Hollow-fiber membrane devices are used in a number of applications in bio-engineering and biochemical engineering. A typical unit consists of thousands of small hollow fiber tubes packed in a tubular...

Hollow-fiber membrane devices are used in a number of applications in bio-engineering and biochemical engineering. A typical unit consists of thousands of small hollow fiber tubes packed in a tubular device (Figure 3.28a). Components within the fibers can be isolated from components outside the fibers

based on solubility and/or size restrictions. Some materials can easily diffuse across the membrane between the fibers to the annular space. In this problem, the hollow-fiber membrane device is modeled as an inner tube, representing the membrane fibers, and an outer tube, representing the outer (annular) space (Figure 3.28b). A hollow-fiber membrane device is operated to concentrate a bacterial suspension. The flow rate of cell suspension into the fibers is 350 kg/min. The inlet cell suspension is comprised 1.0 wt% bacteria; the rest of the suspension can be considered water. An aqueous buffer solution enters the annular space at a flow rate of 80.0 kg/min. Because the cell suspension in the membrane tubes is under pressure, water is forced from the tubes, across the membrane, and into the buffer. Bacteria in the cell suspension are too large to pass through the membrane, and thus, they remain in the membrane tubes throughout the device. The outlet cell suspension is comprised 6.0 wt% bacteria. Assume that the cells do not grow. Also assume that the membrane does not allow any molecules other than water to pass across it. (Adapted from Doran PM, Bioprocessing Engineering Principles, 1999.)

(a) Determine the mass flow rates of the outlet cell suspension stream and the outlet buffer stream.

(b) Determine the mass flow rate of the water across the membrane.

(c) Determine the mass flow rate of the cells in the outlet cell suspension stream.