Surface flux

An alternative defining equation for surface diffusion coefficient Ds is that the surface flux Js is Js = - Ds dT/dx. Show what the dimensions of Js must be. 

In general, therefore, the surface flux of each substance is linearly related Co all the concentration gradients in the adjacent bulk phase. The coefficients in this linear relation depend on the bulk phase concentrations,... 

This may be particularly important when modeling the behavior of porous catalysts, where adsorption is strong and surface fluxes may be substantial. 

As pointed out in Chapter 7, the surface fluxes may be neglected in developing models for gaseous phase transport and re-introduced at a later stage. 

We begin our analysis by comparing the surface fluxes. According to the indicated partitioning factors, 74% of the 11 Mg DMS-S/m /h emitted from the ocean surface should be returned as nss-SO in rain. This leads to a predicted wet deposition flux of nss-SO of 8.1 Mg S/(m /h), which is 37% lower than the measured flux of 13 Mg S/(m /h). Since the estimated accuracy of the DMS emission flux is 50% (Andreae, 1986), this is about as good agreement as can be expected. It indicates that our "closed system" assumption is at least a reasonable first approximation. (A more sophisticated treatment would consider sulfur oxida-... 

Gr/v Re = 9.6) without causing recirculation, and thus nonuniform surface flux. Since the disk temperature is fixed in this simulation, a smaller value of the mixed-convection parameter corresponds to a larger value of the disk spin rate. 

Sw = substrate concentration in the bulk water phase (g m-3) ra = biofilm surface flux (g nr2 s-1, g nr2 h 1 or g nr2 d-1) ku2 = 1/2-order rate constant per unit biofilm surface area... 

Theoretical knowledge is available for a detailed description of the biofilm processes (Characklis, 1990 Gujer and Wanner, 1990). However, a fundamental requirement to establish applicable experimental procedures for determination of components and process parameters delimits the use of details. A simple description of the biofilm processes in terms of a surface flux model according to the description in Section 3.2.2 is selected. 

Focusing on sulfide formation, the sediment is often simply taken into account by considering it covered with a biofilm. The potential for sulfide production in terms of the surface flux will typically exceed what is observed for sewer biofilms, e.g., being 50-100% higher (Schmitt and Seyfried, 1992 Bjerre et al., 1998). 

The hopping model This model assumes that molecules can hop over the surface. The surface flux is calculated by the mean hopping distance and the velocity, with which the molecules leave their site. Weaver and Metzner (1966) developed a detailed model to calculate the mean hopping distance. Ponzi et al. (1977) developed a simpler way of estimating the mean hopping distance. 

Equations (8.1)-(8.13) can be solved to provide transient- or steady-state profiles of O2 and CH4 concentration, reaction rates and surface fluxes for any combination of the controlling variables 9q,0], v,k, a, Vm,Vq and Vr. Where, as is usual, one or more of the controlling variables may be further simplified, approximated or neglected, process-based simulation of CH4 emission becomes possible using a relatively limited set of input data. 

Equation (10.6) and can be directly substituted into Eq. (10.1) resulting in the expression for surface flux, Jz. 

Figure 14. Simple model demonstrating how adsorption and surface diffusion can co-Urnit overall reaction kinetics, as explained in the text, (a) A semi-infinite surface establishes a uniform surface coverage Cao of adsorbate A via equilibrium of surface diffusion and adsorption/desorption of A from/to the surrounding gas. (b) Concentration profile of adsorbed species following a step (drop) in surface coverage at the origin, (c) Surface flux of species at the origin (A 4i(t)) as a function of time. Points marked with a solid circle ( ) correspond to the concentration profiles in b. (d) Surface flux of species at the origin (A 4i(ft>)) resulting from a steady periodic sinusoidal oscillation at frequency 0) of the concentration at the origin.

Carboxylic acids The smallest carboxylic acid, formic acid, can be measured using infrared spectroscopy (Table 11.2), since it has characteristic absorption bands. As discussed earlier and seen in Fig. 11.33b, mass spectrometry with chemical ionization using SiF5 also revealed HCOOH in an indoor environment (Huey et al., 1998). However, since the sensitivity in these initial studies was about two orders of magnitude less than that for HN03, the detection limit may be about the same as that for FTIR and TDLS. Formic and acetic acids have been monitored continuously from aircraft (Chapman et al., 1995) and their surface flux determined by eddy correlation (Shaw et al., 1998) using atmospheric pressure ionization mass spectrometry. Detection limits are about 30 ppt. 

A method to interpret the solution fields in terms of design objectives. Often this task is accomplished by evaluating surface fluxes from derivatives of the solution fields (e.g., fluid mechanical drag, material deposition rates, and surface heat transfer)... 

The flux summary within the boxes in Fig. 17.2 shows the mass flux (g/cm2-s) of both the silane and silylene to the surface, resulting in deposition of silicon and release of volatile hydrogen. At low temperature, the film growth is primarily from silane, although it is quite low. By Ts = 925 K, there is sufficient silane decomposition that the surface fluxes of the two species are becoming comparable. At Ts = 1300 K, the silylene flux is dominant, carrying most of the silicon to the surface. 

The requirements for chemical sensors suitable for use in eddy correlation direct measurements of surface fluxes are examined. The resolution of chemical sensors is examined and defined in terms of surface flux and commonly measured micrometeorological parameters. Aspects of the design and operation of sensor systems are considered. In particular, the effects of the inlet ductingy the sensing volume, and the signal processing on the ability to measure surface fluxes were analyzed. 

This atmospheric stability versus friction velocity plot is capable of representing any atmospheric condition except that when the stability is neutral. The information contained in Figure 1 and equation 2 allows the relationship between the value of the surface flux and the required chemical sensor resolution to be estimated for a full range of atmospheric conditions. 

Concentrations at surface sites are often affected by the proximity of the surface. The surface may emit the species, as is the case for NO, or the species may be deposited at the surface, as is the case for HN03. In either case, the atmospheric concentration measured within several meters of the surface may be significantly perturbed from the average for the troposphere as a whole or even for the boundary layer (the lowest layer of the troposphere in direct thermal contact with the surface its thickness varies from 102 m or less at night to 103 m or more during the day, at least over land). Therefore, the surface complicates the interpretation of concentration measurements. However, proper measurements near the surface can be used to determine surface fluxes of the species. 

This system represented a somewhat less formidable problem than quasi-reversible charge transfer [15]. The surface flux equation is given by... 

These boundary conditions correspond to the constant surface-flux diffusion problem in Section 5.2.5, in which the surface concentration increased proportionally to t1/2. Therefore, adapting the solution given by Eq. 5.69 to the grainboundary grooving model,... 

Lake Core location Site name Date collected Surface conc n (ngg- dw) Surface flux (ug rrr2 yr-1) Maximum flux (u-gm yr1) Year of max deposition % per year decline from maxima Average open lake decline1 % per year Refs. 

Table 3 BB-153 surface and maximum concentrations, inventories, burdens, surface fluxes, and load rates in sediment from Lakes Michigan and Erie. From Zhu and Hites [22]...

Table 8 Average PBDE surface concentrations, doubling times, inventories, burdens, surface fluxes, and load rates in sediment from the Great Lakes. Data were from Zhu and Hites [22] and Song et al. [46-48]. The errors are 1 standard error (N = 2- 4) NS indicates that the concentrations did not change significantly with depth in this core ...

A second situation is where the boundary layer may contain an additional term in its energy budget from surface fluxes as the air moves along its surface trajectory. This leads to a decoupling of the moist static energy in the boundary layer from the values in the upper... 

From the voltammograms of Fig. 5.12, the evolution of the response from a reversible behavior for values of K hme > 10 to a totally irreversible one (for Kplane < 0.05) can be observed. The limits of the different reversibility zones of the charge transfer process depend on the electrochemical technique considered. For Normal or Single Pulse Voltammetry, this question was analyzed in Sect. 3.2.1.4, and the relation between the heterogeneous rate constant and the mass transport coefficient, m°, defined as the ratio between the surface flux and the difference of bulk and surface concentrations evaluated at the formal potential of the charge transfer process was considered [36, 37]. The expression of m° depends on the electrochemical technique considered (see for example Sect. 1.8.4). For CV or SCV it takes the form... 

The continental cycle of phosphorus is determined by ten fluxes (Figure 4.1) closed by a single component Ps indicating the phosphorus supplies on land in soil-vegetation formations and in animals. The supplies of phosphorus in soils are replenished due to fluxes Hf (l = 2,4,5,8,9,10). The loss of phosphorus from the soil is determined by fluxes Hj ( / = 3,6,7,11). As the detailing of surface reservoirs of phosphorus and consideration of more ingenious effects in the interaction between these reservoirs gets more complicated, so the classification of the surface fluxes of... 

De Rosnay P. Bruen M. and Polcher J. (2000). Sensitivity of surface fluxes to the number of layers in the soil model used in GCMs. Geophys. Res. Lett., 27(20), 3329-3332. 

---