Monte Carlo simulation of colloidal membrane filtration: Model development with application to characterization of colloid phase transition, страница 12

5.3.  Cake irreversibility

Finally,besidesthepointofparticlecontactandthecritical flux,anotheralternativefordefiningphasetransitionrelieson the idea of cake irreversibility [40,43,44]. After the particles come into contact, continued exertion of pressure will lead to their adhesion, which produces an irreversible cake layer. An irreversible cake layer will remain on the membrane even after a release of the applied pressure. The cake layer formed is permanent in contrast to the case of mere particle contact where the solidified deposit will disintegrate upon release of the applied pressure. The formation of an irreversible cake layer bears serious ramifications for filtration operations. A typical membrane filtration system will operate according to cycles of membrane cleaning. An irreversible cake layer may persist after the cleaning procedure and permanently exacerbate the system performance. So, another practical designationofphasetransitionhasbeenrecognized.Phasetransition indicates the occurrence of an irreversible cake layer where particles are in contact and adhered. The cake layer formed is permanent and will persist upon a release of pressure and may be resistant to cleaning. This viewpoint bases its justi-

Fig. 12. Summary of the strong and weak forms of the critical flux. The following parameters (in addition to those listed in Table 1) were used in the simulations: zeta potential=−30mV, ionic strength=10−³ M, particle radius=100nm.

fication on the idea of permanence of the phase transition. A solid phase should be enduring and not temporal in that it should remain regardless of the applied pressure, which precisely defines an irreversible cake formation.

So, a multiplicity of perspectives is available to characterize the point of phase transition from a fluid-like polarized layertoasolidcake.Fig.13providesasummaryoftheseclassifications.Whichdefinitionofphasetransitionisvalidwould depend on the mode of operation of the filtration system. For instance, if efficient productivity is sought, the weak form of the critical flux would be the relevant parameter for gauging phase transition. Likewise, if effective membrane cleaning is the guideline for operation, then the criterion for phase transition can be relaxed to correspond to the point of cake irreversibility. The definitions of phase transition should remain multifarious and flexible so that it can be adaptable to a vast range of operating conditions and standards of performance.

6.  Conclusion

This study endeavors to develop a comprehensive Monte Carlo simulation of colloidal membrane filtration for the purposesofinvestigatingthephasetransitionphenomenonofthe particle deposit from a fluid-like polarization layer to a solid cake. Colloidal membrane filtration involves a complex array of counterworking forces acting simultaneously. The set of physical processes that govern filtration includes crossflow shear, permeation drag, inter-particle interaction potential, gravitational compression, restructuring of the deposit, particle aggregation, breakage of aggregate, and particle collisions. Such an elaborate system bewilders macroscopic modeling techniques that apply averaged values of the physical parameters and thereby lose valuable information about the innerworkingsoftheintricatesystem.So,theproblemofcolloidal membrane filtration casts hydrodynamic bias Monte Carlo simulation as an extremely advantageous alternative that possesses the efficacy to capture the minute details of everydistinctforceandparticledisplacement.MonteCarlosimulation has traditionally been widely accepted in the physical sciences. Among the objectives of this study is to reinforce the fledgling extension of this powerful modeling technique into membrane separation and fouling studies.