Nanofibers are attractive to use in air filtration, due to the high surface-to-volume ratio, low flow resistance and enhanced filtration performance. However, the cost of nanofibers and slowing down in production process when using them leads to the desire to use as few nanofibers as possible. We treat such optimization issues by simulating filter media and filtration processes resolving the smallest scale.

The low pressure drop for nanofiber filters is explained with the slip flow effect, which states that in nano regime, the velocity of air at a surface does not vanish in the tangential direction. Since in our modeling, we convert a 3D fiber structure into voxels, applying a wall shear stress on such a staircase shape of the fiber surface is quite a challenge.

Previously, the slip-flow boundary condition could not be implemented directly into voxel-based flow solvers in a satisfactory fashion. In our previous work [1-5] we used two methods, the equivalent shrunk fiber and the equivalent permeable fiber, as workarounds. In the equivalent shrunk fiber method, the fiber is shrunk to make a flow possible in the fiber surface voxels. In the equivalent permeable fiber method, the nanofiber is permeable to make flow pass through it. However, there are limitations and disadvantages to both methods. They require either very high resolution of the structure or a lot of computational efforts to find the appropriate hypothetical permeabilities.

In this new approach, the expression of the slip velocity, which assumes the slip velocity proportional to the shear stress at the surface [6], is now reformulated for a locally quadratic velocity profile instead of the standard linear profile, and reimplemented in our flow solver. The direct simulation of the slip flow is then possible. The validations with analytic solutions are presented.

The influence of slip flow in nanofiber structures then is investigated and the results of flow and filtration simulations are compared with measurements.

Speaker: Liping Cheng, PhD / Math2Market GmbH

[1] A. Wiegmann, S. Rief and A. Latz, Soot Filtration Simulation - Generation of Porous Media on the Micro Scale from Soot Deposition on the Nano Scale, Proceedings of the 2nd European Conference on Filtration and Separation, Compiegne, France, October 2006, pp 141-147.

[2] A. Wiegmann, Computation of the permeability of porous materials from their microstructure by FFF-Stokes, Berichte des Fraunhofer ITWM, Nr. 129, 2007.

[3] L. Cheng, S. Rief and A. Wiegmann, Nano Filtration Media – Challenges of Modelling and Computer Simulation, Filtech, Wiesbaden, Deutschland, Vol. II, 2009, pp 413-419.

[4] L. Cheng, S. Rief and A. Wiegmann, Simulation of nano fibers and filtration processes, 10. Symposium Textile Filter Chemnitz, 2010. 

[5] A.Wiegmann, L. Cheng and S. Rief, Filtration simulation on the nano scale – the influence of slip flow, European Conference on Fluid-Particle Separation FPS, Lyon, France, 2010.

[6] L.M.H. Navier, Mem. Acad. R. Sci. Inst. France 1, 414 (1823).