Normal-hemispherical Transmittance Research Articles

Rigorous Accounting for Dependent Scattering in Thick and Concentrated Nanoemulsions.

Concentrated and thick oil-in-water nanoemulsions have been observed to become more transparent with increasing oil volume fraction. This study demonstrates rigorously experimentally and numerically that such unusual behavior is due to dependent scattering including not only far-field but also near-field effects. Indeed, when the droplet concentration is sufficiently large, their interparticle distance becomes small compared to the wavelength of light and scattering by a given droplet may be affected by the proximity of others. This situation is referred to as dependent scattering. Light transfer through nanoemulsions and other colloids has previously been modeled by solving the radiative transfer equation accounting for dependent scattering using the static structure factor based on far-field approximations. Here, oil-in-water nanoemulsions were prepared with oil volume fraction ranging between 1 and 20% and a peak droplet radius of 16 nm. The spectral normal-hemispherical transmittance of the different nanoemulsions in 10 mm thick cuvettes was measured experimentally between 400 and 900 nm. Numerical predictions for nonoverlapping randomly distributed nanoscale oil droplets in water and accounting for dependent scattering including near-field effects-using the recently developed radiative transfer with reciprocal transactions (R2T2) method-were in excellent agreement with experimental measurements. Simulations revealed that assuming independent scattering underestimated the normal-hemispherical transmittance even for a relatively small oil volume fraction. Additionally, simulations using the dense medium radiative transfer (DMRT) and static structure factor predicted that dependent scattering prevailed for oil volume fractions slightly greater than those predicted by the R2T2 method. Interestingly, the DMRT method predicted large increases in transmittance when the oil droplet size and volume fraction were larger than 10 nm and 10%, respectively. Finally, simulations also revealed that dependent scattering enables the design of oil-in-water nanoemulsions to backscatter or absorb light by tuning the oil droplet size and volume fraction. The results validate that the R2T2 method could be used to characterize nanoemulsions or to investigate their formation, composition, and stability for drug delivery, food, and cosmetics applications. Future studies could extend the use of the R2T2 method to colloidal suspensions with particles of arbitrary shapes and to radiation transfer of polarized light in turbid media.

Dependent Scattering in Thick and Concentrated Colloidal Suspensions

This study demonstrates numerically and experimentally that dependent scattering occurs in colloidal suspensions and can, counterintuitively, cause their transmittance to increase with increasing particle volume fraction. Radiation transfer through colloidal suspensions has been modeled with the radiative transfer equation (RTE) assuming independent scattering. Then, the effective absorption and scattering coefficients of the disperse medium are predicted as the sum of the cross sections of all particles divided by the volume of suspension. However, this approach is not valid when the average interparticle distance is on the same order of magnitude as the wavelength, corresponding to large particle concentrations. The latter situation is referred to as dependent scattering. Rigorously accounting for dependent scattering requires solving Maxwell’s equations, but is limited to relatively thin suspensions. Here, we extend the Radiative Transfer with Reciprocal Transactions (R2T2) method to predict the normal-hemispherical transmittance of thick and concentrated plane-parallel slabs of nonabsorbing nanoparticle suspensions and to rigorously account for dependent scattering effects. The radiation characteristics of a large number of particle ensembles were estimated using the superposition T-matrix method and the RTE was solved using Monte Carlo method combined with strategies for sampling the previously computed radiation characteristics. A wide range of particle size parameter, volume fraction, and optical properties as well as colloidal suspension thickness were investigated. Dependent scattering effects were found to prevail for particle volume fractions as low as 1% depending on the particle size and refractive index. Evidences of dependent scattering were also observed experimentally in the visible normal-hemispherical transmittance of 10 mm thick colloidal suspensions of silica nanoparticles with diameter between 16 and 30 nm and particle volume fraction ranging from 2% to 15%. Moreover, good agreement was found between experimental measurements and numerical predictions from the R2T2 method. By contrast, assuming independent scattering underestimated systematically the normal-hemispherical transmittance, especially for large particle volume fraction. As such, this paper presents, for the first time, experimental validation of the R2T2 method and its ability to account for dependent scattering.

Temperature-controlled spectrophotometry: a simultaneous analysis of phase transition, thermal degradation and optical properties of semi-transparent composites from 20 °C to 450 °C.

So far, optical and effective radiative properties of polymer matrix based composites were investigated at temperatures well below their degradation temperature. At the same time, polymers exhibit temperature dependent physical properties and may undergo structural changes as their temperature raises. In this work, we employ the "Temperature-Controlled Spectrophotometry", a new method enabling to identify simultaneously phase transitions, thermal degradation and radiative properties of semi-transparent composites over a large temperature range. The method consists of measuring simultaneously the normal-normal and the normal-hemispherical transmittances and reflectances of the sample subjected to a laser irradiation with tuneable wavelength while the temperature is rised from room temperature up to 450 °C by means of a CO2 laser. Physical changes of the sample are identified from the temperature variation of normal-normal transmittance and specular reflectance measurements. Most of the results here are presented at a specific wavelength of 1070 nm but the proposed method is suitable over the semi-transparency spectral domain of the material by changing the wavelength of the probe laser. An inverse method for parameter identification based on normal-hemispherical measurements is employed to determine the transport effective radiative properties of the sample, namely the transport extinction coefficient and the transport scattering albedo from room temperature to 325 °C.

Droplet effect on the infrared transmittance of radiative cooler for direct water condensation

Accessibility to freshwater has become a global issue and many approaches have been developed to tackle this question. One promising way is using radiative coolers to condense dew from the air. This study aims to quantify systematically the effects of droplet diameters, spacial distribution, projected surface coverage ratio, and surface wettabilities on the normal-hemispherical transmittance and cooling performance. The Monte Carlo ray tracing method is employed to simulate the infrared light transfer through the droplets. For the first time, the normal-hemispherical transmittance and cooling performance of radiative cooler with different droplet contact angles were investigated theoretically. The weighted transmittance is found to be independent of droplet spacial distribution, but dependent on droplet (i)diameter, (ii)projected surface coverage ratio, and (iii)contact angle. Results show that the water condensed on the emitting surface can improve the cooling power. A super-hydrophilic PDMS film with a 90% projected surface coverage ratio can reach a cooling power of 109.3 W m−2. In the process of water condensation, a cooling power loss of up to 23.4 W m−2 will appear due to surface wettability, so super-hydrophilic surfaces are preferred. These results provide guidance on surface wettability preference for better performance of radiative cooler for direct water condensation.

All-day effective radiative cooling by optically selective and thermally insulating mesoporous materials

Due to serious solar absorption and poor thermal insulation on the cold side, current daytime radiative cooling falls far short of the theoretical potential. The mesoporous film can be used for both thermal insulation and optical selection. In this study, the radiative properties of infrared transparent mesoporous materials are investigated. The Diffusion Limited Cluster Aggregation algorithm is employed to reproduce the micro-structures of the mesoporous materials. The structure-dependent normal hemispherical transmittance is predicted by the combination of discrete dipole approximation and Monte Carlo method. The effects of material type and structure characteristics (particle size, volume fraction and cover thickness) on the infrared transmittance and all-day radiative cooling performance are quantified. The results show that the polyethylene (PE) aerogel achieves the best thermal insulation performance and good spectral selectivity. It can work as a thermally insulating barrier and an infrared transparent window for the radiative cooling surface. By integrating with PE aerogel, the radiative cooling surface can enable the passive cooling up to 13 K below the ambient temperature during the day and 15 K below the ambient temperature during the night at a wind speed of 2.8 m/s. This work provides an optimal design of optically selective and thermally insulating mesoporous materials in passive all-day radiative cooling applications.

Behind electrochromic glazing: Assessing user's perception of glare from the sun in a controlled environment

The adaptable transmittance of electrochromic glazing allows to control the solar radiation entering buildings, yet the level of transmittance needed to protect from glare is still an unanswered question. To bridge this gap, this study evaluates the level of visible light transmittance (τv) required for blue-tinted low transmittance glazing to prevent discomfort glare when the sun is visible through the glazing. Twenty participants were exposed to four visual scenarios with varying viewing directions and window transmittance. Results indicate that when the sun is close to the central field of view, a normal-hemispherical transmittance, τv, n-h of 0.6% prevents disturbing glare for most users but does not provide a comfortable situation (this condition corresponds to a “seen” sun disc’s luminance of 4.8 M cd/m2). To achieve comfortable situations, a τv, n-h of 0.14% was found suitable. For non-critical viewing directions, τv n-h of 0.6% is sufficient to achieve visually comfortable space for most participants. This study also examined the reliability of five discomfort glare metrics by comparing their objective output to subjective responses for the tested conditions. The contrast-based metrics (Daylight Glare Probability, CIE Glare Index, Unified Glare Probability, Daylight Glare Index) possess a valid positional sensitivity and show higher Spearman’s rank correlations (ρ – 0.56–0.59) compared to solely saturation-based metrics as the vertical illuminance (Ev) (ρ – 0.44).

Transmittance of transparent horizontal and tilted windows supporting large non-absorbing pendant droplets

This study establishes that the deviation of large pendant droplets from an ideal cap-shape due to gravity can have significant and complex impacts on the normal-hemispherical and directional-hemispherical transmittances of light through horizontal and tilted transparent windows. First, the shape of pendant droplets larger than the capillary length was predicted numerically by balancing gravitational and surface tension forces for various droplet volumes, contact angles, and window tilt angles. Then, light transfer through windows supporting such numerically generated droplets was simulated using the Monte Carlo ray-tracing method. The window transmittance for large droplets was found to be nearly independent of droplet spatial arrangement and size distribution for relatively narrow size distributions. Furthermore, the droplets could be assumed to be cap-shaped in predicting the normal-hemispherical transmittance for droplet volumes V< 10 µL and contact angles θc<θcr where θcr is the critical angle for total internal reflection at the droplet/air interface. However, for larger droplets and/or contact angles, assuming droplets to be cap-shaped caused the transmittance to be overestimated by as much as 37% for horizontal windows. This was due to gravity-induced deformation of the droplet shape resulting in increased reflection at the droplet/air interface. For tilted windows, the droplet deformation caused the normal-hemispherical transmittance to increase with increasing droplet volume and window tilt angle. For both horizontal and tilted windows, transmittance decreased linearly with increasing droplet surface area coverage. These results and numerical tools can be used to design energy efficient solar stills, greenhouses, and covered photobioreactors, for example.

An approach to determine radiative properties of solid struts of open-cell foams by pore scale identification from macro scale measurements

Open-cell foams consisting of interconnected struts are widely used in thermal applications such as volumetric solar receivers. The thermal performance of foams strongly relies on their radiative behaviors which intrinsically depends on the radiative properties of struts. This study proposed a feasible approach to determine the radiative properties of solid struts by a pore scale identification from a macro scale measurement. First, the normal-hemispherical transmittance and reflectance spectra of two nickel foams were measured by an experimental system. Second, a pore scale forward calculation was conducted by a combination of Monte Carlo Ray-tracing method and real foam structures obtained from micro-computed tomography technique. Last, an Adaptive Particle Swarm Optimization algorithm was adopted to retrieve the spectral reflectivity and specularity of nickel struts from the measured spectra. The results show that it is unreasonable to assume the reflection behavior of strut surface simply as either specular or diffused, and also, it is unreliable to assign the reflectivity of strut surface directly by Fresnel's law. Within the investigated wavebands 0.4–2.2 μm, the average reflectivity of nickel struts is 12% lower than that of a nickel mirror. The proportion of specular reflection at nickel strut surface is between 37%–52%, almost increasing with wavelengths.

A modified inverse method for determining spectral radiative properties of participating medium from normal-hemispherical transmittance and reflectance

This paper presents a modified inverse method for retrieving the spectral absorption and transport scattering coefficients of participating medium, the method combines (i) several analytical expressions obtained from the modified two-flux (TF) approximation, (ii) the Monte Carlo (MC) method for predicting normal-hemispherical transmittance Tnh and reflectance Rnh generally obtained from experiments, as well as (iii) an optimization method employing the genetic algorithm (GA). Three types of typical participating medium, the green glass, the low-iron glass, and the silica aerogel with known radiative properties taken form the literatures, were used to illustrate the accuracy and robustness of the modified method by retrieving the input properties from the inverse identification in which the Tnh and Rnh ‘experimental data’ were obtained from the MC predictions. The results show that the modified inverse method was able to retrieve accurately the absorption and transport scattering coefficients of participating medium.

Pore scale simulation of spectral radiative properties of Voronoi open-cell carbon foams at high temperatures

A pore scale model was established to investigate the high-temperature radiative properties of carbon foams with high porosity. Voronoi Tessellation for the random structure of carbon foams and Monte Carlo ray-tracing method was employed to simulate the apparent radiative behaviors and volumetric radiative properties. By compared with the measured data at room temperature in Ref. (Celzard et al., 2012), the numerical model was verified to possess a high precision, which the maximum deviation are 1.8% for normal absorptance, 0.3% for normal-hemispherical transmittance and 1.5% for normal-hemispherical reflectance, respectively. It is also acceptable for the simulated results of volumetric radiative properties. Based on the spectral radiative properties of carbon basic material found in Ref. (Touloukian and DeWitt, 1972), the spectral radiative properties of carbon foam sheets at high temperature between 1183 K and 2073 K were predicted. It was found that absorptance is dominant in the apparent radiative behaviors of carbon foams at high temperatures with a wavelength of 0.665 μm. Then, the bidirectional reflectance distribution function was numerically investigated. The results showed a backward scattering of the reflected energy at the foam sheet surface and reflected energy peaks are always located at around respective incident angles. For volumetric radiative properties at high temperatures, extinction coefficient ranged between 200 m−1 and 450 m−1, which had been verified with relation formula in an error of less than 1%. In addition, scattering albedo and scattering phase function were not only simulated but also compared with the empirical formulas, to some extent, agreed well with them.

A development to determine spectral radiative properties of semitransparent struts of open-cell ceramic foams: From macro-scale measurement to pore-scale simulation

The radiative properties of a ceramic strut cannot be strictly the same as that of a dense sintered ceramic bulk composed of the same material. This contribution develops an approach to determine the radiative properties of semitransparent ceramic struts of open-cell foams. First, a macro-scale measurement was conducted to obtain the normal-hemispherical transmittance and reflectance spectra of alumina foam slices. Second, a pore-scale forward model was established to predict the radiative behaviors of 3D digital porous structures obtained from micro-computed tomography technique. Last, an identification method was proposed to retrieve the radiative properties of semitransparent ceramic struts from the measured data. The results indicate that it is unreasonable to simply assume the radiative properties of alumina struts as that of corresponding dense bulks. Within the investigated wavebands 0.4–2.2 μm, the average extinction coefficient of alumina struts is 33.5% lower than that of dense bulks. The scattering albedo shows a slight difference between alumina struts and dense bulks. Besides, the retrieved extinction coefficients and scattering albedos of alumina struts are proposed as a function of wavelengths, which can be used in potential applications.

Light transfer through semi-transparent glass panes supporting pendant droplets

This paper quantifies experimentally the effect of pendant droplets condensed on the back of semi-transparent glass panes on their normal-hemispherical transmittance and reflectance in the visible and near-infrared. To enable sample characterization and ensure repeatability, acrylic droplets were deposited on the back side of 3 mm-thick soda-lime silicate glass slabs with or without hydrophobic surface treatment including perfluorinated silane, perfluorinated silane-coated silica nanoparticle monolayer, or Teflon coatings. The droplet contact angle θc was varied between 26° and 76° and the projected surface area coverage reached up to 60%. For contact angle θc smaller than the critical angle θcr for total internal reflection at the droplet/air interface, the presence of droplets did not significantly affect the normal-hemispherical transmittance and reflectance. However, for droplet contact angle θcr ≤ θc < 90°, the normal-hemispherical transmittance decreased significantly with increasing droplet contact angle and/or surface area coverage while the normal-hemispherical reflectance increased. The measurements of the normal-hemispherical transmittance were in excellent agreement with numerical predictions obtained from Monte Carlo Ray Tracing method. These results further validate our previous numerical simulations and the different optical regimes identified. The results of this study can provide guidelines for the design and operation of energy efficient flat-plate solar collectors, outdoor photobioreactors, greenhouses, solar desalination systems, and other solar energy conversion systems.

Thermally-induced structural changes and optical properties degradation of fiber-loaded aerogel composites under thermal exposures

Fiber-loaded aerogel composites possess remarkable physical and chemical properties, making them extensively used in a variety of science and technology fields. Structural changes were usually taken place inside the aerogel composites under an elevated thermal environment. However, scarce research can be found on the resulted optical properties degradation provoked by thermal exposures, possibly due to technical limitations in the characterization method of aerogel composites. With this motivation, the thermally-induced microstructural changes in fiber-loaded aerogel composites were firstly characterized and discussed in this work by in-situ characterization techniques. For comparison of optical properties of samples under various levels of thermal exposures, an inverse measurement method was developed to characterize intrinsic optical properties of samples based on the measured and predicted normal-hemispherical transmittance and reflectance spectra. The intrinsic optical properties evolution was then correlated with the microstructural developments caused by high-temperature annealings for the samples. The provided information is indispensable for promoting fundamental insights on the underlying physical mechanisms of aerogel composites and provide guidelines for further design and optimization under thermal environments.

Experimental study of the radiative properties of hedgehog-like ZnO–Au composite particles

The hedgehog-like ZnO particles (HPs) and ZnO–Au composite particles (HP-Au) show great potential in the application of photocatalysis, due to their special nanostructure and unusual dispersion behavior in fluids. To improve the efficiency of photocatalysis, one needs to analyze and optimize the radiative transfer of nanofluids containing HPs and HP-Au. Therefore, knowledge of the radiative properties of HPs and HP-Au is of great significance. In this work, the radiative properties of HPs and HP-Au are experimentally measured in the visible spectral range, and the effect of the deposited Au nanoparticles on the radiative properties of HP-Au is investigated. The extinction cross section is obtained from the normal-normal transmittance of particle water suspensions by the improved transmission method. The absorption cross section and the asymmetry parameter are retrieved from the measured normal-hemispherical transmittance and reflectance. It is found that the extinction cross sections of HPs and HP-Au range from 9 to 11 µm2, and peak at the wavelengths of about 380 and 650 nm due to the strong scattering ability of the particles. The deposited Au nanoparticles decrease the extinction cross section of HP-Au notably in the spectral range from 500 to 800 nm. The absorption cross section of HP-Au is enhanced by Au nanoparticles, which can be more than two times that of HPs. The absorption cross section of HP-Au peaks at the wavelength of about 520 nm due to the localized plasmon resonance of Au nanoparticles, which can reach 2.2 µm2. The asymmetry parameters of both HPs and HP-Au increase rapidly with increasing wavelength in the spectral range from 400 to 600 nm, but for wavelength larger than 600 nm their asymmetry parameters are round 0.9 and show very small spectral variation. The deposited Au nanoparticles, however, tend to decrease the asymmetry parameter of HP-Au.

Light transfer through windows with external condensation

This study investigates systematically light transfer through windows supporting cap-shaped droplets on their external face. The presence of such droplets may have negative effects on the conversion efficiency of solar cells, distorts image quality of lenses, or hinders visibility through windows and windshields. Here, the directional-hemispherical transmittance was predicted by the Monte Carlo ray-tracing method. The droplets were monodisperse or polydisperse randomly distributed on the outside face of optically smooth windows. For nonabsorbing droplets, the diameter and size distribution did not have a significant effect on the window directional-hemispherical transmittance. The latter was nearly independent of contact angle for incident angle θi ≤ 30°. However, the directional-hemispherical transmittance decreased monotonously with increasing incident angle and droplet contact angle for contact angle θc ≤ 70° to reach a minimum at a contact angle θc,min beyond which it increased with increasing contact angle before reaching a plateau at large contact angles. This was attributed to total internal reflection at the back window/air and droplet/air interfaces. For absorbing droplets, the normal-hemispherical transmittance decreased significantly with increasing droplet contact angle, mean diameter, polydispersity, and projected surface area coverage due to strong absorption within the droplets. Moreover, the normal-hemispherical transmittance decreased with increasing contact angle for θc < 90° and remained constant and independent of the droplets’ absorption index, mean diameter, and contact angle for θc ≥ 90°. Finally, Analytical expressions for the upper and lower bounds of the normal-hemispherical transmittance as a function of droplet contact angle, optical properties, and projected surface area coverage were derived.

Transmittance of semitransparent windows with absorbing cap-shaped droplets condensed on their backside

This study aims to investigate systematically light transfer through semitransparent windows with absorbing cap-shaped droplets condensed on their backside as encountered in greenhouses, solar desalination plants, photobioreactors and covered raceway ponds. The Monte Carlo ray-tracing method was used to predict the normal-hemispherical transmittance, reflectance, and normal absorptance accounting for reflection and refraction at the air/droplet, droplet/window, and window/air interfaces and absorption in both the droplets and the window. The droplets were monodisperse or polydisperse and arranged either in an ordered hexagonal pattern or randomly distributed on the backside with droplet contact angle θc ranging between 0 and 180° The normal-hemispherical transmittance was found to be independent of the spatial distribution of droplets. However, it decreased with increasing droplet diameter and polydispersity. The normal-hemispherical transmittance featured four distinct optical regimes for semitransparent window supporting nonabsorbing droplets. These optical regimes were defined based on contact angle and critical angle for internal reflection at the droplet/air interface. However, for strongly absorbing droplets, the normal-hemispherical transmittance (i) decreased monotonously with increasing contact angle for θc< 90° and (ii) remained constant and independent of droplet absorption index kd, droplet mean diameter dm, and contact angle θc for θc≥ 90° Analytical expressions for the normal-hemispherical transmittance were provided in the asymptotic cases when (1) the window was absorbing but the droplets were nonabsorbing with any contact angles θc, and (2) the droplets were strongly absorbing with contact angle θc> 90° Finally, the spectral normal-hemispherical transmittance of a 3mm-thick glass window supporting condensed water droplets for wavelength between 0.4 and 5 μm was predicted and discussed in light of the earlier parametric study and asymptotic behavior.

Light transfer in agar immobilized microalgae cell cultures

This paper experimentally and theoretically investigates light transfer in agar-immobilized cell cultures. Certain biotechnological applications such as production of metabolites secreted by photosynthetic microorganisms require cells to be immobilized in biopolymers to minimize contamination and to facilitate metabolite recovery. In such applications, light absorption by cells is one of the most important parameters affecting cell growth or metabolite productivity. Modeling light transfer therein can aid design and optimize immobilized-cell reactors. In this study, Parachlorella kessleri cells with areal biomass concentrations ranging from 0.36 to 16.9 g/m2 were immobilized in 2.6 mm thick agar gels. The average absorption and scattering cross-sections as well as the scattering phase function of P. kessleri cells were measured. Then, the absorption and transport scattering coefficients of the agar gel were determined using an inverse method based on the modified two-flux approximation. The forward model was used to predict the normal-hemispherical transmittance and reflectance of the immobilized-cell films accounting for absorption and scattering by both microalgae and the agar gel. Good agreement was found between the measured and predicted normal-hemispherical transmittance and reflectance provided absorption and scattering by agar were taken into account. Moreover, good agreement was found between experimentally measured and predicted mean rate of photon absorption. Finally, optimal areal biomass concentration was determined to achieve complete absorption of the incident radiation.

Transmittance of transparent windows with non-absorbing cap-shaped droplets condensed on their backside

This study aims to quantify systematically the effect of non-absorbing cap-shaped droplets condensed on the backside of transparent windows on their directional-hemispherical transmittance and reflectance. Condensed water droplets have been blamed to reduce light transfer through windows in greenhouses, solar desalination plants, and photobioreactors. Here, the directional-hemispherical transmittance was predicted by Monte Carlo ray-tracing method. For the first time, both monodisperse and polydisperse droplets were considered, with contact angle between 0 and 180°, arranged either in an ordered hexagonal pattern or randomly distributed on the window backside with projected surface area coverage between 0 and 90%. The directional-hemispherical transmittance was found to be independent of the size and spatial distributions of the droplets. Instead, it depended on (i) the incident angle, (ii) the optical properties of the window and droplets, and on (iii) the droplet contact angle and (iv) projected surface area coverage. In fact, the directional-hemispherical transmittance decreased with increasing incident angle. Four optical regimes were identified in the normal-hemispherical transmittance. It was nearly constant for droplet contact angles either smaller than the critical angle θcr (predicted by Snell’s law) for total internal reflection at the droplet/air interface or larger than 180°-θcr. However, between these critical contact angles, the normal-hemispherical transmittance decreased rapidly to reach a minimum at 90° and increased rapidly with increasing contact angles up to 180°-θcr. This was attributed to total internal reflection at the droplet/air interface which led to increasing reflectance. In addition, the normal-hemispherical transmittance increased slightly with increasing projected surface area coverage for contact angle was smaller than θcr. However, it decreased monotonously with increasing droplet projected surface area coverage for contact angle larger than θcr. These results can be used to select the material or surface coating with advantageous surface properties for applications when dropwise condensation may otherwise have a negative effect on light transmittance.

Factors influencing starch accumulation in microalga Chlorella sorokiniana

The spectral absorption cross-section of microalgae is an essential parameter in modeling the microalgae metabolism and growth kinetics as well as in estimating the productivity and efficiency of photobioreactors. This paper presents a simple experimental procedure for retrieving the average spectral absorption cross-section of concentrated microalgal suspensions. The method combines experimental measurements of the normal–hemispherical transmittance and reflectance of the suspensions in conventional cuvettes with an inverse method and analytical expressions obtained from the modified two-flux approximation accounting for absorption and multiple scattering. The method was validated with direct measurements of the scattering phase function and of the absorption and scattering cross-sections of freshwater microalgae Chlorella vulgaris. It was able to retrieve the absorption cross-section with acceptable accuracy. The latter was then used to estimate successfully the fluence rate using a simplified light transfer model, the local rate of photon absorption, and the biomass productivity in flat plate PBRs.

Simple method for measuring the spectral absorption cross-section of microalgae

The spectral absorption cross-section of microalgae is an essential parameter in modeling the microalgae metabolism and growth kinetics as well as in estimating the productivity and efficiency of photobioreactors. This paper presents a simple experimental procedure for retrieving the average spectral absorption cross-section of concentrated microalgal suspensions. The method combines experimental measurements of the normal–hemispherical transmittance and reflectance of the suspensions in conventional cuvettes with an inverse method and analytical expressions obtained from the modified two-flux approximation accounting for absorption and multiple scattering. The method was validated with direct measurements of the scattering phase function and of the absorption and scattering cross-sections of freshwater microalgae Chlorella vulgaris. It was able to retrieve the absorption cross-section with acceptable accuracy. The latter was then used to estimate successfully the fluence rate using a simplified light transfer model, the local rate of photon absorption, and the biomass productivity in flat plate PBRs.