Permeate flux in crossflow ultrafiltration under intermediate pressures

The intermediate pressure range stands for an important condition for ultrafiltration operations where permeate flux falls below that predicted from a linear flux-pressure relationship but does not reach the limiting flux. Optimal performance of ultrafiltration might be achieved on the upper end of the intermediate pressure range because the maximum permeate flux will be obtained at the lowest possible pressure. Unlike in the low pressure range or in the high pressure range, little has been known about the behavior of permeate flux in the intermediate pressure range. A general theory of permeate flux in the intermediate pressure range is developed in this study. The theory includes the linear-increasing and limiting fluxes as two special cases and, therefore, can be used to study the behavior of permeate flux in ultrafiltration in the whole pressure range.