Laplace-transform-based method to calculate back-reflected radiance from an isotropically scattering half-space

We present a method to determine the back-reflected radiance from an isotropically scattering half-space with matched boundary. This method has the advantage that it leads very quickly to the relevant equations, the numerical solution of which is also quite easy. Essentially, the method is derived from a mathematical criterion that effectively forbids the existence of solutions to the transport equation which grow exponentially as one moves away from the surface and deeper into the medium. Preliminary calculations for infinitely wide beams yield results which agree very well with what is found in the literature.

Calculation of the radiance distribution at the boundary of an isotropically scattering slab

The radiance arising from an anisotropically scattering illuminated stack of n slabs is calculated using the equation of radiative transfer. It appears to be unnecessary to calculate the radiance inside the material; including only the radiance at the boundary surfaces is sufficient to obtain the desired result. The novel method used for the solution of this problem leads immediately in a straightforward and systematic way to the known appropriate basic equations valid for the problem at hand, otherwise derived by ad hoc methods. A new simple set of linear equations for the radiance at the boundary surfaces is derived. This method applies equally well to similar problems with other geometries. Apart from this analytical derivation, this paper presents the results of the numerical solution of the set of equations that we obtained from the equation of radiative transfer, for n = 1. The results of the numerical calculations are compared with what is found in the literature and are found to give very good agreement.

Anaerobic treatment of wastewater with high concentrations of lipids or sulfate

This thesis describes research on the application of granular sludge bed upflow reactors for anaerobic treatment of wastewaters contaminated with lipids and sulfate, two contaminants that have so far seriously hampered the application of anaerobic treatment in several branches of industry. The Upflow Anaerobic Sludge Bed reactor is the most popular anaerobic treatment system at this moment. However, it is mainly applied to wastewaters with readily biodegradable dissolved contaminants, and hardly to more complex wastewaters.Two problems can occur in anaerobic treatment of lipid containing wastewater, viz. (1) inhibition of anaerobic bacteria by long chain fatty acids, and (2) flotation of the biomass. Sulfate may cause direct and indirect inhibition of methanogenic and acetogenic bacteria.The first part of the thesis deals with the inhibitory effect of long chain fatty acids (LCFA) in anaerobic digestion. Inhibition can occur after overloading, i.e. during the start-up period of the digester, or as a result of a shock load. LCFA affect especially the acetotrophic methanogens, above a critical threshold concentration they exert a bactericidal effect. The methanogens do not adapt to LCFA. The threshold concentration for capric acid - one of the most toxic saturated acids - is approximately 1 kg/m 3. The precise value of the threshold concentration depends upon the mass transfer characteristics of the anaerobic reactor, and upon the particle size and specific activity of the biomass aggregates. Furthermore, the presence of phospholipids may enhance the inhibitory effect of LCFA. Inhibition can be prevented by addition of soluble calcium salts to the wastewater. However, the addition of calcium cannot eliminate the second deleterious effect of a shock load of LCFA, viz. flotation and subsequent wash-out of biomass aggregates.The second part of this thesis describes the anaerobic treatment of solutions of LCFA and emulsions of triglycerides in the Expanded Granular Sludge Bed reactor. With LCFA solutions this modified upflow reactor can achieve a mineralization efficiency of at least 85-90% at space loading rates of ca. 30 kg COD/m 3.day. Modification of the sludge separation system is required to reduce sludge wash-out during treatment of triglyceride emulsions. A novel sieve-drum separator was developed, which allows stable operation. Although the treatment capacity is significantly lower with triglyceride emulsions than with LCFA solutions, the EGSB reactor with sieve-drum separator can accommodate higher organic and hydraulic loading rates than previously described anaerobic filter reactors. Upscaling of the EGSB system and flotation of lipids require further research.The third part of the thesis deals with the inhibitory effect of sulfide and sodium sulfate. From pH 6.4 to 7.2 approximately 250 mg H 2 S per litre causes a 50% decrease of the maximum specific activity of acetotrophic methanogens. The inhibitory effect of a given H 2 S concentration increases significantly when the pH approaches 8. Consequently, an increase of the pH level in the anaerobic digester above ca. 7.2 is not beneficial. Immobilization in biomass aggregates or films may provide protection against H 2 S inhibition. Propionate degradation may be the rate limiting step during treatment of sulfate containing wastewater, because it is affected more severely by sulfide than acetotrophic methanogenesis. At extremely high sulfate concentrations, also inhibition by cations has to be considered. At neutral pH levels, sodium concentrations up to 5 g/l cause no inhibition of acetotrophic methanogens. A sodium concentration of 10 g/l causes a 50% decrease of the maximum specific acetotrophic methanogenic activity, 14 g/l causes complete inhibition. Acetotrophic methanogens do not adapt to high sodium concentrations

Training mathematical skills for physics by means of a web-based tool

This article describes the use of a web-based course to enhance the learning of mathematical concepts and skills in a university Physics course. Both the coupling of a symbolic language (Maple) and adequate feedback enable to simulate in a computer program the way students should perform. The learning effect which is aimed for is to improve both concepts and skills. Moreover, this tool helps to correct possible misunderstandings or misconceptions. Web-based training was offered in an electromagnetism course. The training consists of several exercises which focus on applying complex mathematical skills in the field of electromagnetism, one at a time

Waste lipids to energy: how to optimize methane production from long-chain fatty acids (LCFA)

The position of high-rate anaerobic technology (HR-AnWT) in the wastewater treatment and bioenergy market can be enhanced if the range of suitable substrates is expanded. Analyzing existing technologies, applications and problems, it is clear that, until now, wastewaters with high lipids content are not effectively treated by HR-AnWT. Nevertheless, waste lipids are ideal potential substrates for biogas production, since theoretically more methane can be produced, when compared with proteins or carbohydrates. In this minireview, the classical problems of lipids methanization in anaerobic processes are discussed and new concepts to enhance lipids degradation are presented. Reactors operation, feeding strategies and prospects of technological developments for wastewater treatment are discussed. Long-chain fatty acids (LCFA) degradation is accomplished by syntrophic communities of anaerobic bacteria and methanogenic archaea. For optimal performance these syntrophic communities need to be clustered in compact aggregates, which is often difficult to achieve with wastewaters that contain fats and lipids. Driving the methane production from lipids/LCFA at industrial scale without risk of overloading and inhibition is still a challenge that has the potential for filling a gap in the existing processes and technologies for biological methane production associated to waste and wastewater treatment.Fundação para a Ciência e a Tecnologia (FCT) - project FAT-METHANE (POCTI/CTA/46328/2002), grants PRAXIS XXI/BD/20326/99, SFRH/BPD/14591/2003, SFRH/BD/24256/2005Instituto Nacional da Propriedade Industrial (INPI)Netherlands Science FoundationLettinga Associates Foundatio

Anaerobic biodegradation of oleic and palmitic acids : evidence of mass transfer limitations caused by long chain fatty acid accumulation onto the anaerobic sludge

Palmitic acid was the main long chain fatty acids (LCFA) that accumulated onto the anaerobic sludge when oleic acid was fed to an EGSB reactor. The conversion between oleic and palmitic acid was linked to the biological activity. When palmitic acid was fed to an EGSB reactor it represented also the main LCFA that accumulated onto the sludge. The way of palmitic acid accumulation was different in the oleic and in the palmitic acid fed reactors.Whenoleic acid was fed, the biomass-associated LCFA (83% as palmitic acid) were mainly adsorbed and entrapped in the sludge that became ‘‘encapsulated’’ by an LCFA layer. However, when palmitic acid was fed, the biomass-associated LCFA (the totality as palmitic acid) was mainly precipitated in white spots like precipitates in between the sludge, which remained ‘‘non-encapsulated.’’ The two sludges were compared in terms of the specific methanogenic activity (SMA) in the presence of acetate, propionate, butyrate, and H2CO2, before and after the mineralization of similar amounts of biomassassociated LCFA (4.6 and 5.2 g COD-LCFA/g of volatile suspended solids (VSS), for the oleic and palmitic acid fed sludge, respectively). The ‘‘non-encapsulated,’’ sludge exhibited a considerable initial methanogenic activity on all the tested substrates, with the single exception of butyrate. However, with the ‘‘encapsulated’’ sludge only methane production from ethanol andH2/CO2 was detected, after a lag phase of about 50 h. After mineralization of the biomass-associated LCFA, both sludges exhibited activities of similar order of magnitude in the presence of the same individual substrates and significantly higher than before. The results evidenced that LCFA accumulation onto the sludge can create a physical barrier and hinder the transfer of substrates and products, inducing a delay on the initial methane production. Whatever the mechanism, metabolic or physical, that is behind this inhibition, it is reversible, being eliminated after the depletion of the biomass-associated LCFA.Fundação para a Ciência e Tecnologia (FCT) Fundo Social Europeu (FSE

Microbial and operational response of an anaerobic fixed bed digester to oleic acid overloads

The effect of oleic acid overloads on biomass accumulation and activity in an anaerobic filter was investigated. An anaerobic fixed-bed reactor specially designed to allow the regular withdrawal of accumulated biomass was used for that purpose. Organic and hydraulic shocks were performed during four days, by stepwise increasing the substrate concentration from 4000 to 20 000 mg COD/l or by reducing the hydraulic retention time from 16 to 3.2 h. During the organic shock, operational performance was more affected than in the hydraulic one, which was the result of the higher degree of inhibition detected in the acetoclastic, hydrogenophilic and syntrophic activities. The ratio adhered/total biomass remained between 17 and 32% during the hydraulic shock, and between 13 and 60% during the organic shock, suggesting a more stable biofilm during the hydraulic shock. A long time (900 h) after the hydraulic shock, hydrogenophilic and syntrophic activities recovered to higher values than before the shock, but after the organic shock only acetoclastic activity recovered pre-shock values. Hydraulic shock induced an increase in tolerance to oleic acid toxicity, evidenced by an increase in the toxicity limit (IC50) from 140+/-30 to 215+/-25 mg/l.Fundação de Ciência e Tecnologia

Effect of sulfate on methanogenic communities that degrade unsaturated and saturated long-chain fatty acids (LCFA)

Anaerobic bacteria involved in the degradation of long-chain fatty acids (LCFA), in the presence of sulfate as electron acceptor, were studied by combined cultivation-dependent and molecular techniques. The bacterial diversity in four mesophilic sulfate-reducing enrichment cultures, growing on oleate (C18:1, unsaturated LCFA) or palmitate (C16:0, saturated LCFA), was studied by denaturing gradient gel electrophoresis (DGGE) profiling of polymerase chain reaction (PCR)-amplified 16S rRNA gene fragments. These enrichment cultures were started using methanogenic inocula in order to assess the competition between methanogenic communities and sulfate-reducing bacteria. Phylogenetic affiliation of rRNA gene sequences corresponding to predominant DGGE bands demonstrated that members of the Syntrophomonadaceae, together with sulfate reducers mainly belonging to the Desulfovibrionales and Syntrophobacteraceae groups, were present in the sulfate-reducing enrichment cultures. Subculturing of LCFA-degrading methanogenic cultures in the presence of sulfate resulted in the inhibition of methanogenesis and, after several transfers, archaea could no longer be detected by real-time PCR. Competition for hydrogen and acetate was therefore won by sulfate reducers, but acetogenic syntrophic bacteria were the only known LCFA-degrading organisms present after subculturing with sulfate. Principal component analysis of the DGGE profiles from methanogenic and sulfate-reducing oleate- and palmitate-enrichment cultures showed a greater influence of the substrate than the presence or absence of sulfate, indicating that the bacterial communities degrading LCFA in the absence/presence of sulfate are rather stable.This work was possible through grants attributed to D. Z. Sousa by Fundacao para a Ciencia e Tecnologia (FCT) and Fundo Social Europeu (FSE) (SFRH/BD/8726/2002), and by the Wageningen Institute for Environmental and Climate Research (WIMEK)

Modeling lipid accumulation in oleaginous fungi in chemostat cultures. II: Validation of the chemostat model using yeast culture data from literature

A model that predicts cell growth, lipid accumulation and substrate consumption of oleaginous fungi in chemostat cultures (Meeuwse et al. in Bioproc Biosyst Eng. doi:10.1007/s00449-011-0545-8, 2011) was validated using 12 published data sets for chemostat cultures of oleaginous yeasts and one published data set for a poly-hydroxyalkanoate accumulating bacterial species. The model could describe all data sets well with only minor modifications that do not affect the key assumptions, i.e. (1) oleaginous yeasts and fungi give the highest priority to C-source utilization for maintenance, second priority to growth and third priority to lipid accumulation, and (2) oleaginous yeasts and fungi have a growth rate independent maximum specific lipid production rate. The analysis of all data showed that the maximum specific lipid production rate is in most cases very close to the specific production rate of membrane and other functional lipids for cells growing at their maximum specific growth rate. The limiting factor suggested by Ykema et al. (in Biotechnol Bioeng 34:1268–1276, 1989), i.e. the maximum glucose uptake rate, did not give good predictions of the maximum lipid production rate