Power‐law polymer solution flow in a converging annular spinneret: Analytical approximation and numerical computation

Abstract

A simplified analytical solution for the flow of power-law liquids through a conical annulus was derived to estimate the flow profile, wall shear rate, and elongation rate in the spinneret during the spinning of hollow fiber membranes. The velocity profiles and shear and elongation rates of the power-law fluid showed good agreement with those obtained from computational fluid dynamic simulations. Although the actual spinneret is characterized by an annulus with a converging cross section, most studies to date have used a geometrical concentric annulus for the sake of simplicity. The results of the current work indicate that neglecting the converging characteristics of the actual spinneret can lead to significant underestimation of the wall shear rate. Using the equations derived in our work, we were able to predict not only the velocity profile but also the wall shear rate and the elongation rate; the influence of the spinneret design on the membrane morphology and properties were also examined.

Semianalytical solution for power‐law polymer solution flow in a converging annular spinneret

“…Table shows the analytical and CFD results along the z ‐axis at the inner and outer walls of a conical spinneret. The semianalytical results for the shear rate obtained in this study agree more closely with the CFD simulated results than the model that neglects the effect of radial flow . From the results shown in Table , the average deviations of shear stresses derived from the approximate analytical solution reached 47% and 21% at the outer and inner walls, respectively, while the wall shear stresses derived in this study deviated from the CFD simulation results by approximately 10%.…”

“…The semianalytical results for spinnerets at different flow angles are compared with the CFD simulation results and the approximate analytical results derived by Tung et al The performance of a hollow fiber predicted by the derived semianalytical solution has also been compared with the experimental data reported by Cao et al to validate the theoretical work derived in this study. The spinneret models are illustrated in Figure , and the dimensions of the spinnerets are listed in Table .…”

“…The essential details of CFD simulation including general conservation equations, boundary conditions, physical properties of the dope solution, and the iterations are described in our previous work . The steps for CFD simulation are listed as follows.…”

“…Therefore, spinneret designs typically feature a converging cross‐section; designs with straight annuli have been found to be inappropriate for predicting general membrane spinning processes. CFD methods can be used to simulate the flow profile in a spinneret during spinning and have been widely applied for designing membrane modules . Cao et al first implemented CFD methods to simulate the flow profiles for a dope solution flowing through spinnerets for three different flow angles.…”

“…Cao et al concluded that the elongation rate contributes more to the membrane permeability, while the shear rate contributes more to the membrane selectivity. To provide a convenient method for engineers to predict the flow behavior within a spinneret, Tung et al derived an approximate analytical solution for a power‐law fluid flowing through the conical spinneret neglecting the effect of radial flow. Although the results were more accurate than those derived for a straight annulus, neglecting of the effect of radial flow introduced significant error.…”