21 November 2013
Filtrodynamic behavior of trans-filter time-dependent pressure signals DeltaP(t) was determined for membrane and frit filters using latex spheres of varying diameter D. Membrane data were best interpreted via a time-dependent, accreting filtration bed, based on Darcy’s law. A single parameter, permeability k, described each membrane/particle pair. For small particles k increased with increasing D, then became D-independent for large ones. This was rationalized by the fluid velocity boundary layer size compared to the size of interstices between spheres. Predictable behavior for polydisperse mixtures of small spheres was obtained, which failed for larger spheres. The mechanism and behavior of filtration for non-membrane metallic frits was dramatically different, and better described by a previous ’Characteristic Loading’ model. k vs D was opposite that of membranes. Broad pore size distributions and volume loading in 3-D frits explain the behavior and lead to a filtrostatic theorem with a testable corollary that loading capacity for a fixed volume of injected particles is independent of filtrodynamic path. In the Darcy model d(DeltaP(t))/dt is proportional to Q² (Q=flow rate), whereas it is linear in Q in the ’characteristic loading’ model. Use of frit and membrane filters in series allowed monitoring each filter’s separate response to particle accumulation.
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