Flux volume

At any point within the boundary layer, the convective flux of the macromolecule solute to the membrane surface is given by the volume flux,/ of the solution multipfled by the concentration of retained solute, c. At steady state, this convective flux within the laminar boundary layer is balanced by the diffusive flux of retained solute in the opposite direction. This balance can be expressed by equation 1 ... 

Because high quaHty, low cost, and optimum performance are required for spray equipment, improved analytical and experimental tools are iadispensable for increasing productivity ia many competitive iadustries. In most iastances, it is no longer adequate to characterize a spray solely on the basis of flow rate and spray pattern. Information on droplet size, velocity, volume flux, and number density is often needed and can be determined usiag advanced laser diagnostic techniques. These improvements have benefited a wide spectmm of consumer and specialized iadustrial products. 

Mumber Density and Volume Flux. The deterrnination of number density and volume dux requires accurate information on the sample volume cross-sectional area, droplet size and velocity, as well as the number of droplets passing through the sample volume at any given instant of time. Depending on the instmmentation, the sample volume may vary with the optical components and droplet sizes. The number density represents the number of droplets contained in a specified volume of space at a given instant. It can be expressed as follows, where u is the mean droplet velocity, t the sample time, andM the representative cross-sectional area at the sampling location. 

Hollow Sprays. Most atomizers that impart swid to the Hquid tend to produce a cone-shaped hoUow spray. Although swid atomizers can produce varying degrees of hoUowness in the spray pattern, they aU seem to exhibit similar spray dynamic features. For example, detailed measurements made with simplex, duplex, dual-orifice, and pure airblast atomizers show similar dynamic stmctures in radial distributions of mean droplet diameter, velocity, and Hquid volume flux. Extensive studies have been made (30,31) on the spray dynamics associated with pressure swid atomizers. Based on these studies, some common features were observed. Test results obtained from a pressure swid atomizer spray could be used to iUustrate typical dynamic stmctures in hoUow sprays. The measurements were made using a phase Doppler spray analyzer. 

The phase Doppler method utilizes the wavelength of light as the basis of measurement. Hence, performance is not vulnerable to fluctuations in light intensity. The technique has been successfully appHed to dense sprays, highly turbulent flows, and combustion systems. It is capable of making simultaneous measurements of droplet size, velocity, number density, and volume flux. 

Initial plume volume flux for dense gas dispersion, voliime/time Continuous release rate of material, mass/time Instantaneous release of material, mass Release duration, time T Absolute temperature, K... 

The model requires a specification of the initial cloud volume, the initial plume volume flux, the duration of release, and the initial gas density. Also required is the wind speed at a height of 10 m, the distance downwind, and the ambient gas density. 

Fig. 5-4. (a) Separation of d,1-phenylalanine by an amino aeid immobilized in the pores of a polysulfone ultrafiltration membrane, (b) Effeet of volume flux on the separation faetor, Jv = volume flux, T = 37 °C [32],... 

If r < r,., there is no interfacial slippage. Thus, the improved fluidity, i.e., the increased volume flux under a constant pressure through a capillary, can only be attributed to the TLCP-rich interlayers formed in the area where r > r. ... 

Table 4 also reports dependence of the mechanical tensile properties of the samples on the processing conditions. The highest tensile properties of sample 1, injection molded with a lower melt temperature and a lower volume flux, are attributed to the highest degree of fibrillation of the TLCP fibers, as shown in Fig. 12, by so-called in situ reinforcement. 

Figure 14 Calculated shear rate as function of the halved sample thickness for two injection volume fluxes Q.

Figure 15 Calculated viscosity as function of the halved sample thickness for two melt temperatures and for (a) injection volume flux of 8 cmVs and (b) injection volume flux of 80 cm /s.

Figure 13-5 is the box model of the remote marine sulfur cycle that results from these assumptions. Many different data sets are displayed (and compared) as follows. Each box shows a measured concentration and an estimated residence time for a particular species. Fluxes adjoining a box are calculated from these two pieces of information using the simple formula, S-M/x. The flux of DMS out of the ocean surface and of nss-SOl back to the ocean surface are also quantities estimated from measurements. These are converted from surface to volume fluxes (i.e., from /ig S/(m h) to ng S/(m h)) by assuming the effective scale height of the atmosphere is 2.5 km (which corresponds to a reasonable thickness of the marine planetary boundary layer, within which most precipitation and sulfur cycling should take place). Finally, other data are used to estimate the factors for partitioning oxidized DMS between the MSA and SO2 boxes, for SO2 between dry deposition and oxidation to sulfate, and for nss-SO4 between wet and dry deposition. 

Even then, the formulation of the system of fluxes and driving forces is not yet satisfactory, because of the quantity Acw. Thus, a new definition of the fluxes will be introduced, i.e. the volume flux of the solution, defined by the equation... 

Of the remaining three cross phenomenological coefficients, Lwn can be found from the volume flux during dialysis (Ap =0, A = 0, because electrodes Wx and W2 are short-circuited) ... 

By definition, Lnjl > 0. The sign of Js is determined by the sign of the cross coefficient Lvjr and its absolute value. If Lv <0, the volume flux of the solvent occurs in the direction from more dilute to more concentrated solutions (i.e. in the direction of the osmotic pressure gradient). If LVJt is smaller than then the solute flows in the direction of the drop of... 

D is a characteristic length jG, jL are the volume fluxes of the gas and liquid, respectively and m, C are constants. For turbulent flow, m is equal to unity. The value of C is found to depend on the design of the ends of the tubes and the way in which the liquid and gas are added and extracted. It may have values ranging from 0.725 to 1. For viscous flow in a liquid, m and C are functions of the dimensionless inverse viscosity, NF, where... 

Here Jv is the volumetric flow rate of fluid per unit surface area (the volume flux), and Js is the mass flux for a dissolved solute of interest. The driving forces for mass transfer are expressed in terms of the pressure gradient (AP) and the osmotic pressure gradient (All). The osmotic pressure (n) is related to the concentration of dissolved solutes (c) for dilute ideal solutions, this relationship is given by... 

The volume flux, denoted Jv, is the rate of volume change divided by the cross-sectional area of the tube and is identical to the drift velocity u,... 

As discussed earlier, the mean drift velocity is the volume flux, Jv [see Eq. (70)]. Using the ideal gas equation to relate volume flow to molar flow [see Eq. (71)], the relationship between mean drift velocity and molar flux J may be written as um = (RTIPa)J. With this expression for um, Eqs. (80) and (81) are combined to give the desired expression for molar flux,... 

Note that the total volume flux (/m) of the mixture is the same as the superficial velocity (Vm), i.e., the total volumetric flow divided by the total flow area. However, the local velocity of each phase (F,) is greater than the volume flux of that phase (/, ), because each phase occupies only a fraction of the total flow area. The volume flux of each phase is the total volume flow rate of that phase divided by the total flow area. 

Dc is the characteristic source dimension for continuous releases of dense gases (length), q0 is the initial plume volume flux for dense gas dispersion (volume/time), and u is the wind speed at 10 m elevation (length/time). 

Volume changes, by vitreous silica, 22 438 Volume flux, of droplets, 23 187 Volume fraction, in filtration, 11 328 Volume fraction calculation, in equivalent box model, 20 345—346 Volume mean diameter, 23 186 Volume of activation, 13 407-408... 

In the phase-Doppler method, the volume flux, V, is obtained from ... 

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