Dr. Roy would like to acknowledge RIG and OPERA grants from BITS Pilani for carrying out the work.

Abstract

The chapter introduces the book to the reader. This chapter discusses about the evolution of membrane technology as well as related mathematical modeling. It is needless to state that mathematical modeling is imperative as far as industrial scale up or process feasibility analysis is concerned. However, the interplay of various mathematical modeling has contributed significantly to the development of membrane technology. From molecular interaction to transport models to computational fluid dynamics models to thermodynamic perspectives, mathematical modeling has been an “inseparable” ingredient to one of the most advanced “separation” technology devised by man.

Keywords: Mathematical modeling, simulation, membrane technology

Membrane Separation Process is a frontier area of research with diversified portfolio of applications [1]. The history of membrane based separation process can be traced back to the discovery by Thomas Graham (1805-1869) where he observed solute transported through a vegetable parchment to water. He was the first person to coin the term ‘dialysis’ for the phenomenon [2]. However, experimental inquisitiveness and industrial translation is a long road to transverse with innumerable challenges to overcome. Two world wars did not serve any good too, but definitely changed the demographic sensitivities as well as did the unthinkable [3]. The wars pushed the human civilizations to look for solutions which challenged the framework of contemporary thought processes. Biomedical engineering to nuclear technology, tremendous advances made in short periods to vanquish the enemy, laid the path for posterity. In this whole journey,mankind witnessed and experienced scarce resources become a plenty and resources, otherwise thought to be inexhaustible became challenged. Water is one such example.

Fast forward to the 1960’s, the revolutionary discovery by Sidney Loeb and S.Souirajan changed the complete scenario with invention of phase inversion technology [4-5]. The feasibility of obtaining drinking water from sea became a reality and mankind took a giant leap to it’s sustenance. Suddenly it seemed that challenges posed by nature could be overcome by technological advances. Soon the dry lands were dryno more and agricul-turebloomed, civilizations prospered and humankind advanced [4].

Similar is the story of biomedical sectors. From the world war II, “Surgeon Hero” era, where collaborative knowledge enhancement between section became restricted, this sector experienced exponential growth [3]. During World War II, the government regulations were minimum with regard to human protection from medical trials. The doctors enjoyed tremendous freedom but on the other hand, were continually pressurized to preserve a resource which ran cant life of a soldier. The doctors had to resort to desperate measures in order to preserve a dying soldier’s life and often took unthinkable risks in order to try various avenues to restore an organ/ organs for a soldier. Thus the term “Surgeon Hero” was coined as they were the indeed the less celebrated heroes of a deadly war. However during these years, a number of solutions were either tried or their seeds were sown to reap benefits later. From dental implants to intralocular lenses to vascular grafts as well as pacemakers- all were either conceived or tried, attributed to the “Surgeon Hero” era [3, 7, 8]. However, the field of membranes also had its foundation laid due to successful trials of an artificial kidney during these years, which laid to the foundation of Hemodialysis. Hemodialysis had an interesting history as during 1913-1944, as a consequence of two wars, the technological development went on simultaneously in the respective nations involved in the conflict [7-11]. However, one was oblivious of the development of other, so much so that the research of John Abel at Jokhns Hopkins was halted as anticoagulant obtained from leeches were not available. Good quality leeches were soured from Hungary which the WW I stopped to be imported to USA, thereby inhibiting development. Fast forward 1970’s, with development of capillary membranes, and Seattle groups “1 m² hypothesis”, membranes for artificial kidney became a lifesaving technology [5].

The two most important fluids in human life- water and blood- in today’s world has some relation or the other with membrane technology. Both the reverse osmosis and hemodialysis technology enjoy the major share of a membrane market. Thus, market driven needs of two most important needs for human survival has led to both maturity of technological development as well as customer segmentation. Now, membranes find application in oxygenation, hemoconcentration, artificial kidney, reverse osmosis for desalination, ultrafiltration for general water treatment, as well as for applications like bioreactor systems [6]. In fact, state of art of membranes are being researched and developed for specialized applications like generating power from salinity gradients. Technologies like Pressure Retarded Osmosis (PRO) is the next challenge where the Gibbs Energy of mixing of rivers and sea water is harvested to run turbines [7]. The membrane market is projected to reach a USD 2.8 billion by 2020 [8]. It is thus a great success story for the human race to be able to conceive, prototype, build and sustain a technology and eventually make it a commercial success. However, the most important aspect to note is that such a scale of application as well as commercial maturity took time. It took almost a century for simple “ideas” to find their way, meandering through a plethora of challenges to reach this stage. For any process or technological development at the laboratory scale, there lies innumerable hindrances towards its successful implementation at the commercial level. For developing proper understanding and related challenges for scaling up, mathematical modeling is a very important tool [9]. It provides quick insights in the parameters like flux, fouling and resistance building in membrane system [10] [11]. Modeling not only provides scaling up insights, but also helps understand the irreversibility’s occurring in modules. Membrane coupon scale results are often misleading when one tries to understand phenomenon like fouling and pressure loses [12]. Flat sheet membrane coupon scale experiments can yield certain results which can either underpredict or overpredict real life scaled up results. This can, more often than not, give rise to false expectations, thereby giving encouragement or discouragement which is false placed. There are generally three broad kinds of mathematical modeling encountered in literature. The first is modeling for transport process which involves first principle based models and simulation of results. This is the oldest approach which membrane engineers have been resorting to. From simple to fairly complicated systems can easily be solved using this approach. From liquid filtration to gas permeation, first principle based modeling approach has proven to be a versatile approach to understand membrane separation. The second type of modeling approach is based on classical thermodynamics. This approach is extremely useful for modeling systems like phase inversion and pore formation in polymer membrane synthesis [13]. Thermodynamics also helps us in understanding the entropy generation and thus related irreversibilities in processes, which in itself an indication on the probable steps which could be taken to mitigate them. Thermodynamic approach also helps us in understanding feasibility of processes and thus gives an idea on how membrane technology intervention can improve efficiencies. The third kind of modeling approach is more recent and has gained popularity over the years due to (i) advent of computers and (ii) robust algorithms to solve non-linear fluid flow equations. This is called Computational Fluid Dynamics (CFD) modeling and is now extensively used in membrane related applications [14] [15]. A schematic representation is shown in Figure 1.1.

CFD is now being implemented in areas like membrane module design, packing efficiency calculations, flow phenomena understanding and various other domains which was previously unexplored. A classic example of mathematical modeling in membrane systems is design of reverse osmosis (RO) modules [16]. While first principle based modeling and calculations were used previously to understand flux and fouling, thermodynamic modeling has been used to understand the minimum energies of desalination [17]. The first principle modeling and thermodynamic modeling gave an idea on the deviation from theoretical limits and ideas started developing on how to actually engineer systems so that minimum energies for desalination can be obtained [18]. CFD modeling of flow in commercial modules and design of modules were implemented to get better hydrodynamic flow patterns evolving better results in minimized fouling and greater fluxes. This coupled with energy recovery devices have significantly improved the energies of separation in desalination applications. Another practical example is design of dialyzers [19]. The artificial kidney or a hemodialyzer is the example of a wonderful engineering design which has elements of first principle modeling coupled with CFD simulations. These have helped industries pack more surface area in a given dialyzer volume without compromising on separation efficiencies. Hemodialyzer design involves a complicated set of components assembled to give rise to an optimum clearance of toxins from blood. The components include space fibers and hollow fibers packed in a particular efficiency such that the dialysate fluid can flow within the filters to wash out the toxins being filtered. Around 10000 to 15000 hollow fine fibers are packed in a dialyzer yielding surface areas of 1.5-2 m² in a cartridge of length 30 cms and diameter of 5-6 cms [20]. CFD modeling has helped immensely in recent years towards achieving this perfection. With the evolution of new membrane technologies, mathematical modeling has a major role to play to make them feasible industrially applicable and economically operable. Thus, membrane based solution or “ideas” which seemingly is infeasible now, can definitely be a solution to several decades into the future. Hence any technological development in this field is of prime importance for our progeny and sustenance of the species.

In this regard, the current book has been designed to focus on the understanding of existing matured technologies, their challenges as well as technologies which have the potential to impact the membrane market in the future. The book starts of with the understanding of thermodynamics of casting solutions which impact the morphology of polymer membranes. The chapter lays the foundation of the underlying mechanism and governing principles which determines the pore formation in phase inversion technology. The next chapter deals with a “state of art” computational fluid dynamic modeling of membrane based desalination technologies. In this, the authors have developed in detail the modeling and simulation related to desalination technologies like Reverse Osmosis, Forward Osmosis, Membrane Distillation and Electrodialysis/Reverse Electrodialysis. Thus a comprehensive understanding of CFD in desalination is dealt with. The next chapter is dedicated on the role of thermodynamics in water-energy nexus, where the authors have dealt with the thermodynamic benchmarks and feasibility of various membrane based technologies which finds application in the “Water-Energy Nexus”. The next chapter deals with one of the most challenging aspects of membranes, i.e., gas separation. The authors have delved in detail the modeling of various gas purification technologies, as well as technologies for CO₂ removal. In continuation the next chapter is on state of art Mixed Matrix membrane based solutions and understanding the mechanism of gas transport and modeling of the same. Traversing from bulk scale modeling to molecular modeling, the next chapter explains molecular dynamics and simulation in relation to study the transport properties of carbon nanotubes based membranes. This is followed by a chapter on modeling of sorption behavior of water-ethylene glycol mixtures in composite membranes. This gives an insight into polymer thermodynamics and application in membrane synthesis and related properties. The next chapter is onapplication of Artificial Intelligence models to understand and predict membrane fouling in waste water treatment technologies.The last chapter is a niched studyon transport modeling in desalination processes involving membranes.

Thus, the book gives a glimpse to the readers on “State of Art” existing matured membrane technologies as well as future direction of membranes. As discussed earlier, the seemingly impossible today can be a life savior tomorrow. Technological innovation, leading to industrial revolution has been the benchmark of human existence. To gainer the positive side of every industrial revolution depends on the thought and sensitivities of the contemporary generation. As John F Kennedy said “A revolution is coming: a revolution which will be peaceful if we are wise enough, compassionate if we care enough, successful if we are fortunate enough-but a revolution is coming whether we like it or not. We can affect it’s character, we cannot alter its inevitability.”