Effect of the particle shape on flow through porous media

Abstract

In order to study the performance of shaped particles flow in porous media, filtration of two different shape - spherical and rod-like – micro particles was performed through a porous bed. Filtration was investigated at a constant flow rate of 0.04 cm/s with yeast cells, diameter 5 microns, micro spheres, diameter 1 micron, and rod-like bacilli Lactobacillus bulgaricus with 6 microns average length and 0.5 micron diameter. Yeast diameter is close to the bacillus length and micro-sphere diameter is in the scale of the bacillus diameter. All particles have similar density. For the packing, the following glass beads were used: coarse particles, size 1.125 mm; fine particles, size 0.1115 mm. Experiments were carried out using a column loaded with a binary packing (volume fraction of coarse particles in the mixture 0.7) or with a monosize packing with the same amount of coarse or fine particles as used in the binary packing. The analysis of the experimental results was based on two models: pure exclusion effect and hydrodynamic separation model (HDC). Results for spheres show that the classic HDC model ( B = 1.0) fits well the data whenever the ratio of particle size to the bend scale is high (~ 1/100, as for micro spheres). However, if this ratio increases and becomes ~ 1/20, the HDC model needs to be corrected due to the effect of channel wall curvature on the exclusion effect. This assumption leads to a modified HDC equation - R = B/ (1+2λ -2.8λ²), where B ≥ 1 and λ represents the ratio of microparticle size to the pore size. The effect of pore topology plays an important role in the separation of shaped particles when the aspect ratio λ approaches 0.1 and, in the case of bacillus, separation occurs by an exclusion mechanism. For the binary packing, the rod-like particles behave differently from the spherical particles having a length or a diameter in the same scale of bacillus length and diameter. The explanation is the interference of rod-like particles with the pore topology. The exclusion model for particles was formulated in a general form as R = A/(1-λ)², where A is a coefficient proportional to the tortuosity and parameter z = 1, 2 or 3 depends mainly on the pore shape. For instance, in a parallel-plate channel flow: R ~ 1/(1-λ), for a cylindrical pore R ~ 1/(1-λ)² , and for 3-D pore R ~ 1/(1- λ)³ . Further investigation is needed to clarify the particle – pore topology interaction and its effect on particle separation.