In this paper, Smoothed Particle Hydrodynamics (SPH) and Molecular Dynamics (MD) methods are used to respectively simulate the flow and mass transfer phenomena inside a pore at microns scale, and then at nanons scale. The trans-membrane filtration velocities acquired using SPH method are in good agreement with the results calculated by simplified K-K equation when the pore’s diameter of the membrane is between 1 μm and 200 μm. The simulation accuracy is also discussed in the paper. However, the MD numerical results reveal that the micro-scale effect dominates and could not be neglected near the wall surface inside a nano sized pore. In this size, slip boundary appears at the wall surfaces. This situation is different from the flow in macro-scale that the velocity at the wall could be considered as zero. The MD numerical results also reveal the variational nature of the viscosity with the applied body force. Finally, we find that the ultra-filtration velocity acquired by MD simulation is different from the results estimated from the simplified K-K equation in nano-scale.

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