapes and phase dimensions). (Jenerally, the volumetric or areal speed cannot be defined. Despite thus, a certain nrrmber of heterogeneorrs reactions follow the law , which means that the rate can be written as a product of two functions as in the case of the elementary steps ... 

One of these, ( ), is expressed in mol/m /s and only depends on intensive quantities pressure, temperature, concentrations, light intensity, electric or magnetic fields, etc. It acts as an areal speed. 

By making the flux expression explicit through the Pick s first law [3.32] and by introducing the areal speeds (i.e. per unit of area), we obtain ... 

In systems with concentrations that are held constant, the speeds with constant space function - which is the term ( ) of product isothermal conditions. This is true for the volumetric speed of a homogeneous system as well as for the areal speed of a catalytic system. This will be also true in the case of a strictly heterogeneous reaction that obeys the law of < E. Space functions are, however, frequently a function of time, which leads to absolute speeds or to rates that vaiy with time through this space function. 

We retain this distinction between elementary steps to which we attribute a reactivity that follows an order and obeys Arrhenius law and the multi-step reactions for which the notion of specific speed is retained (volumetric or areal) and whose expression of speed is far from obvious. 

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