Optimized Tree-Type Cylindrical-Shaped Nanoporous Filtering Membranes with 6 or 7 Branch Pores in each Pore Tree

Abstract

<span class="fontstyle0">The performances of the optimized tree-type cylindrical-shaped nanoporous fltering membranes with six or seven branch pores in each pore tree are analytically studied. The radius R</span><span class="fontstyle0" style="font-size: 4pt;">b,1 </span><span class="fontstyle0">of the branch pore for fltration is normally on the 1 or 10 nm scales. The larger trunk pore is for improving the flux of the membrane. For liquid-particle separations, the radius R</span><span class="fontstyle0" style="font-size: 4pt;">b,1 </span><span class="fontstyle0">of the branch pore is determined by the particle size, and the radius R</span><span class="fontstyle0" style="font-size: 4pt;">b,2 </span><span class="fontstyle0">of the trunk pore is optimized for yielding the lowest flow resistance of the membranes; The optimum ratios of R</span><span class="fontstyle0" style="font-size: 4pt;">b,2 </span><span class="fontstyle0">to R</span><span class="fontstyle0" style="font-size: 4pt;">b,1 </span><span class="fontstyle0">are typically calculated respectively for weak, medium-level and strong liquid-pore wall interactions when the operational parameter values are widely varied. The capability of the liquid-liquid separation of these membranes is also analytically shown.</span>