Momentum balance analysis of permeate flux for ultrafiltration in tubular membranes with gradually increasing incidental angles of a wired-rod insert

It was reported in previous works that the performance of ultrafiltration in tubular membranes could be improved by concentrically inserting a steel rod, and further improved by wrapping a wired spiral of uniform angles on the entire rod, to increase fluid velocity and thus, to decrease the concentration polarization resistance. Since the thickness of the concentration polarization layer increases along the cross-flow channel while transmembrane pressure decreases. Thus, the smaller inclined angle of wire spiral, as well as smaller increment in fluid velocity, around the inlet region, is sufficient to reduce the lower concentration polarization resistance, while still preserving the effective transmembrane pressure around the outlet region. Accordingly, it was found that membrane performance with inserts with a varying angle wire wrap on the rod was considerably higher then those with constant angle wrapping. The new theoretical analysis of present modified module was based on the momentum balance coupled with the application of resitance-in-series model. Correlation predictions are qualitatively agreement with the experimental results for ultrafiltration of dextran T500 aqueous solution in a tubular ceramic membrane with gradually increasing angles of a wired-rod insert.