Filtration is an operation that has found an important place in the processing of biotechnology products. In general, filtration is used to separate particulate or solute components in a fluid suspension or solution according to size by flowing under a pressure differential through a porous medium. There are two broad categories of filtration, which differ according to the direction of the fluid feed in relation to the filter medium. In conventional or dead-end filtration, the fluid flows perpendicular to the medium, which generally results in a cake of solids depositing on the filter medium. In crossflow filtration (which is also called tangential flow filtration), the fluid flows parallel to the medium to minimize buildup of solids on the medium. Conventional and crossflow filtration are illustrated schematically in Figure 4.1. Conventional filtration is typically used when a product has been secreted from cells, and the cells must be removed to obtain the product that is dissolved in the liquid. Antibiotics and steroids are often processed by using conventional filtration to remove the cells. Conventional filtration is also commonly used for sterile filtration in biopharmaceutical production. Crossflow filtration has been used in a wide variety of applications, including the separation of cells from a product that has been secreted, the concentration of cells, the removal of cell debris from cells that have been lysed, the concentration of protein solutions, the exchange or removal of a salt or salts in a protein solution, and the removal of viruses from protein solutions. Filtration often occurs in the early stages of bioproduct purification, in keeping with the process design heuristic “remove the most plentiful impurities first” (see Chapter 12, Bioprocess Design and Economics). At the start of purification, the desired bioproduct is usually present in a large volume of aqueous solution, and it is desirable to reduce the volume as soon as possible to reduce the scale and thus the cost of subsequent processing operations. Filtration, along with sedimentation and extraction (see Chapters 5 and 6), is an effective means of accomplishing volume reduction.
$\mathbb {L}^p(p\ge 2)$-solutions of generalized BSDEs with jumps and monotone generator in a general filtration