To separate and collect microparticles such as cells, the behavior of particles in fibrous filters was investigated. It is essential to understand, in detail, the motion of particles in microscale flows, because Re is often small, and particles exhibit complex behaviors such as changes in relative position and spreading owing to hydrodynamic interactions. We calculated the motion of microparticles passing through the fibrous bed using the Stokesian dynamics method, in which hydrodynamic interaction is considered, theoretically. The fibrous bed was modeled by particles and five types of structures (a monolayer with fiber volume fractions ϕ of 3%, 4%, and 5%, and a bilayer with ϕ = 3−5% and 5−3%) were considered. Our numerical results showed that the particles moved in a complicated manner, and spread throughout the fibrous bed. It was found that the behavior of individual microparticles varied depending on the internal structure, although the average permeation velocity was primarily determined by the fiber volume fraction. This great dependence of the behavior of particle assemblage on the internal structure of the fibrous bed was caused by the individual particle motion under the influence of the layers in front of and behind them, owing to the hydrodynamic interaction.

We have simulated the motion of particle assemblage passing through fibrous media. On the assumption that the particle size is of the order of micrometers, the velocity of individual particles was calculated by use of the Stokesian dynamics that describes the Stokes flow in the presence of multiple particles. The results show that a part of particles is captured by fibers while others avoid them and permeate the media. From the velocity, traveling distance and direction of the particles which are not captured, the diffusion caused by the hydrodynamic interaction was observed. The results indicated that the motion of each particle greatly differs depending on the particle size particularly for the large fiber volume fraction, which would be closely related to the hydrodynamic diffusive behavior.

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