Theories Of Scaling Down/Scale-Up Tangential Flow Filters

Permeation flux and permeability are two crucial parameters in membrane filtration. Permeation flux is the volume of liquid that can pass through per unit time and per unit membrane area. Permeability is the ratio of the concentration of the target product in the permeate to its concentration in the return solution. When comparing tangential flow filters of different sizes , it is necessary to control variables to minimize interference: select membranes with consistent material, pore size, and manufacturer; use feed solutions with identical composition and concentration; and conduct experiments under uniform room temperature conditions. Once these initial conditions are met, it is also necessary to control the experimental conditions according to three principles (the same feed solution volume per unit membrane area, the same shear force, and the same initial water flux) to ensure that the permeation flux and permeability of filters of different sizes are approximately consistent at every moment.

 

Principle 1: The same feed liquid filtration volume corresponds to a unit membrane area.

Permeation flux, permeability, and membrane properties are closely related. Besides ensuring the same membrane material and pore size, to achieve the same permeation flux and permeability, the membrane surface conditions (filter cake and concentration polarization) of the large and small filters should be similar at any given time. To make the filter cake and concentration polarization similar on the membrane surface, the volume of the same feed liquid (substance, concentration) filtered per unit area should be the same for both the large and small filters. Therefore, the ratio of feed liquid volume between the large and small filters should be equal to the ratio of their membrane areas, i.e., the volume of feed liquid corresponding to the same unit membrane area.

 

Principle 2: The shear forces on the membrane surface are the same.

In the biopharmaceutical industry, the feed solutions that need to be filtered are mostly biologically active. The shear force on the membrane surface not only affects the formation of filter cake and concentration polarization, but also the bioactivity of biological products. Therefore, it is necessary to ensure that the shear force on the membrane surface of both large and small tangential flow filters is the same during experimental operations.

 

Principle 3 : Same initial flux

Under the same conditions of feed liquid, membrane surface properties and operating conditions, if the initial flux is the same and the membrane surface changes are similar, the subsequent flux will usually be similar. Therefore, it is necessary to ensure that the initial flux is the same so that the flux corresponding to each time of the large and small filters is similar.

Although the membrane material, pore size, and manufacturer of the large and small filters are the same, their total filtration resistance differs due to differences in membrane packing structures. When the filtration resistances of the large and small filters differ, different transmembrane pressure values (TMP) are required to achieve the same permeate flux. Typically, the transmembrane pressure (TMP) is the difference between the average inlet and outlet pressures and the permeate pressure. Since the permeate in both large and small filters is connected to atmospheric pressure, the permeate pressure in both is 0 Pa. (Gauge pressure). Therefore, the transmembrane pressure in the experiment is the average of the inlet pressure and the outlet pressure.

When all three principles above are satisfied, and with the same initial conditions, theoretically, the permeation flux at the same moment after the filtration begins for both large and small filters will be the same. When the permeation flux at all moments is exactly the same, it can be concluded that the total filtration time for both types of filters is equal. See the figure below.

 

 

Schematic diagram of the internal interactions of relevant physicochemical and operational parameters

References: Guo Shuyin. Design and verification of a small tangential flow filter and the theory of tangential flow filter scaling down/up [D]. East China University of Science and Technology, 2016.