Mass-flux dependence

The j° term denotes the ordinary concentration diffusion (i.e., multi-component mass diffusion). In general, the concentration diffusion contribution to the mass flux depends on the concentration gradients of all the substances present. However, in most reactor systems, containing a solvent and one or only a few solutes having relatively low concentrations, the binary form of Pick s law is considered a sufficient approximation of the diffusive fluxes. Nevertheless, for many reactive systems of interest there are situations where a multi-component closure (e.g., a Stefan-Maxwell equation formulated in terms... 

In compressible flows, the mass flux depends on both the velocity component normal to the cell face and the variable density. To correct the mass flux imbalance, both the density and the velocity must be corrected. The corrected mass flux on the e face of a grid volume can be expressed as ... 

Now, consider the term The mass flux depends mainly on the vapour... 

In the case of material exchange in the gas phase at low pressure or in small cavities and pores, the gas molecules collide more often with the enclosing walls than with other gas molecules, i.e., the mean free path length is longer than the distances to be travelled. In this case, the mass flux depends linearly on the mean velocity of the molecules w, and on the concentration difference Ac, see Sect. 3.1.7 ... 

The quantity c nj(Nj is the concentration of analyte emerging from the last theoretical plate into the detector, so Equation [3.11] corresponds to the desired theoretical expression for Rd(V) for cases in which the chromatographic detector has a concentration dependent response (Section 4.4.8 and Appendix 4.1) UV-visible absorption detectors are an important example since their response is described by the Beer-Lambert Law, but elecirospray ion sources for mass spectrometers can also behave in this fashion in some circumstances (Section 5.3.6b). Electron ionization ion sources provide a response that is mass flux dependent (Section 4.4.8) however, for a fixed mobile phase flow rate U (volume per unit time), the conversion from c ni(N) to the mass flow rate is trivial and this distinction is not important in the discussion of the present Section although the practical imphcations are discussed in Section 5.3.6b. 

Appendix 4.1 Responses of Chromatographic Detectors Concentration vs Mass-Flux Dependence... 

The corresponding treatment for the (mass flux dependant) El mass spectrometer is similar but contains an additional complication. Now, instead of a beam of light, the analytical probe is a beam of energetic electrons that interact with the analyte molecules in a variety of ways, one of which is to create ions of a particular m z value chosen as characteristic of the analyte and selectively transmitted to the detector by the mass selection portion of the instrument. Then the observed signal is given by ... 

The positive radial direction has been chosen to be into the droplet (i.e., condensation corresponds to a positive mass flux). Generally, the mass fluxes depend on the droplet radius, the total gas pressure, the droplet and gas temperatures, the mole fractions of the vapors just above the droplet surface and far from it, and the diffusivities of vapors in the gas mixture. 

Wu and Cheng [1] conducted experiments using 8 parallel silicon microchannels heated from the bottom. They observed water flows with large-amplitude or long-period oscillating boiling modes as a function of heat flux and mass flux depending on whether the water outlet is at saturation temperature or superheated. 

Mass flux for low subcooling region. The mass flux depends on the type of flow. 

Calculation of the (O parameter and mass flux depend on two different sets of conditions as explained in the following subsections. 

The rate of mass transfer (qv) depends on the interfacial contact area and on the rate of mass transfer per unit interfacial area, ie, the mass flux. The mass flux very close to the Hquid—Hquid interface is determined by molecular diffusion in accordance with Pick s first law ... 

It is important to note here that the CHF depends on the flow conditions, including the mass flux and the vapor quality. Using Eq. (2.25) to eliminate q, we find... 

Bo = q/Gh] Q, where t is the period between successive events, U is the mean velocity of single-phase flow in the micro-channel, Jh is the hydraulic diameter of the channel, q is heat flux, m is mass flux, /zlg is the latent heat of vaporization). The dependence t on Bo can be approximated, with a standard deviation of 16%, by... 

Traditionally, an average Sherwood number has been determined for different catalytic fixed-bed reactors assuming constant concentration or constant flux on the catalyst surface. In reality, the boundary condition on the surface has neither a constant concentration nor a constant flux. In addition, the Sh-number will vary locally around the catalyst particles and in time since mass transfer depends on both flow and concentration boundary layers. When external mass transfer becomes important at a high reaction rate, the concentration on the particle surface varies and affects both the reaction rate and selectivity, and consequently, the traditional models fail to predict this outcome. 

Much of the geographic variability in sedimentary ( Paxs/ °Thxs) observed in modern sediments may be explained by variability in the composition of biogenic particles arising from variability in the structure of the planktonic ecosystem. This can be inferred from the composition-dependence of F(Th/Pa) (Fig. 8), and is shown explicitly by the relationship between sediment trap ( Paxs/ °Thxs) and the opal/calcite ratio of the trapped particles (Fig. 9). Sediment trap ( Paxs/ °Thxs) also exhibits a positive relationship with the mass flux of particles, but the correlation is poorer than that with particle composition (Fig. 9). Indeed, the relationship between particulate ( Paxs/ °Thxs)... 

For diabatic flow, that is, one-component flow with subcooled and saturated nucleate boiling, bubbles may exist at the wall of the tube and in the liquid boundary layer. In an investigation of steam-water flow characteristics at high pressures, Kirillov et al. (1978) showed the effects of mass flux and heat flux on the dependence of wave crest amplitude, 8f, on the steam quality, X (Fig. 3.46). The effects of mass and heat fluxes on the relative frictional pressure losses are shown in Figure 3.47. These experimental data agree quite satisfactorily with Tarasova s recommendation (Sec. 3.5.3). 

Two types of dryout exist in the high and medium mass fluxes, respectively. The boundary between these two mass flux regimes lies in the range from 0.1 X 106 to 0.5 X 106 lb/hr ft2 (136 to 678 kg/m2 s), depending on pressure and channel length (Macbeth, 1963a). 

The correction factor K is thus strongly dependent on the flow conditions (Wong et al., 1990). For values of mass flux below a limit, Gmin, the flow is fully stratified and hence g"rithor is zero, or K = 0. On the other hand, if mass fluxes are... 

---