Steady State Permeate Flux Estimation in Cross-Flow Ultrafiltration of Protein Solution

Abstract

In the membrane separation process, the cross-flow configuration in which the fluid flows parallel to the membrane is widely utilized. Due to the shear stress exerted by the tangential feed flow, the accumulation of the retained species in the membrane is reduced, and the nearly steady state operation can be attained. The determination of steady state permeate flux is significant in the design and optimization problem. Several mechanisms of transport phenomena have been proposed to estimate the steady state permeate flux such as concentration polarization and Brownian diffusion, shear-induced diffusion, inertial lift, and surface transport. Another approach is using dimensional analysis to give the correlation equation with the operating condition instead of a deep focus on mechanism. In this study, we apply the model proposed in our previous study to predict the steady state permeate flux from the experimental data. After that, a new method using dimensional analysis is also developed to predict the steady state permeate flux from the operating conditions such as the trans-membrane pressure, the feed flow rate, and the feed volume fraction in a wide range. The correlation equation provides a good estimation of the experimental results.

Keywords:

• ultrafiltration
• cross-flow
• steady state permeate flux
• dimensional analysis
• combined model