Average surface residence

If no readsorption occurs, the 1. order rate constant is equal to the inverse of the average surface residence time (t) ... 

In the structure with all the surfactant molecules located at monolayers, the volume fraction of surfactant should be proportional to the average surface area times the width of the monolayer divided by the volume, i.e., Ps (X Sa/V. The proportionality constant is called the surfactant parameter [34]. This is true for a single surface with no intersections. In our mesoscopic description the volume is measured in units of the volume occupied by the surfactant molecule, and the area is measured in units of the area occupied by the amphiphile. In other words, in our model the area of the monolayer is the dimensionless quantity equal to the number of amphiphiles residing on the monolayer. Hence, it should be identified with the area rescaled by the surfactant parameter of the corresponding structure. 

Tmobiie tjme for transition of bubble surface to rigidity, s tr average bubble residence time, s... 

In steady-state isotopic transient kinetics, the average smface residence time can he calculated as the area under the normalized transient curve [11-13], Equation (3) gives the concentration of active surface intermediates, N. 

It is difficult to obtain the surface residence time of the liquid for mass transfer processes by experimental measurement. Yet we may consider that the resident time of a solute particle at the interface equals to the traveling time of a solute particle from bulk fluid to the interface in order to avoid solute accumulation or depletion and keep constant solute concentration at the interface. Thus, the interfacial residence time of the solute can be computed by the average interfacial velocity and the average characteristic scale. Characteristic scale was referred to the largest turbulent eddy in the fluid as defined in Sect. 8.8.2. On the assumption that the interfacial solute renewal is controlled by the large-scale vortex ranging from bulk liquid to the interface, the surface residence time can be obtained by the following relationship ... 

The subscript MIN denotes that tw,min is the minimum possible long-term average atmospheric residence time due to wet deposition processes for chemicals that are efficiently scavenged by rain. The maximum possible long-term average flux of chemical to the surface due to wet deposition processes is... 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

Air pollution problems in which adsorption is considered a unit operation involve gaseous contaminants. The number of molecules present at the carbon surface is dependent on the number that reach the surface and on the residence time of these molecules on the carbon surface. If n molecules strike a unit area of a surface per unit time, and remain there for an average time, t, then a number of molecules are present per unit area of surface ... 

The residence time or contact time discussed in the preceding section is a simple average. Hyman (H21) pointed out that the residence time of any one gas molecule could vary widely from the mean because of the tortuous paths followed by the gas bubbles from the gas inlet to the surface. Knowledge of gas residence time is important for design purposes and is necessary for an understanding of the behavior of gas-liquid dispersions (W5). Relatively little experimental effort has been devoted to this area. 

Pneumatic conveying dryers normally take particles 1-3 mm dia but up to 10 mm when the moisture is mostly on the surface. Air velocities are 10-30 m/sec. Single pass residence times are 0.5-3.0 sec but with normal recycling the average residence time is brought up to 60 sec. Units in use range from... 

The deposition velocities depend on the size distribution of the particulate matter, on the frequency of occurrence and intensity of precipitation, the chemical composition of the particles, the wind speed, nature of the surface, etc. Typical values of and dj for particles below about 1 average residence time in the atmosphere for such particles is a few days. 

Many hydrologic reservoirs can be further subdivided into smaller reservoirs, each with a characteristic turnover time. For example, water resides in the Pacific Ocean longer than in the Atlantic, and the oceans surface waters cycle much more quickly than the deep ocean. Similarly, groundwater near the surface is much more active than deep reservoirs, which may cycle over thousands or millions of years, and water frozen in the soil as permafrost. Typical range in turnover times for hydrospheric reservoirs on a hillslope scale (10-10 m) are shown in Table 6-4 (estimates from Falkenmark and Chapman, 1989). Depths are estimated as typical volume averaged over the watershed area. 

Solution The surface is estimated to contain 0.067mol of A in adsorbed form. The inlet gas contains 1.6 mol of A per cubic meter and is flowing at 150cm /s so that A is entering the reactor at a rate of 0.00024 mol/s. Five minutes are needed to supply the surface if all the incoming gas were adsorbed. Fifteen to thirty minutes would be a reasonable startup time. Recall that the reactor has a gas-phase residence time VjQout of only 1.5 s The residence time of the adsorbed species is 700 times larger than the average (nonadsorbed) molecule. 

When solid particles are subject to noncatalytic reactions, the effects of the reaction on individual particles are derived and then the results are averaged to determine overall properties. The general techniques for this averaging are called population balance methods. They are important in mass transfer operations such as crystallization, drop coagulation, and drop breakup. Chapter 15 uses these methods to analyze the distribution of residence times in flow systems. The following example shows how the methods can be applied to a collection of solid particles undergoing a consumptive surface reaction. 

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