Inverse fluxes

For a reversibly soluble gas, one needs to retain both the flux from the gas to the aqueous phase and the inverse flux. The mass balance of (20.15) is still valid, so combining it with (20.11), we get... 

Thus, at the start of a crossflow menoibrane filtration the inverse flux rate is proportional to the cumulative fihrate volume, in much the same way as described in Section 2.6.1. The intercept of such a plot can be used to provide an in situ value for the membrane resistance, via Equation (10.15). This resistance is usually much greater than the clean water permeation st value for the same membrane. This is due to the effect of the interaction of the initial layers of deposit within the membrane structure. These layers add substantially to the effective membrane resistance, ie. additional resistances due to adsorption and blocldng, see Section 10.4. This situation is again very similar to that for conventional filtration, where the filter medium resistance increases at the start of the filtration. If the membrane was a true surface filter this would not happen, but almost all membrane filters do permit some initial penetration of particulates. 

Figure 10.18 Inverse flux rate with filtrate volume for oil emulsion...

Equation 42 describes the inverse flux when concentration polarization in the solution is taken into account. We note that a clean separation of the various rate-limiting terms is not achieved in this case. 

As velocity continues to rise, the thicknesses of the laminar sublayer and buffer layers decrease, almost in inverse proportion to the velocity. The shear stress becomes almost proportional to the momentum flux (pk ) and is only a modest function of fluid viscosity. Heat and mass transfer (qv) to the wall, which formerly were limited by diffusion throughout the pipe, now are limited mostly by the thin layers at the wall. Both the heat- and mass-transfer rates are increased by the onset of turbulence and continue to rise almost in proportion to the velocity. 

In a free jet the absence of a pressure gradient makes the momentum flux at any cross section equal to the momentum flux at the inlet, ie, equations 16 and 17 define jet velocity at all points. For a cylindrical jet this leads to a center-line velocity that varies inversely with (x — aig), whereas for slot jets it varies inversely with the square root of (x — Xq As the jet proceeds still further downstream the turbulent entrainment initiated by the jet is gradually subordinated to the turbulence level in the surrounding stream and the jet, as such, disappears. 

Most commercially available RO membranes fall into one of two categories asymmetric membranes containing one polymer, or thin-fHm composite membranes consisting of two or more polymer layers. Asymmetric RO membranes have a thin ( 100 nm) permselective skin layer supported on a more porous sublayer of the same polymer. The dense skin layer determines the fluxes and selectivities of these membranes whereas the porous sublayer serves only as a mechanical support for the skin layer and has Httle effect on the membrane separation properties. Asymmetric membranes are most commonly formed by a phase inversion (polymer precipitation) process (16). In this process, a polymer solution is precipitated into a polymer-rich soHd phase that forms the membrane and a polymer-poor Hquid phase that forms the membrane pores or void spaces. 

Note The speed of the motor ean be varied by vai-ying the frequeney alone but this docs not provide satisfactory performance, A variation in frequeney causes an inverse variation in the flux, for the same system voltage. The strength of magnetic field, p, develops, the torque and moves the rotor, but at lower speeds. / would be reduced, which would raise 0 , and lead the magnetic circuit to saturation. For higher s )ccds, / would be r.nised, but that would reduee which would adversely diminish the torque. Hence frequency variation alone is not recommended practice for speed control. The recommended practiee is to keep V/fas constant, to maintain the motor s vital operatin.c parameters, i.e. its torque and 0 ,. within acceptable limits. 

With regard to the enantioselective transport through the membrane, one advantage of liquid membrane separation is the fact that the diffusion coefficient of a solute in a liquid is orders of magnitude higher as compared to the diffusion coefficient in a solid. The flux through the membrane depends linearly on the diffusion coefficient and concentration of the solute, and inversely on the thickness of the membrane [7]. 

Several selective interactions by MIP membrane systems have been reported. For example, an L-phenylalanine imprinted membrane prepared by in-situ crosslinking polymerization showed different fluxes for various amino acids [44]. Yoshikawa et al. [51] have prepared molecular imprinted membranes from a membrane material which bears a tetrapeptide residue (DIDE resin (7)), using the dry phase inversion procedure. It was found that a membrane which contains an oligopeptide residue from an L-amino acid and is imprinted with an L-amino acid derivative, recognizes the L-isomer in preference to the corresponding D-isomer, and vice versa. Exceptional difference in sorption selectivity between theophylline and caffeine was observed for poly(acrylonitrile-co-acrylic acid) blend membranes prepared by the wet phase inversion technique [53]. 

A number of studies have recently been devoted to membrane applications [8, 100-102], Yoshikawa and co-workers developed an imprinting technique by casting membranes from a mixture of a Merrifield resin containing a grafted tetrapeptide and of linear co-polymers of acrylonitrile and styrene in the presence of amino acid derivatives as templates [103], The membranes were cast from a tetrahydrofuran (THF) solution and the template, usually N-protected d- or 1-tryptophan, removed by washing in more polar nonsolvents for the polymer (Fig. 6-17). Membrane applications using free amino acids revealed that only the imprinted membranes showed detectable permeation. Enantioselective electrodialysis with a maximum selectivity factor of ca. 7 could be reached, although this factor depended inversely on the flux rate [7]. Also, the transport mechanism in imprinted membranes is still poorly understood. 

The inverse relationship between dissolved solids concentration and pressure is illustrated by the figures given for low-pressure boiler waters in Table 17.6. That there is room for different opinions is shown by contrasting the BSS and ASME recommendations. Whilst both of these authorities propose essentially similar figures for feed-water (Table 17.7), some of the ASME boiler-water figures are substantially below their BS equivalents. This is probably due to the increasing trend towards higher heat fluxes than formerly in some low-pressure plant, particularly waste-heat boilers. 

Where general corrosion occurs, the rate of hydrogen production is relatively independent of heat flux. Thus, the concentration of hydrogen is inversely proportional to steam flow. 

Sediment trap studies in the open ocean show that the flux of organic carbon at any depth is directly proportional to the rate of primary productivity in the surface water and inversely proportional to the depth of the water column (Suess, 1980) ... 

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