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important issue as they might be unhealthy for the water body and alter the membrane stability. In the same study, it was reported that the as-synthesized membrane
had no leaching of hydrous iron–nickel–manganese trimetal oxide nanoparticles
within a wide range of pH (2–14) at the end of 12 h of batch adsorption experiments.
Dynamic filtration study revealed that the polysulfone hollow fiber composite membrane could maintain the arsenite level below the maximum allowable concentration of 0.01 mg/L for approximately 3665 mL of filtrated volume, and this membrane
configuration could be efficiently used for the treatment of wastewater containing
arsenic that has lower concentration of 1.0 mg/L under 0.5 bar.
6.6 Modelling the Performance of the Membrane Adsorber
The primary reason for considerable interest in the application of membrane adsorbers comes from the fact that membrane tailor is made to accomplish high selectivity
in a specified separation process. Introducing inorganic nanoparticles with a polymeric matrix increases the membrane selectivity while preserving its high throughput. In the conventional membrane filtration concept, mechanism of the flux decline
and rejection are mainly ascribed to the concentration polarization phenomena
caused by a reduction in driving force, formation of gel layer, electrokinetic effects,
and pore blocking. Conversely, solute adsorption coupled with diffusion and convection in the membrane separation process displays a great significance on the
mechanisms of both rejection and the flux profile in the membrane adsorber.
Therefore, understanding the details in the mechanisms of the transport processes is
important for membrane adsorbers. In addition, membrane adsorber similar to any
adsorption-based processes has a definite lifetime, beyond which the concentration
of foulant in the filtrate exceeds the allowable limit, known as breakthrough time.
Prior to the breakthrough time, the filtrated volume is known as the breakthrough
volume. Generally, dead-end modes of filtration with flat sheet membranes are
selected in lab-scale applications for forecasting their short-term behaviors. During
the transport of solute molecules, model equations were developed for the two limiting cases of adsorption or diffusion dominating at steady-state conditions (Doshi
2011). However, filtration is a dynamic process, in which adsorptive and diffusive
processes might be in transient region that covers both of the terms in the model
equation. In the case of cross-flow filtration that uses either flat sheet or hollow fiber
types of membranes, modelling is required to achieve the proper scaling up in longterm sustainable filtration. This can be accomplished by comprehensive modelling
which enables concrete and a reliable forecasting of the long-term characteristics of
the filtration unit including fluid flow in lumen side, coupling of velocity and concentration field, transmembrane and osmotic pressures, channel length, and timedependent permeate flow. Below, a comprehensive unsteady-state two-dimensional
model for solute filtration though hollow fiber membrane adsorber, which was
developed by Mukherjee et al., by considering the equations of continuity, momentum, and convective+diffusive+adsorptive-based species transport through cylindrical membrane adsorber, is given (Mukherjee et al. 2019).
Y. Yurekli
important issue as they might be unhealthy for the water body and alter the membrane stability. In the same study, it was reported that the as-synthesized membrane
had no leaching of hydrous iron–nickel–manganese trimetal oxide nanoparticles
within a wide range of pH (2–14) at the end of 12 h of batch adsorption experiments.
Dynamic filtration study revealed that the polysulfone hollow fiber composite membrane could maintain the arsenite level below the maximum allowable concentration of 0.01 mg/L for approximately 3665 mL of filtrated volume, and this membrane
configuration could be efficiently used for the treatment of wastewater containing
arsenic that has lower concentration of 1.0 mg/L under 0.5 bar.
6.6 Modelling the Performance of the Membrane Adsorber
The primary reason for considerable interest in the application of membrane adsorbers comes from the fact that membrane tailor is made to accomplish high selectivity
in a specified separation process. Introducing inorganic nanoparticles with a polymeric matrix increases the membrane selectivity while preserving its high throughput. In the conventional membrane filtration concept, mechanism of the flux decline
and rejection are mainly ascribed to the concentration polarization phenomena
caused by a reduction in driving force, formation of gel layer, electrokinetic effects,
and pore blocking. Conversely, solute adsorption coupled with diffusion and convection in the membrane separation process displays a great significance on the
mechanisms of both rejection and the flux profile in the membrane adsorber.
Therefore, understanding the details in the mechanisms of the transport processes is
important for membrane adsorbers. In addition, membrane adsorber similar to any
adsorption-based processes has a definite lifetime, beyond which the concentration
of foulant in the filtrate exceeds the allowable limit, known as breakthrough time.
Prior to the breakthrough time, the filtrated volume is known as the breakthrough
volume. Generally, dead-end modes of filtration with flat sheet membranes are
selected in lab-scale applications for forecasting their short-term behaviors. During
the transport of solute molecules, model equations were developed for the two limiting cases of adsorption or diffusion dominating at steady-state conditions (Doshi
2011). However, filtration is a dynamic process, in which adsorptive and diffusive
processes might be in transient region that covers both of the terms in the model
equation. In the case of cross-flow filtration that uses either flat sheet or hollow fiber
types of membranes, modelling is required to achieve the proper scaling up in longterm sustainable filtration. This can be accomplished by comprehensive modelling
which enables concrete and a reliable forecasting of the long-term characteristics of
the filtration unit including fluid flow in lumen side, coupling of velocity and concentration field, transmembrane and osmotic pressures, channel length, and timedependent permeate flow. Below, a comprehensive unsteady-state two-dimensional
model for solute filtration though hollow fiber membrane adsorber, which was
developed by Mukherjee et al., by considering the equations of continuity, momentum, and convective+diffusive+adsorptive-based species transport through cylindrical membrane adsorber, is given (Mukherjee et al. 2019).
Y. Yurekli