Flux enhancement

Fouling is one of the most prevalent operational problems associated with microfiluation and ultrafiltration applications. The high mechanical strength and chemical as well as structural stabilities of many inorganic membranes (especially the ceramic types) and 

When operating the backflushing system optimally the resulting flux with rapid backflushing can be 20 to 30 times higher than the long-term flux in the absence of backflushing [Redkar and Davis, 1995]. 

For the reason of possible blocking of the membrane pores on the permeate side, only permeate or other prefiltered cleaning agent should be used in the backpulses. 

Flux enhancement by backflushing can conuol fouling in inorganic membranes and consequently reduce the operating costs. Most of the cost savings lie in the decrease of the membrane replacement costs [Muralidhara, 1991]. 

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A halide flux enhances the growth of single crystals of intermetallic compounds such as CaNi, and compounds in the Dy-Mg and Ce-Mg " systems which have... 

Figure 8 Griseofulvin flux enhancement factor = . Closed symbols represent TW 20 solutions, open symbols represent emulsions plotted as a function of the apparent TW 20 concentration in the emulsion aqueous phase.

In natural waters, unattached microorganisms move with the bulk fluid [55], so that no flux enhancement will occur due to fluid motion for the uptake of typical (small) solutes by small, freely suspended microorganisms [25,27,35,41,56,57], On the other hand, swimming and sedimentation have been postulated to alleviate diffusive transport limitation for larger organisms. Indeed, in the planar case (large r0), the diffusion boundary layer, 8, has been shown to depend on advection and will vary with D according to a power function of Da (the value of a is between 0.3 and 0.7 [43,46,58]). For example, in Chapter 3, it was demonstrated that in the presence of a laminar flow parallel to a planar surface, the thickness of the diffusion boundary layer could be estimated by ... 

This author has previously suggested that the mechanism of flux enhancement might be due to the "tubular pinch effect" ( ). The lower density (0.94 g/cc) MMA beads show less tendency to... 

Table 3.14 shows the results of some of Madronich s calculations of the actinic flux enhancements for two cases of a collimated direct beam of light striking the top of a cloud, first under typical summer conditions at... 

For the situation described by Eq. 20-47, the flux enhancement is given by the expression ... 

Figure 20.13 Air-water flux enhancement t / for reactive species as a function of the reaction/ diffusion parameter q = (2tv Q n for different equilibrium constants K,. See Eqs. 12-17, 20-51, 20-52, and 20-54.

In Fig. 20.13 flux enhancement V / is shown as a function of the reaction/diffusion parameter q for different equilibrium constants Kr. Remember that q2 is basically the ratio of reaction time kr and diffusion time k (Eq. 20-52). Thus, q 1 corresponds to case (1) mentioned at the beginning of this section flux enhancement should not occur (V / = 1). The other extreme (vp 1, that is tT /w) was discussed with the example of proton exchange reactions (Eq. 8-6). We found from Eq. 20-49 that for this case the water-side exchange velocity v/w is enhanced by the factor (1 + Ka /[H+]). By comparing Eqs. 8-6 and 12-17 we see that for the case of proton exchange ATa/[H+] plays the role of the equilibrium constant KT between the two species. Thus, flux enhancement is ... 

The V)f(q) curves in Fig. 20.13 indeed reach constant values for q — °° which are (approximately) equal to Kv This result also follows directly from evaluating Eq. 20-51 for q —> °°. Since tanh(g — °°) = 1, the second term in the denominator approaches zero for q — °°. Finally, Fig. 20.13 nicely demonstrates how p(maximum value (1 + Kr) for q — o°. Note that for large Kt values, this transition extends from q 1 to fairly large q values. Thus, for these cases flux enhancement remains -dependent in situations where tT is much smaller than tw. Thus, our first attempt to characterize the intermediate case with tT /w should rather be replaced by ... 

In conclusion, Eqs. 20-51 and 20-52 include the quantitative description of all three cases. A numerical example for the flux enhancement of formaldehyde is given in Illustrative Example 20.5. 

For both aldehydes you are interested in the flux enhancement of the water-phase exchange velocity v,w as well as of the overall exchange velocity v(a/w. Evaluate these numbers for two wind velocities, m10 = 1 m s 1 and 10 m s 1. 

The following table summarizes the results, vy is the water-phase flux enhancement (Eq. 20-52) and iy is the overall flux enhancement, that is, the ratio of the enhanced vlWw and the normal via/w. 

Since the nondimensional Henry s law constants ja/w of both aldehydes are fairly small (order 10 2), the influence of the air-side boundary layer on vlVw is not completely negligible. The considerable flux enhancement of formaldehyde reverses the role of the boundary layer the resistance in the air-phase becomes dominant. Therefore, the enhancement of v/w (V / = 21.5) is reduced to vy = 8.5 when the overall transfer velocity v,Ww is considered. 

To summarize, the effective size of flux enhancement is controlled by a fairly complex interplay of different compound properties and environmental factors. 

Then it can be concluded that an extremely small advection velocity is sufficient to produce a significant flux enhancement and to deform the TCE profile correspondingly. Note that case (2) (Pe 1) only occurs under extremely quiet conditions. 

Pyrrolidones show activity with numerous molecules including hydrophilic (e.g., mannitol, 5-fluorouracil, and sulfaguanidine) and lipophilic (betamethasone-17-benzoate, hydrocortisone, and progesterone) permeants. As with many studies, higher flux enhancements have been reported for the hydrophilic molecules. Recently, NMP was employed with limited success as an absorption promoter for captopril when formulated into a matrix-type trans-dermal patch [20]. 

Ninety-eight percent of formulations were eliminated as poorly potent, 99.5% were discarded after irritation studies, the remaining 0.5%> was tested for flux enhancement and 0.02% was finally assessed for bioavailability. The investigators thus revealed rare nonirritant... 

Hoogstraate, A.J., et al. 1991. Kinetics, ultrastructural aspects and molecular modelling of transdermal peptide flux enhancement by V-alkylazacycloheptanones. Int J Pharm 76 37. 

This model has been used to predict flux, flux enhancement, and the reduction in the lag time when a voltage is applied [55,56]. An enhancement factor (EF) has been defined as the ratio of the steady-state flux with an applied voltage (/ion) to the corresponding passive flux (7pas) ... 

Peck, K.D., et al. 1996. Quantitative description of the effect of molecular size upon electroosmotic flux enhancement during iontophoresis for a synthetic membrane and human epidermal membrane. J Pharm Sci 85 (7) 781. 

Peck, K.D., J. Hsu, S.K. Li, A.H. Ghanem, and W. Higuchi. 1998. Flux enhancement effects of ionic surfactants upon passive and electroosmotic transdermal transport. J Pharm Sci 87 1161. 

Pikal, M.J. 1990. Transport mechanisms in iontophoresis. I. A theoretical model for the effect of electroosmotic flow on flux enhancement in transdermal iontophoresis. Pharm Res 1 (2) 118. 

In an early study by Schery and Gaeddert (1982), an accumulator device was used to measure the effect of atmospheric pressure variations on the flux of Radon (222Rn), an inert radioactive element with a half-life of 3.8 days, from the soil. Fluxes measured by the accumulator were compared with predictions for flow-free diffusion from a model developed by Clements and Wilkening (1974), which applies Fick s law. A mean 222Rn-flux enhancement of about 10%, with a high value of 20%, due to cyclic atmospheric pressure variations was observed. However, the device s effectiveness was limited by back diffusion from the accumulator to the subsurface, leading the authors to view the flux values as semi-quantitative. 

It will be clear that, to be conceptually sound, any enhancement effect should exclude these factors. This requires careful definition of the flux enhancement due to the particles, for which we proposed [76]... 

Figure 9 Soup spoon confonnation with van der Waals contours of N-dodecylaza-cycloheptan-2-one, obtained through torsion of the peptide bond over 10", with tpci-C2-C3-C4 = 62 . Refer to original reference for computational details. (From Ref. 83. Reprinted from International Journal of Pharmaceutics, 76(1-2), Hoogsraate et al. Kinetics, ultrastructural aspects and molecular modelling of transdermal peptide flux enhancement by W-alkylazacycloheptanones, pp. 37-47, 1991, with kind permission from Elsevier Science, NL, Sara Burgerhartstraat 25, 1055 KV, Amsterdam, The Netherlands.)...

Henderson, J. A., Richards, R. W., Penfold, J., Shackelton, C. and Thomas, R. K. (1991). Neutron reflectometry from stereotactic poly (methylmethacrylate) monolayers spread at the air-water interface. Polymer 32 3284-3293. Hoogstraate, A. J., Verhoef, J., Brusse, J., Ijzerman, A. P, Spies, P. and Bodd6, H. E. (1991). Kinetics, ultrastructural aspects and molecular modelling of transder-mal peptide flux enhancement by A-alkylazacycloheptanones. Int. J. Pharm. 76 31-41. 

Pikal, M. and Shah, S. Study of the mechanisms of flux enhancement through hairless mouse skin by pulsed dc iontophoresis. Pharm. Res. 8 365,1991. 

V. Kuberkar, P. Czekaj, R.Davis (1998), Flux Enhancement for Membrane Filtration of Bacterial Suspensions Using High-Frequency Back washing, Biothchnology and Bioengineering, 60, 77-87. 

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