Archive for March, 2010

Theory of porous media

March 9th, 2010 No comments

In the mid-19th century, the theory of porous media were unknown, it was a long vacuum since the development of volume fractions by Woltman in 1794. However, the fundamental discoveries were found by Delesse, Fick and Darcy. Delesse develop the concept of surface fraction in 1848, Fick studied the problem of diffusion through membrane in 1855, and then Darcy in 1856 investigated the permeability of water running through sand as a basic study in multiphase continuum [1].

The Darcy equation actually was derived from the Navier-Stokes equation by assuming stationary, creeping, incompressible flow through porous medium. Since the Darcy’s equation becomes invalid for liquid for high velocity, or gases for very low or very high velocities, the corrections was build by Brinkmann. Brinkman’s filtration equation is usually used to describe the low-Reynolds-number flow in porous media in situations where velocity gradients are non-negligible [2].


  1. R. de Boer, Theory of porous media: Highlights in the historical development and current state, Springer-Verlag, Berlin-Heidelberg, 2000.
  2. F. J. Valdes-Parada, J. A. Ochoa-Tapia, and J. Alavarez-Ramirez, On the effective viscosity for the Darcy-Brinkmann equation, Physica A, 2007, 385, 69-79.
Categories: Mathematics Tags:

Navier-Stokes equations

March 9th, 2010 No comments

The viscous fluids theory is marked by the Navier-Stokes equations, that’s named after Claude-Louis Navier and George Gabriel Stokes, applying Newton’s idea written in his Philosophiae naturalis principia mathematica in which describing the motion of mass point and Euler’s equations in his Mechanica in which formulated the axioms of continuum mechanics, that is: the balance of mass, the balance of momentum, the balance of moment of momentum, and the cut principle. The historical development of Navier-Stokes equations was based on the Newton’s hypothesis that notices that the motion of fluid past other bodies is held back by friction. Navier introduces both types of friction into the equations of motions, for the material points inside as well as on the boundary in his Memoir sur les lois du movement des fluids. This work was continued by Poisson, De Saint-Venant, and finally by Stokes [1].

Stokes briefly explained his theory of fluid motion in various initials and boundary conditions in Transactions of the Cambridge Philosophical Society and Cambridge Mathematical Journal, and describe in On the steady motion of incompressible fluids in 1842. He also wrote about flow in cylindrical coordinate in On the motion of a piston and of the air in a cylinder in 1843 [2]. The development of this equation was built more than 150 years, however a fundamental problem is to decide whether such smooth, physically reasonable solutions exist for the Navier-Stokes equations. It is make the Navier-Stokes equations is one of seven unsolved mathematical problems in this millennium [3].


  1. R. de Boer, Theory of porous media: Highlights in the historical development and current state, Springer-Verlag, Berlin-Heidelberg, 2000.
  2. G. G. Stokes, Mathematical and physical papers, Cambridge University Press, Cambridge, 1880.
  3. K. J. Devlin, The millennium problems: The seven greatest unsolved mathematical puzzles of our time, Basic Books, 2002.
Categories: Mathematics Tags: ,

Inorganic membrane

March 2nd, 2010 No comments

The membrane separation process can be packaged in one of four common integrated arrangements that called membrane modules: plate and frame, spiral wound, hollow fiber, capillary and tubular [1]. Both plate and frame and spiral wound modules, the flat sheet membrane is used. In the case of plate and frame modules, the membrane sheets are simply attached frames which are stacked together in such a fashion that a feed flow channel is formed between the frames. Plate and frame modules suffer from the fact that the packing density, or the amount of membrane area which can be packed into a given volume, is quite low and the manufacturing costs tend to be high. Spiral wound elements neatly address both these problems. In this modules, two membrane sheets are placed back to back separated by a permeate spacer and sealed with glue on three sides. Then, the remaining side is connected to a porous permeate tube which runs through the centre of the completed module. Finally, a feed spacer is placed adjacent to each active membrane surface and the membrane sheet is rolled around the permeate tube to create a cylindrical module. The feed spacers create feed channels by insuring that the rolled up membrane do not contact each other while the permeate spacers provide a spiral path for the permeate to reach the central tube [2].

The other common used membrane module is the tubular membrane. The membrane belonging to this group all have a tubular shape (high ratio of length to diameter). The length is ranging from one to three meter and the diameter of the membrane is ranging from half a millimeter to two centimeter. Tubular membranes with a diameter below than 0.5 mm are called hollow fiber membranes, ones with the diameter ranging from 0.5 to 5 mm are called capillary membranes, while membrane with a diameter larger than 5 mm a called tubular membrane. Tubular membranes are made by casting a membrane onto porous supporting tubes. These supporting tubes are manufactured from fiber glass, ceramics, carbon, porous plastics, stainless steel or paper and must be strong enough to withstand the feed pressures [3].

The advantages of inorganic membranes compares with organic membranes have been recognized i.e.: thermal and pH resistances, generally can withstand organic solvents, chlorine and other corrosive chemicals (see Figure 1.3). Most of inorganic membrane have multi-layered structure and consist of the separating layer and the underlying support layer(s). The available filtration area per unit per volume of support varies from 300 to 2,000 m2/m3. Each layer contains different pore size and porosity. The support, made of alumina, zirconia, titania, silica, spinel, aluminosilicate, cordierite or carbon, typically has a pore diameter of about 1 to 20 mm and a porosity of 30 to 60%. Any additional intermediate support layers have progressively smaller pore size than the underlayer of support. The intermediate support layers are typically 20-60 mm in thickness and 30-40% in porosity. The selective membrane material varies from alumina, zirconia, glass, titania, cordierite, mullite, carbon to such metals as stainless steel, palladium and silver. The overall membrane element shape comes in different types: sheet, single tube, hollow fiber and multi-channel monolith. A monolithic multi-channel honeycomb shape provides more filtration area per unit volume than either a sheet or a single tube [4].


  1. R. Rautenbach and R. Albrecht, Membrane Processes, John Wiley and Sons, Ltd., Chichester, 1989, 459 pp.
  2. J. G. Pharoah, Fluid dynamics and mass transport in rotating channels with application to centrifugal membrane separation, PhD Dissertation, University of Victoria, 2002.
  3. J. Q. J. C. Verbeck, Application of air in membrane filtration, PhD Dissertation, Technische Universiteit Delft, 2005.
  4. H. P. Hsieh, Inorganic membranes for separation and reaction, Membrane Science and Technology Series 3, Elsevier Science B.V., Amsterdam, 1996, 591 pp.
Categories: Membrane Tags:

Basic principle of membrane filtration

March 2nd, 2010 No comments

Filtration is convective discriminating mass transport of liquid mixtures or gaseous dispersions (aerosols) through porous barriers, mass transport ideally being confined to the void space of the barriers. Membrane filtration, accordingly, is pressure driven barrier separation of aqueous solutions, loosely grouped into a number of process variants with reference to the size brackets of the solutes handled:  nanofiltration (NF) 0.01−0.001 μm (<10nm), ultrafiltration (UF) 0.2−0.005 μm (5−200nm) and microfiltration (MF) 10−0.1 μm (>100nm) [1]. The artificial membrane as a barrier differs to a wide variety, like polymer, ceramic, metal and liquid based materials, microporous and dense membrane based structure characteristics, or symmetric and anisotropic refers to the distribution of the pores. Membrane filtration is the surface or screening removal that differs from depth filtration [2]. Filtration operations are performed in one of two modes: tangential flow filtration (TFF) or normal flow filtration (NFF), with the latter commonly called cross-flow filtration and dead-end filtration. Viscous feed suspensions or ones that have high particulate concentrations are typically processed by cross-flow filtration to reduce the accumulation of retained material at the membrane surface, while dead-end filtration tends to be used for more dilute suspensions or smaller batch sizes [3].


  1. K. W. Böddeker, Liquid separations with membranes, an introduction to barrier interference. Spriger-Verlag Berlin Heidelberg, 2008, 146 pp.
  2. M. Cheryan, Ultrafiltration Handbook, Technomic Publishing Company, Inc., Pennsylvania, 1986.
  3. M. A. Chandler, Fouling mechanisms during depth and membrane filtration of yeast cell suspensions, PhD Thesis, The Pennsylvania State University, 2006.
Categories: Membrane Tags:

Jatropha curcas: an overview

March 2nd, 2010 No comments

Consider the food or energy crops priority, it is important to choose the suitable energy crops converting to biofuels. Corn has become the very emblem of plenty, with rich golden cobs of corn overspilling from some of the most effectively farmed arable lands on the earth. Jatropha curcas, on the other hand, is an unprepossessing and indeed toxic plant, better suited to scrubland and hedges. Yet in the world of biofuels, ugly-duckling jatropha has the potential to be, if not a hero, and a harbinger of better things to come [1].

Jatropha curcas L. is a drought-resistant shrub or tree belonging to the genus Euphorbiaceae, which is cultivated in Central and South America, South-east Asia, India and Africa [2]. J. curcas is easy to establish, grows relatively quickly and is hardy, being drought tolerant. It is not browsed, for its leaves and stems are toxic to animals, but after treatment, the seeds or seed cake could be used as an animal feed. J. curcas meals contain high true protein, high energy and low fiber [3]. Various parts of the plant are of medicinal value, its bark contains tannin, the lowers attract bees and thus the plant has a honey production potential; its wood and fruit can be used for numerous purposes including fuel. Of particular importance, the fruit of J. curcas contain viscous oil that can be used for soap making, in the cosmetics industry and as a diesel or kerosene substitute or extender. This latter use may be of importance when examining practical substitutes for fossil fuels to counter greenhouse gas accumulation. Also, like all trees, it fixes atmospheric carbon, stores it in wood and assists in the build up of soil carbon [4].

There are many positive claims on J. curcas, include that the crop: reclaims marginal soil, grows well under saline conditions, is drought tolerant and may have low water use (or high water use efficiency), has low nutrient requirements, is an energy crop, grows seeds with high oil contents, provides high oil yields, provides oil with high quality, requires low labor inputs, does not compete with food production, is tolerant or resistant to pests and diseases. These claims have been proved in traditional and low scale production. However, related to high oil yield production, is not backed up by scientific finding so far, especially in large scale production [5]. J. curcas is still a wild plant which exhibits a lot of variability in yield, oil content and oil quality. Given the booming interest which J. curcas receives nowadays, there is an urgent need for better data to guide investments. Preliminary results on the lifecycle energy balance and global warming potential of biodiesel from J. curcas are favorable, but it is important to note that the GHG balance is tightly linked to the type of land use which is removed and to the intensity of the cultivation [6]. Due to this unproved claims, various ministerial meetings that might have given the national mission on biofuel the seal of approval have been postponed in favour of higher-priority issues. Despite this, several states like India and China have enthusiastically hopped aboard the J. curcas express, providing free plants to small-scale farmers, encouraging private investment in J. curcas plantations and setting up biodiesel processing plants [7].

However, Jatropha biodiesel had comparable fuel properties with those of diesel and conforming to the latest standards for biodiesel (see Table 1.4) [8]. The choice of using J. curcas bio-diesel (i.e. methyl esters) or the J. curcas oil depends on the goal of the use (e.g. electricity or transport) and the available infrastructure. Studies show that transesterified J. curcas oil achieves better results than the use of pure J. curcas oil, straight or in a blend, in unadjusted diesel engines. Changing engine parameters shows considerable improvement of both the performance and the emission of diesel engines operating on neat J. curcas oil. More trials on the use of straight J. curcas oil in different diesel engine setups should be tested and investigated. Accurate measuring and reporting on emissions contributing to global warming, acidification, eutrophification, photochemical oxidant formation and stratospheric ozone depletion is very relevant. The long-term durability of the engines using bio-diesel as fuel requires further study as well [9].

Table 1.4. Fuel properties of jatropha oil, jatropha biodiesel and diesel [8]

Property Unit Jatropha oil Jatropha biodiesel Diesel Biodiesel standards
ASTM D 6751-02 DIN EN 14214
Density at 15 oC kgm-3 940 880 850 860-900
Viscosity at 15 oC mm2s-1 24.5 4.80 2.60 1.9-6.0 3.5-5.0
Flash point oC 225 135 68 > 130 > 120
Pour point oC 4 2 -20
Water content % 1.4 0.025 0.02 < 0.03 < 0.05
Ash content % 0.8 0.012 0.01 < 0.02 < 0.02
Carbon residue % 1.0 0.20 0.17 < 0.30
Acid value mgKOHg-1 28.0 0.40 < 0.80 < 0.50
Calorific value MJ kg-1 38.65 39.23 42


  1. Nature Editorial, Kill king corn, Nature, 2007, 449, 637.
  2. G. M. Gübitz, M. Mittelbach, and M. Trabi, Exploitation of tropical oil seed plant Jatropha curca L., Bioresources Technology, 1999, 67, 73-82.
  3. H. P. S. Makkar, A. O. Aderibigbe, and K. Becker, Comparative evaluation of non-toxic and toxic varieties of Jatropha curcas for chemical composition, digestibility, protein degradability and toxic factors, Food Chemistry, 1998, 62 (2), 207-215.
  4. K. Openshaw, A review of Jatropha curcas: an oil plant of unfulfilled promise, Biomass and Bioenergy, 2000, 19, 1-15.
  5. R. E. E. Jongschaap, W. J. Corre, P. S. Bindraban and W. A. Bradenburg, Claims and facts on Jatropha curcas L.: Global Jatropha curcas evaluation, breeding and propagation programme, Plant Research International B.V., Wageningen, 2007, 44 pp.
  6. W. M. J. Achten, E. Mathijs, L. Verchot, V. P. Singh, R. Aerts, and B. Muys, Jatropha biodisesel fueling sustainability?, Biofuels, Bioprod. Bioref., 2007, 1, 283-291.
  7. D. Fairless, The little shrub that could – maybe, Nature, 2007, 449, 652-655.
  8. A. K. Tiwari, A. Kumar, and H. Raheman, Biodiesel production from jatropha oil (Jatropha curcas) with high free fatty acids: An optimized process, Biomass and Bioenergy, 2007, 31, 569-575.
Categories: Energy Tags: ,

Renewable energy

March 2nd, 2010 No comments

The world community today faces many problems, from economical instability to biodiversity extinction, from governance crisis to natural disasters. Addressing these problems calls out for a huge amount of research to be conducted to rescue human life. Scientists have to work by identifying the problems, developing future scenarios and evaluating management options.

Some researchers and policy makers prioritized several world’s biggest problems especially which ones relatively non-economic and political related problems were the unsafe water and sanitation, rapid global warming, and the limitation of known petroleum reserves. However, air pollution and climate change are major threats to living species health and also political stability. Energy insecurity and increasing prices of conventional energy sources are also greatest tendency to the fragility of politic and economic.

Air pollution and climate change problems are caused primarily by exhaust from solid, liquid, and gas combustion during energy production and use. Then, such problems can be addressed only with large-scale changes to energy sector, include how to secure undisrupted energy demand from world population, especially with the fossil-fuels production which close to peak and that peak will be followed by rapid decline. The proposed fuel and electric power sources were solar photovoltaic (PV), concentrated solar power (CSP), wind turbines, geothermal power plants, hydroelectric power plants, wave devices, tidal turbines, nuclear power plants, coal power plants fitted with carbon capture and storage (CCS) technology, and ethanol/gasoline and biodiesel as biofuels [1]. Other options like algae, butanol, hydrogen combustion, and solar hot water heaters.

The prospects for biofuels have improved tremendously over the last 2 years driven foremost by concerns for energy security and climate change and the high oil prices in combination with decreasing production costs. Global biofuel production has increased by 70% over the last 2 years reaching 1.1 mmbls/d in 2007, accounting for 1.3% of global liquids supply. The USA, Brazil and Europe account for the bulk of global biofuel production. While ethanol is the dominating biofuel product in Brazil and the USA, biodiesel is the main product within Europe accounting for more than 80% of total biofuel production [2].


  1. M. Z. Jacobson, Review of solutions to global warming, air pollution, and energy security, Energy Environ. Sci., 2009, 2, 148-173.
  2. J. Kjarstad and F. Johnsson, Resources and future supply of oil, Energy Policy, 2009, 37, 441–464.
Categories: Energy Tags: