A flat-bottomed bioreactor with a volume of 0.1 m and a diameter of 45 cm is used to grow cells. The cells are immobilised on plastic beads with a diameter of 1 mm. (a) A Rushton turbine has been installed in the reactor. The bioreactor is initially used ungassed. Calculate, using the Zwietering equation, the minimum stirrer speed, Ni min required to ensure suspension of beads. Given: D/DT= 0.33; H/DT = 0.25; D, is the stirrer diameter, Dr the tank diameter, and H. the off-bottom clearance. Zwietering equation (in SI units): Ni min Svi do.2 [gAp/P10.45X0.13 Ni min is given in rotations per second (rps). S is a constant, VL is the liquid kinematic viscosity, d is the particle diameter, g is the gravitational constant, Ap is the difference in the density of the particle and the fluid, p, is the density of the liquid, X is the weight percentage of particles and Di is the diameter of the stirrer. Table 4.1. Fluid properties. G 9.81 m/s VL Ps 0.15 x105 1100 m/s kg/m 0.85 PL 1000 kg/m X 5 w/w% Impeller Rushton Rushton Rushton Rushton Rushton Rushton Propeller Dimpeller/Dtank 0.25 0.33 0.33 0.33 0.5 0.5 0.33 Himpeller/Dtank 0.25 0.17 0.25 0.5 0.25 0.17 0.25 IS 12 5.8 6.7 8 4.25 3.9 6.6 (b) As the cells that are grown on the surface of the beads can also be grown aerobically it is decided to change to a gassed system. In gassed bioreactor systems, however, there can be a reduction in the liquid pumping capacity of the impeller because of the formation of ventilated cavities behind the impeller blades. The result of this is a drop in the solids suspension capacity of the impeller. To compensate for this a higher stirrer rate is needed. The new increased minimum impeller rate can be calculated with the equation: Ni min gassed = Ni min ungassed + 2.4Fgv Ni min gassed and Ni min ungassed are in rotations per second. The gas flow rate Fi is in units of vvm (volume of gas per volume of liquid per minute). A gas flow of 1 vvm is sparged into the bioreactor. Calculate the new (increased) minimum impeller rate. (c) Because of the relative high gas flow rate used there is a chance that the impeller will be flooded. Make a sketch that shows what is meant by flooding of an impeller. (d) Flooding occurs if the gas flow number Flg is too high. F Flg ND Fg is the volumetric air flow rate (in m/s). For a Rushton turbine the flooding-loading transition occurs at Fig = 30 0 Fr is the Froude number. 3.5 Fr= Fr NZD 9 Determine whether flooding will occur when the smallest impeller speed needed to suspend the beads is used in the aerated bioreactor.