FLUID-DYNAMICS IN A TUBULAR MEMBRANE - THEORY AND EXPERIMENT

Measurements of trans-cartridge [axial] pressure drops for pure liquid flowing in a porous tube under all regimes of flow as a function of w all suction and axial flow rate are reported. At very low axial flow r ates [Re(F) < 1,000], low values of wall suction [Re(W) < 0.25] have a minimal effect on the non-dimensional axial pressure drop. At very hi gh axial flow rates [Re(F) > 20,000], however, all values of wall suct ion have a minimal effect on the axial pressure drop. Wall suction, on the other hand, has its maximum effect on the axial pressure drop at intermediate axial flow rates [1,000 < Re(F) < 15,000]. It is in this range that most commercial membrane modules operate. Starting with the equations of continuity and Navier-Stokes we have developed two relat ively simple approximate analytical solutions of this problem. The fir st approach assumes an average constant wall flux and includes the eff ect of the inertial terms while the second approach accounts for axial pressure-dependent flux but neglects the inertial terms. Both analyti cal models are useful qualitatively. However, neither was able to pred ict performance accurately. The model with constant wall flux and iner tia predicts quite well the pressure drop as a function of Re(F) for l ow suction (Re(W) = 0.25). Deviations between model and experiment inc reased with increasing Re(F) and Re(W). Results from the model with pr essure-dependent wall flux but without inertia fluctuated widely about the measurements for increasing Re(W). This model is useful only for very small Re(W). When the experimental conditions were such that the parabolic profile was distorted [i.e., for Re(W) > 0.5], the theories were invalid and were unable to predict the measurements accurately.