The model presented in this study has completed the preliminary stages of development. It competently models the concurrent effects of the permeation hydrodynamic drag and inter-particleinteractionpotentialonthedynamicsofparticle depositionontothemembranesurface.Theinterplaybetween these two forces is shown to be among the most crucial elementsthatdeterminethephysicalaccuracyofthemodel.Furthermore, the model is applied to gain insights into the phase transition phenomenon of the particle deposit. Three possible criteria for phase transition are identified—weak form of the critical flux, particle contact, and irreversible adhesion of particles. Multiple characterizations of the point of phase transition allow for incorporation of practical considerations such as filtration performance and, therefore, offer the flexibility for adaptation to a wide range of physical situations.
The current study will continue by progressively adding further considerations for the variegated array of forces and phenomena mentioned above. The model in its final form will approach a close facsimile of real systems. Many of the important topics of study in membrane filtration such as membrane fouling and locally varying dynamics of cake layer formation can be simulated by a comprehensive robust model. The outlook of the current model is optimistic with promising new developments and applications to follow.
This research was supported by the U.S. National Science Foundation (Grant BES 0114527), the U.S. Geological Survey (Grant 01HQGR0079), through the Water Resources Research Center, University of Hawaii at Manoa, Honolulu, and Saehan Industries, Seoul, Korea.
|
Nomenclature a particle radius a0 uniform random number between 0 and 1 AH Hamaker’s constant D(φ) concentration-dependent diffusion coefficient of particles e charge of an electron I ionic strength of the solution kB Boltzmann’s constant n0 ion number concentration NA Avogadro’s number P applied pressure within the system rc specific cake resistance rim particle location R parameter characterizing ratio of hydrodynamic drag to inter-particle potential Rc cake layer resistance Rm membrane resistance s dimensionless center-to-center separation T absolute temperature u crossflow velocity VEDL inter-particle electrostatic potential VVDW van der Waals’ potential Vn,m change in potential energy zs valence of ions in the bulk solution Greek letters δc cake layer thickness δrmax maximum allowable displacement εr relative permittivity of water ε0 permittivity of free space κ−1 Debye screening length µ absolute dynamic fluid viscosity v permeate flux vw permeate flux in magnitude ξ a uniform random number between 0 and 1 ρn/ρm Boltzmann factor of the energy difference φ volume fraction of particles in the cake layer φb bulk volume fraction of particles φc cake layer volume fraction φm particle volume fraction at the membrane surface ψs surface potential of the particles Ω Happel’s correction factor |
[1] S. Chang, A.G. Fane, S. Vigneswaran, Modeling and optimizing submerged hollow fiber membrane modules, AIChE J. 48 (2002) 2203–2212.
[2] B.D. Cho, A.G. Fane, Fouling transients in nominally sub-critical flux operation of a membrane bioreactor, J. Membr. Sci. 209 (2002) 391–403.
Уважаемый посетитель!
Чтобы распечатать файл, скачайте его (в формате Word).
Ссылка на скачивание - внизу страницы.