The permeate flow rate is determined with the pore model via the resistance in series models, as described in Sections 12.3.2.
Different authors use the resistance in a series of models and describe mathematical approaches as well as experimental investigations for estimation of the resistances used in Eq. (12.43) (Fu and Dempsey 1998; Melin et al. 2001; Geissler et al. 2003; Wintgens et al. 2003). For example, resistances were summarized by Chang et al. (2002) for microfiltration in MBR with Rm = 3-22 ■ 1011 m-1, Rc = 3-48 ■ 1011 m-1 and Rf=10-11m-1 for different membrane materials. In ultrafiltration processes for the reuse of surfactants Rm = 5-1012 m-1 and Rf = 5-9.1 ■ 1012 m-1 was experimentally determined for PES membranes for various surfactants (Goers 2000).
The resistance of the sludge cake Rc is a function of the concentration at the membrane surface. It follows from Eq. (12.43) according to the concentration polarization model.
Chang and Fane (2000) describe the shear stress on micro and ultrafiltration membrane surfaces from air bubbling of submerged hollow fibers by slug flow conditions, i.e. based on two-phase flow conditions influenced by the formation of Taylor bubbles. Melin et al. (2001) and Wintgens et al. (2003) use the same model of slug flow conditions, considering concentration polarization and hydrodynamic effects. They use experimental data from the full-scale wastewater treatment plant Rödingen in Germany to obtain coefficients for their model. Further investigations are summarized by Stephenson et al. (2000).
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