AAAR 32nd Annual Conference
September 30 - October 4, 2013
Oregon Convention Center
Portland, Oregon, USA
Abstract View
Determination of the Single Fiber Collection Efficiency for Fibrous Filters through Mean First Passage Time Analysis
BENJAMIN HUNT, Thaseem Thajudeen, Christopher Hogan Jr., University of Minnesota
Abstract Number: 50 Working Group: Control Technology
Abstract We propose and present a new method of determining the single fiber efficiency for the fibrous filtration of arbitrarily-shaped particles. Specifically, this method utilizes mean first passage time calculations for determination of the collision rate between nanoparticles and a filter fiber, and through these calculations a relation between the collision rate and single fiber efficiency is derived. In addition to demonstrating this new method of single fiber efficiency calculation, there are a number of advantages to this approach and new insights into filtration that can be found. First, single fiber collection efficiency calculations require integration of the efficiencies for individual streamlines. Collision rate calculations, on the contrary, can be performed in the absence of flow and in the zero-flow continuum limit have a known solution. By comparison to this solution, it becomes apparent that many single fiber collection efficiency equations do not have the correct scaling with the Peclet number, Pe, as Pe approaches zero. Second, with the use of dimensionless calculations, the dimensionless collision rate/efficiency can be determined as functions of dimensionless numbers that also describe the equations of motion for the particles. This enables determination via regression of a single function describing the rate/efficiency accounting for the effects of diffusion, interception, and filter solidity together, mitigating the need to assume additivity or to incorporate interaction terms. Finally, we show that with a properly defined length scale for nonspherical entities, the resulting collision rate and single fiber collection efficiency equations can be extended to particles of arbitrary shape, including fibers and agglomerates.