A simple harmonic motion is proposed to make the membrane nove in a simple harmonic way so as to enhance the membrane filtration, and minimize the membrane fouling and concentration polarization. The velocity distribution and pressure distribution are deduced from the Navier-Stokes equation on the basis of a laminar flow when the membrane rotates at the speed of A sin(αt). And then the shear stress, shear force, moment of force on the membrane surface and power consumed by viscous force are calculated. The velocity distribution demonstrates that the phase of membrane velocity does not synchronize with that of shear stress. The simple harmonic motion can result in self-cleaning, optimize energy utilization, provide the velocity field with instability, and make the feed fluid fluctuation. It also results in higher shear stress on the membrane surface than the constant motion when they consume the same quantitative energy.
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