a methodology for the determination of the light distribution profile of a micro-algal
TRANSCRIPT
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Electronic Theses, Treatises and Dissertations The Graduate School
2010
A Methodology for the Determination of theLight Distribution Profile of a Micro-AlgalPhotobopreactorQuinn M. Straub
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THE FLORIDA STATE UNIVERSITY
COLLEGE OF ENGINEERING
A METHODOLOGY FOR THE DETERMIN THE LIGHT DISTRIBUTION PROFILE OF
A MICRO-ALGAL PHOTOBIOREACTOR
By
QUINN M. STRAUB
A thesis submitted to the
Department of Mechanical Engineering
in partial fulfillment of the
requirements for the degree of
Master of Science in Engineering
Degree Awarded:
Fall Semester, 2010
ii
The members of the committee approve the thesis of Quinn M. Straub defended on October 15th
2010.
_______________________________________
Dr. Juan Ordonez
Professor Directing Thesis
_______________________________________
Dr. Ching-Jen Chen
Committee Member
_______________________________________
Dr. Ongi Englander
Committee Member
Approved:
_____________________________________
Dr. Chiang Shih, Chair, Mechanical Engineering Department
_____________________________________
Dr. Ching-Jen Chen, Dean, College of Engineering
The Graduate School has verified and approved the above-named committee members.
iii
This thesis is dedicated to:
My mother Kim, my father Don, and my sister Amber
iv
ACKNOWLEDGEMENTS
The members of my thesis committee, Dr. Ching-Jen Chen, Dr. Ongi Englander, and Dr.
Juan Ordonez have given me their kind support, expertise, time and recommendations for which
I am sincerely grateful.
A number of people at Center for Advanced Power Systems were involved in my
experimental setup, and to all I extend my appreciation and thanks. I especially want to express
my gratitude to Thomas Tracy for his assistance in all aspects of the experimental setup and its
execution.
I would also like to thank Dr. Jefferson Avila De Souza from the University of Parana in
Brazil for the advice and guidance given to me. Dr. De Souza aided in the progression and the
development of this thesis, and for that I am grateful.
v
TABLE OF CONTENTS
List of Tables ................................................................................................................................ vii
List of Figures .............................................................................................................................. viii
Abstract ........................................................................................................................................... x
Introduction ..................................................................................................................................... 1
1.1 Motivation ............................................................................................................................. 1
1.2 Organization .......................................................................................................................... 3
Background ..................................................................................................................................... 5
2.1 Photosynthesis as it Pertains to Algae .................................................................................. 5
2.1.1 Description of Photosynthetic Process............................................................................... 5
2.2 Photobioreactors ................................................................................................................... 8
2.3 Light ...................................................................................................................................... 9
2.4 Absorption Spectroscopy .................................................................................................... 13
Literature Review.......................................................................................................................... 18
3.1 Modeling Photobioreactors ................................................................................................. 18
3.2 Light Distribution Modeling ............................................................................................... 19
3.3 Photobioreactor Productivity .............................................................................................. 20
3.4 How Does Light Effect Productivity .................................................................................. 22
Materials and Methods .................................................................................................................. 24
4.1 Instrumentation ................................................................................................................... 24
4.2 Cell Counting of the Algal Strain Nannochloropsis Oculata .............................................. 25
4.3 Light Absorption Coefficient with Varying Cell Concentration ........................................ 27
4.4 Light Absorption Coefficient with Varying Light Path Length.......................................... 28
vi
4.5 Light Absorption Coefficient with Varying Temperature .................................................. 30
Model Development...................................................................................................................... 34
5.1 Cell Cultivation ................................................................................................................... 34
5.2 External Light Source ......................................................................................................... 35
5.2.1 Light Intensity .................................................................................................................. 36
5.2.2 Average Light Intensity ................................................................................................... 36
5.3 Internally Radiated Light Source(s) .................................................................................... 36
5.3.1 Light Intensity .................................................................................................................. 37
5.3.2 Average Light Intensity ................................................................................................... 39
Results and Discussion ................................................................................................................. 42
6.1 Cell Counting and the Extinction Coefficient with Varying Concentration ....................... 42
6.2 Extinction Coefficient with Varying Light Path Length..................................................... 49
6.3 Variation in Absorbance as a Function of Temperature ..................................................... 52
6.4 Verification of the Model Using Experimental Values ...................................................... 54
Chapter Seven ............................................................................................................................... 57
Conclusion and Suggested Future Work....................................................................................... 57
7.1 Conclusions ......................................................................................................................... 57
7.2 Suggested Future Work....................................................................................................... 57
Appendix A ................................................................................................................................... 59
Appendix B ................................................................................................................................... 62
Appendix C ................................................................................................................................... 63
References ............................................................................................................................... 81
vii
LIST OF TABLES
Table 1: Gallons of oil per acre from biomass NREL .................................................................... 3
Table 2: Energy of a Photon at a given frequency and wavelength in a vacuum ......................... 10
Table 3: Growth Rate Models ....................................................................................................... 20
Table 4: Spectrometer Data/ Cell Counts ..................................................................................... 43
Table 5: Predicted vs. Measured Values ....................................................................................... 54
Table 6: Predicted Average Light Intensity .................................................................................. 55
Table 7: Predicted and Measured Absorbance Internal Light Source .......................................... 56
viii
LIST OF FIGURES
Figure 1: Hubbert's Peak Oil ........................................................................................................... 2
Figure 2: Photosynthesis Cycle ....................................................................................................... 6
Figure 3: Action Spectra for Two Algal Strains ............................................................................. 7
Figure 4: Flat Plate Reactor (left); Concentric Cylinder (middle); Raceway Pond (right) ............. 8
Figure 5: Electric and Magnetic Field Directions ......................................................................... 10
Figure 6: Solar Radiation Spectrum (Falkowski, 2007) ............................................................... 11
Figure 7: Electromagnetic spectrum (Ronan, 2007) ..................................................................... 12
Figure 8: Beer-Lambert's Law (Falkowski, 2007) ........................................................................ 14
Figure 9: Effect of high temperature on absorption (Murthy,S 2004) .......................................... 16
Figure 10: Improved Neubauer Hemocytometer .......................................................................... 25
Figure 11: ImageJ Screen Capture of a Cell Count ...................................................................... 26
Figure 12: Absorbance vs. Wavelength for Various Concentrations ........................................... 28
Figure 13: Temperature Test Setup............................................................................................... 30
Figure 14: 31.4oF Extreme Temperature Test ............................................................................... 31
Figure 15: 144.7oF Extreme Temperature Test ............................................................................ 31
Figure 16: Growth Progression of Nannochloropsis Oculata ....................................................... 35
Figure 17: Vector Description of Light Path Length for External Radiation ............................... 35
Figure 18: Single Source not centered at the origin ...................................................................... 37
Figure 19: Multiple Sources not centered at Origin ...................................................................... 39
Figure 20: Integrating Areas ......................................................................................................... 40
Figure 21: Absorption vs. wavelength w/varying concentrations ................................................ 43
Figure 22: Absorbance vs. concentration at 400.2nm................................................................... 44
Figure 23: Predicted cell concentration vs. measured cell concentration ..................................... 44
Figure 24: Radiant Power vs. Wavelength Cool White Fluorescent (left) Incandescent (right) .. 45
Figure 25: Incandescent Light Source .......................................................................................... 46
Figure 26: LED Light Source ....................................................................................................... 46
Figure 27: Absorbance vs. Concentration ..................................................................................... 47
Figure 28: Predicted vs. Measured ................................................................................................ 47
Figure 29: Absorbance vs. Concentration Power Curve Fit ......................................................... 48
Figure 30: Predicted vs. Measured with using Power Curve Fit .................................................. 48
ix
Figure 31: Absorbance vs. wavelength externally radiated with varying length .......................... 49
Figure 32: Absorbance vs. light path length externally radiated .................................................. 50
Figure 33: Absorbance vs. wavelength with internal radiator with varying light path length...... 51
Figure 34: Absorbance vs. light path length for internal radiator ................................................. 51
Figure 35: Predicted Length vs. Measured Length ....................................................................... 52
Figure 36: Absorbance vs. Wavelength Varying Temperature .................................................... 53
Figure 37:Absorbance Temperature Trend ................................................................................... 53
Figure 38:Absorbance Distribution Profile for Externally Radiated 6” Diameter Cylinder ........ 56
Figure 39: Disposable Hemocytometer ........................................................................................ 59
Figure 40: Improved Neubauer Grid Layout ................................................................................ 59
Figure 41: SpectroVis Spectrophotometer .................................................................................... 59
Figure 42: Pipetman F fixed volume micro-pipette ...................................................................... 60
Figure 43: SpectroVis Optical Fiber ............................................................................................. 60
Figure 44: Celestron Biological Microscope ................................................................................ 61
x
ABSTRACT
The following work presents an in depth analysis of the distribution of the light
absorbance profile. The proper identification of conditions that maximize the growth efficiency
of photosynthetic algae is necessary to optimize the productivity as a whole of the
photobioreactor. In an effort to understand light as it interacts with an absorbing species such as
algae, various tests were completed to extrapolate extinction coefficient � or a calibration curves
based on Beer-Lamberts Law. To characterize the absorbance conditions in a photobioreactor, a
light distribution model was developed. From the basis of an external radiated light system, a
single-source system was developed. Mathematical expressions for the local light intensity and
the average light intensity were derived for a cylindrical photobioreactor with external sources,
single internal sources, and multiple internal sources. The proposed model was used to predict
the light absorbance values inside an externally and internally radiated photobioreactor using
Nannochloropsis Oculata. The effects of cell density and light path length were interpreted
through experimental and model simulation studies. The predicted light intensity values were
found to be within +/- 7% to those obtained experimentally. This level of accuracy could be
better improved with more testing and more precise instrumentation. Due to the simplicity and
flexibility of the proposed model, it was also possible to predict the light conditions in other
complex multiple light source photobioreactors.
1
CHAPTER ONE
INTRODUCTION
Chapter one will outline the motivation for the work, as well as its organization.
1.1 Motivation
Researchers are accelerating their efforts to characterize the most promising strains of
algae, as well as create new ones through genetic engineering, for fuel production. This is in
spite of the fact that the National Renewable Energy Lab (NREL) stated in their report A Look
Back at the U.S. Department of Energy’s Aquatic Species Program: Biodiesel from Algae;
Early in the research program it became obvious the maximal lipid accumulation in the
algae usually occurred in cells that were undergoing physiological stresses, such as
nutrient deprivation or other conditions that inhibited cell division. Unfortunately, these
conditions are the opposite of those that promote maximum biomass production. Thus,
the conditions required for inexpensive biodiesel production, high productivity and high
lipid content, appeared to be mutually exclusive. (Sheehan, Dunahay, Benemann, &
Roessler, 1998)
Due to recent developments, the motivation of record high crude oil prices, instability in
oil exporting regions and global warming concerns; resurgence in the popularity of algae
research has occurred. Today, algae based fuels are not economically competitive with
petroleum, however, that can change with increased efforts in the optimization of
photobioreactors and or the discovery of new useful strains.
Algae are like microscopic factories that have been using techniques refined
(photosynthesis) over time to process carbon dioxide into carbohydrates or sugars. Once created,
these sugars can be used by the algae as energy, or stored in the form of fats or lipids. Under the
proper conditions, some strains can double their weight in a few days. Algae can grow in
freshwater, salt water or even brackish (contaminated) water (Chisti, 1989).
The idea of using micro-
studied for many years in the bio
gained quite a bit of attention th
when the world will run out of
ever increasing demand some po
Shown in the Figure 1 below is
are many).
There has been a great de
optimize the processes that sup
grow. There are many differen
photosynthetic organism can us
delivery, and control of environm
Reactor fluid dynamics for ins
distribution of nutrients, and lig
knowledge is therefore necessa
Dunahay, Benemann, & Roessler
2
-algae as a biofuel feedstock is not a new one.
biological community for this purpose. As stated p
the last twenty years due to the “oil crisis”. It is
f oil; however, what is clear is that the oil suppl
point in the not too distant future, oil reserves
is a plot that shows one prediction of when oil w
deal of research in the academic community into
upport photosynthesis, thus accelerating the rate
rent physical interactions that can determine ho
use light. How the light is exposed to the or
nmental conditions all play a part in how quickly
instance can play a role in the symmetric or
light exposure (due to mixing). The vast array
sary to properly characterize algae photobiorea
ler, 1998)
Figure 1: Hubbert's Peak Oil
e. Algae have been
d previously, it has
is not clear exactly
pply is finite. With
s will be used up.
will run out (there
to various ways to
ate at which algae
how efficiently a
organism, nutrient
ly an algae grows.
or anti-symmetric
ray of engineering
reactors. (Sheehan,
3
Table 1 shows the predicted values for the annual yield of oil in gallons per acre for some
various types of biomass. Micro-algae are clearly the higher yielding crop. Micro-algae are
typically grown in a photobioreactor, which will be explained more within this work.
Photobioreactors have a decreased land use footprint, and an increased total volume; thus making
them a more efficient use of space. This efficient use of space is what allows photobioreactors to
have a competitive advantage over traditional biofuel sources. In order to make predicted oil
production rates a reality, it is imperative that the growth of the algae be optimized. In order to
be economically competitive, continued research into the optimization of algae growth is
necessary (Sheehan, Dunahay, Benemann, & Roessler, 1998). Photoautotrophic micro-algal
growth is largely dependent on light intensity, which in turn depends on the use of an accurate
“extinction coefficient” for particular reactor geometry and microalgae species. The main goal of
this work is to properly show the light distribution within a photobioreactor as a function of the
experimentally determined light extinction coefficient and or the experimentally determined
calibration curve of light absorbance vs. concentration.
Table 1: Gallons of oil per acre from biomass NREL
Biomass Gallons of oil per acre per year
Corn 18
Soybeans 48
Safflower 83
Sunflower 102
Rapeseed 127
Oil Palm 635
Micro-Algae 5,000-15,000
1.2 Organization
Chapter 1 presents the motivation for the work. Chapter 2 provides the necessary
background information to understand the problem of characterizing the light extinction
coefficient. Chapter 3 provides examples of some of the work that has already been completed
by other authors in the form of a literature review. Chapter 4 describes the methodology, i.e.,
4
materials and methods of the experimental setup with any ancillary equipment to be used in the
analysis. Chapter 5 presents a model that has been created using the experimental data from
chapter 4. Chapter 6 presents the results and discussion of the work, consisting of a comparison
of the calculation of light intensities using the experimentally determined extinction coefficients
and measured light intensities for selected cases, and a thorough investigation of design
opportunities. Chapter 7 presents the conclusions and suggestions for future work.
5
CHAPTER TWO
BACKGROUND
Chapter 2 provides the necessary background information to understand the problem of
characterizing the light extinction coefficient.
2.1 Photosynthesis as it Pertains to Algae
Cyanobacteria and algae photosynthesize light in a similar way to plants; however, they
use a different set of mechanisms. Biochemically, photosynthesis is processed inside the
organism; however, chlorophyll is not always the primary pigment in algae. Because of this,
algae can grow in a wider variety of light conditions. In algae, a multitude of accessory pigments
may be used simultaneously to perform photosynthesis; that is why there are so many colors of
algae, including blue-green, brown, and red. Just like in plants, photosynthetic pigments in algae
are stored inside chloroplasts. Also like plants, algae produce oxygen as a by-product of
photosynthesis. Many algal strains are photoautotrophic, dependent upon only the sun to provide
energy necessary for photosynthesis. The rest are either heterotrophic (consumers of
photoautotrophs) or mixotrophs (use a variety of energy forms and carbon). Not all of the
energy from the sun incident to the surface of the planet is useable for photosynthesis. Only
about 20-30% of the energy found on the earth’s surface can be used by photosynthetic
organisms. This estimated 20-30% is represented by the visible spectrum of light. (Nobel, 1991)
2.1.1 Description of Photosynthetic Process
Represented in Figure 2 are the “light reactions” and the “dark reactions” of
photosynthesis. The “dark reactions” are also known as the Calvin-Benson Cycle. It is important
to know all living organisms are carbon-based and as such the chemistry of carbon is quite
important. The inorganic forms of carbon based molecules contain no biologically usable energy,
nor can they be used directly to form organic molecules without undergoing a chemical or
biochemical reaction (Falkowski, 2007). To extract energy from carbon or to use the element to
build organic molecules, the carbon must be chemically broken down, a process which requires
energy. There are only a handful of biological mechanisms in place for the reduction of carbon
dioxide; photosynthesis being the most extensively studied (Nobel, 1991).
6
Figure 2: Photosynthesis Cycle
Photosynthesis begins with the absorption and transfer of light’s energy to special
structures, called reaction centers, where the energy is used in electrical charge separation.
These three processes—absorption, energy transfer, and primary charge separation—constitute
the “light reactions” of photosynthesis. Photosynthesis can be written as an oxidation-reduction
reaction of the general form;
6 CO2 + 6 H2O � C6H12O6 + 6 O2
Carbon dioxide + Water + Light energy � Glucose + Oxygen [1]
In the light reactions, one molecule of the pigment chlorophyll absorbs one photon while
losing one electron. The electron transport chain is described concisely by Falkowski:
The electron is passed to a modified form of chlorophyll called pheophytin, which passes
the electron to a quinone molecule, allowing the start of a flow of electrons down an electron
transport chain that leads to the ultimate reduction of NADP to NADPH. In addition, this creates
a proton gradient across the chloroplast membrane; its dissipation is used by ATP synthase for
the concomitant synthesis of ATP. The chlorophyll molecule regains the lost electron from a
water molecule through a process called photolysis, which releases an oxygen (O2) molecule.
(Falkowski, 2007)
7
Only a selection of the visible spectrum’s wavelengths supports photosynthesis. The
photosynthetic action spectrum depends on the type of pigments and accessory pigments present.
For example, in green plants, the action spectrum resembles the absorption spectrum for
chlorophylls and carotenoids with peaks in ~430nm and ~650nm wavelengths. In the Figure 3,
two different species’ action spectra are shown. The least absorbed part of the light spectrum is
what gives photosynthetic organisms their color. The two algal strains shown in Figure 3 appear
green because they weakly absorb in that wavelength range ~520nm-620nm. (Falkowski, 2007;
Nobel, 1991)
Figure 3: Action Spectra for Two Algal Strains
An understanding of the light reactions requires some understanding of the nature of light
itself, the process of light absorption by electrons, the relationship between light absorption and
molecular structure, as well as the concept of energy transfer between homogeneous and
heterogeneous molecules. (Falkowski, 2007; Nobel, 1991) For the sake of relevance to this
particular work, discussion into the background of photobioreactors, light, as well as how light
absorbance can be explained physically will be this section’s focus.
8
2.2 Photobioreactors
The term photobioreactor should be used to describe single algal cultures that are isolated
from the environment however, in the past it has also been used to express open raceway pond
type systems (Figure 4). Throughout this work, the term will use the former definition. Algal
photobioreactors are closed to the environment in such a way that they allow gas exchange, but
do not allow contamination by other bacteria or another algal species. Photobioreactors come in
various shapes and sizes, however, for the sake of generalization they can be classified as either
tubular devices or flat panels. These can be further categorized according to orientation of tubes
or panels, the mechanism for circulating the culture, the method used to provide light, the type of
gas exchange system, the arrangement of the individual growth units and the materials of
construction employed. Figure 4 shows two examples of algal photobioreactors of types flat and
tubular.
Figure 4: Flat Plate Reactor (left); Concentric Cylinder (middle); Raceway Pond (right)
The understanding of how light interacts or is distributed within the photobioreactor itself
is quite important. Light interactions with algae via photobioreactors will be described in Chapter
3. Chapter 5 will show a methodology for expressing the light distribution profile within a simple
photobioreactor based on the analysis of Beer-Lambert’s Law.
9
2.3 Light
Light is electromagnetic radiation that can be produced by a variety of energy conversion
processes. For example, light is emitted when matter is heated. In the sun, light is produced as a
by-product of nuclear fusion reactions deep in the sun’s core. The fusion reactions produce
gamma radiation, and as the radiation is absorbed by the nuclei of neighboring atoms, intense
thermal energy is produced. The thermal radiation makes it to the sun’s surface, where a portion
of the energy is projected outward in the form of visible light (Falkowski, 2007). It takes
approximately 8 minutes and 20 seconds for light to reach the earth from the sun.
The two components of electromagnetic radiation, namely, the electronic and magnetic
waves, are at right angles to each other and propagate along and around an axis with a velocity c
(Figure 5). The frequency of the wave � corresponds to the frequency of the charged particle
from its radiating surface. The spectrum of emitted energy is delivered by massless particles
called photons. The empirically observed behaviors of light allow these massless particles to
convey the properties of electromagnetic radiation. The energy, �, of a photon is directly
proportional to the frequency (�) of the radiating wave. The proportionality factor is called
Planck’s constant, h:
� = ℎ�� ����
Where h = 6.625 × 10 − 34 J s In a vacuum, the velocity of the photons is a constant at the speed of light �� = 3 ×
10� �� � and is independent of frequency. To meet this constraint, the product of frequency and
wavelength �, must be constant.
� = �� [3]
From the above two equations the following relationship can be shown:
�� = ℎ��
[4]
Figur
It follows then that the s
energy. Photon energies for the
using energy on a molar basis. B
wavelength but directly proporti
domain is more readily interpre
represent spectra as a function of
of Beer-Lambert’s Law the wave
converting wavelength to energy
equal to 1 eV (electron volt); t
as �� = 1240�� !"# . Where ��
Table 2: Energy of a Photon at a
Color
Approxim
Waveleng
range (nm
Violet 400-425
Blue 425-490
Green 490-560
Yellow 560-585
Orange 585-640
Red 640-740
10
gure 5: Electric and Magnetic Field Directions
e shorter the wavelength of the radiation the gr
he visible spectrum of wavelengths are summar
. Because the energy of a photon is inversely pr
rtional to its frequency, representation of light
preted in relation to energy. Biologists, by con
of wavelength, opting for units of nanometers, fo
velength will be represented in (nanometers). A si
gy is as follows: The energy contained in a photo
; therefore, the energy of any wavelength �� ca
�� = 1.602 × 10$%&J
t a given frequency and wavelength in a vacuum
imate
ngth
nm)
Wavelength
Represented
(nm)
Frequency
(hertz) En
410 7.31X1014
292
460 6.52X1014
260
520 5.77X1014
230
570 5.26 X1014
210
620 4.84 X1014
193
680 4.41X1014
176
greater the photon
arized in Table 2
proportional to its
t in the frequency
onvention, usually
for the application
simple method for
oton at 1240 nm is
can be calculated
Energy (kJ mol-1
)
92
60
30
10
93
76
11
The sun emits electromagnetic radiation over a large range of wavelengths—from high-
energy gamma emissions, through ultraviolet, visible, and infrared, to low-energy radio waves
shown in Figure 6. Solar energy peaks in the visible region of the electromagnetic spectrum,
between 400nm and 700nm. This wavelength change corresponds to frequencies between
7.5X1014
and 4.3X1014
s-1
. As shown in Figure 7, the lower wavelength of light is perceived as a
violet color by the human eye, while the longer wavelength appears red. The radiation incident
on the Earth’s atmosphere corresponds to about 1373 W m-2
and is called the solar constant.
Figure 6: Solar Radiation Spectrum (Falkowski, 2007)
Any photon incident on any atom or molecule is to be scattered, fluoresced, or absorbed.
Each of these phenomena is related to the electronic structure of atoms or molecules and the
interaction of these structures with light. Scattering is a process resulting in the change of
direction of photons. Absorption is the process by which an electron in the absorbing matter is
brought to a high excited state. Fluorescence is the re-remittance of absorbed light.
All substances contain negatively charged electrons that oscillate around the positively
charged nuclei. The electrical component of the incident light can interact with the electronic
structure of the atoms or molecules and induce a displacement of electrons with respect to the
nuclei. In water or other liquids, the density of the molecules is so great that the molecules
interact and gradients in thermal
permit a purely homogeneous
volumes of the fluid will, contain
light will become more scattered
purest liquid, light is scattered as
The scattering of light by
shape. This can be visualized by
incident on the glass is refracte
relatively transparent to the naked
will scatter light and the powder
or scatter light, depending on the
at larger angles, and high concen
light.
In aquatic systems, bubbl
the scattering of light; the sm
(Falkowski, 2007). In the case o
are almost never distributed ho
Figure 7:
12
al energy within the fluid cannot be dissipated ra
s distribution. As a result, at any moment in
ain slightly different numbers of molecules. A col
red as it passes through a liquid (Falkowski, 20
as a consequence of fluctuations in the refractive i
by particles is a function not simply of their size,
by considering large fragments of broken glass. M
cted and passes through the glass shard. Large
ked eye. If the glass is ground into a powder, the r
er will appear white. Thus, the same amount of g
the size and number of the particles. Smaller parti
centrations of small particles are extremely effec
bles of air, sediments, viruses, bacteria, and algae
smaller the particle, the greater will be its s
of micro-algae, cellular sizes are on the micron
homogeneously, and their size is usually far
: Electromagnetic spectrum (Ronan, 2007)
rapidly enough to
n time, two equal
collimated beam of
2007). Even in the
e index.
ze, but also of their
s. Most of the light
e glass pieces are
e resulting material
f glass can transmit
rticles scatter light
ective at scattering
ae all contribute to
scattering ability
on scale. Particles
r greater than the
13
wavelength of the incident radiation. Both bacteria and phytoplankton tend to scatter visible light
uniformly across the spectrum (Falkowski, 2007). Scattered light is available for photosynthesis.
To be used for photosynthetic processes however, the available light must first be absorbed.
Absorption of photosynthetic radiation by photosynthetic pigments can be inferred by the basic
concepts of absorption of light by atoms and molecules.
2.4 Absorption Spectroscopy
Light absorption leads to a change in the energy state of atoms or molecules. Before
spectrophotometers spectral lines of the emitted radiation were characterized by eye, using a
handheld spectroscope, as being either sharp(s) or diffuse (d); later the terms principal (p) or
fundamental (f) were added to describe other emission bands. Each element has a unique set of
emission bands; spectroscopists could observe the specific emission and composition of
unknown compounds. In fact, it was from the color of the emission that a number of elements
were discovered. The technique of absorption spectroscopy works in the opposite way in that it
measures absorbed light as opposed to emitted light. Absorption spectroscopy is extremely
sensitive and useful for characterizing specific molecules such as algal strains.
In absorption spectroscopy, the intensity of light or the percent of light transmitted
through an absorbing sample is explained by Beer-Lambert’s Law (Figure 8). Equation 5
represents Beer-Lambert’s Law for liquids.
' = '(10$)*+ ����
In Beer-Lambert’s Law, the incoming light intensity I0 absorbed by a medium is relative
to its concentration C, light path length L, and the absorption coefficient �. The variables I, Io,
and � are all functions of wavelength � (nm). In most applications of Beer-Lambert’s Law, a
spectrophotometer is used to measure I and I0 such that it can output the absorbance A as shown;
, = -./%( 0'(' 1 = �23
����
14
Figure 8: Beer-Lambert's Law (Falkowski, 2007)
Whenever absorbance is measured as a function of wavelength, it is generally
proportional to concentration and light path length. This proportionality simplifies the analytical
calibration of many experiments which are supported by Beer-Lambert’s Law. The absorption
coefficient � is determined experimentally. Solving the above equation for �, you get:
� = ,23
����
Therefore, by measuring the absorbance A of a known concentration C of the absorbing
compound and using a known light path length L, � can be calculated. Absorbance A is unit-
less value (it's the log of a ratio of two intensities), the units of � are the reciprocal of the units of
L and C (Nobel, 1991).
This can become useful later in the estimation of cell concentration without having to
physically count cells under a microscope. Preparing a series of solutions at different known
concentrations and plotting them with the measured absorbance gives a calibration curve for that
medium. The calibration curve shows the linear relationship expressed by Beer-Lambert’s Law.
15
The slope of this curve is �L when the intercept is set equal to 0. So by measuring the slope and
dividing by the length L, the absorption coefficient � is obtained.
It's important to understand that the "deviations" from the Beer-Lambert Law discussed
here and presented later are failures of the measuring experiment to adhere to the condition under
which the law is derived. The fundamental requirement under which then Beer-Lambert Law is
derived is that every photon of light striking the detector must have an equal chance of
absorption. Thus, every photon must have the same absorption coefficient �, must pass through
the same light path length, L, and must experience the same absorber concentration; C.
Disruptions of any of these conditions will lead to an apparent deviation from the law. For
example, every spectrometer has a finite spectral resolution, meaning that an intensity reading at
one wavelength setting is actually an average over a small spectral interval called the spectral
band pass. The polychromatic radiation effect occurs if the absorption coefficient � varies over
the spectral band pass. The calculated absorbance will no longer be linearly proportional to
concentration when this occurs. This effect leads to a general concave-downward of the
analytical curve. Strict adherence to Beer-Lambert’s law is observed only with truly
monochromatic radiation.
If the incident radiation consists of just two wavelengths �1 and �2, with intensities I01 and
I02, then the intensity of the radiation to come out from (I) the cell for each wavelength would be:
'% = '(%10$)4*+ ����
�
'5 = '(510$)6*+ ���
Where �1 and �2 are the extinction coefficients for each wavelength, the measured
absorbance A1,2 will be;
,%,5 = −-./ 0 '% + '5'(% + '(5
1 = -./ 0 '(% + '(5'(%10$)4*+ + '(510$)6*+1
����
The last equation indicates a non-linear relation between A1,2 and C. The proportionality
between A1,2 and C returns only if �1 = �2. The same situation occurs when a radiation consists
16
of many wavelengths. Despite possible deviations from the law it can be easily seen that the
concentration C can be calculated by measuring the absorbance A and dividing it by the product
of the path length L and �. That is, if the absorption coefficient � is known or an experimentally
determined calibration curve is obtained.
Figure 9: Effect of high temperature on absorption (Murthy,S 2004)
It should be mentioned that � varies as a function of wavelength, temperature, and pH, so
if the conditions of the sample do not match those with which the � was measured, the calculated
concentration will be affected by this deviation. Any variable present within a system that can
change local cell density or light path length will lead to the non-linearity in the calibration
curve. Temperature and pressure are two state variables that can fluctuate significantly in nature.
Generally pressure does not change the density significantly enough in fluids to change local cell
densities. On the other hand, temperature does. Figure 9 above shows the effect of temperature
on absorbance. The absorbance values measured on spectrophotometer may not be linear with
concentration, due to the deviations discussed above, in which case no single value of light
extinction coefficient � would give accurate results. In general, to get more accurate results a
series of dilute solutions of known concentrations are prepared, and measured. The data is
plotted and a calibration curve can be found. Once the calibration curve is established, unknown
solutions can be measured and their absorbances converted into concentration using the
3 = ,2�
���
17
calibration curve providing again that the conditions by which they were measured are constant.
(Nobel, 1991; Murthy, Ramanaiah, & Sudhir, 2004)
18
CHAPTER THREE
LITERATURE REVIEW
Chapter 3 provides examples of some of the work that has already been completed by
other authors in the form of a literature review.
3.1 Modeling Photobioreactors
There has been a great deal of effort to characterize the “air-lift” bioreactor. The air-lift
bioreactor is a system that induces mixing by creating localized density changes. Sometimes
called bubble column reactors, gaseous mixes of air and CO2 are pumped into the system. The
gases pass through gas spargers, which create very small bubbles. As the gas rises in the column
of fluid, some gas diffuses into the fluid via mass transfer. The rest, escapes to the atmosphere.
This mass diffusion causes localized density changes and creates an imbalance in the system.
The more dense fluid sinks to the bottom as the less dense fluid rises to the top. This natural
mixing provides circulation as long as the gas pumps through the system (Chisti, 1989).
The study of the hydrodynamics of other bioreactor designs has also been greatly
considered by many authors. Many authors have conducted various forms of analysis in the
effort to properly characterize the “flat plate” bioreactor (Sierra, et al.). They found the major
advantage of flat panel reactors to be that they have a much shorter oxygen path than large scale
tubular photobioreactors. The shorter oxygen path is important due to the fact that oxygen can be
damaging to the growth of the algae. For each photobioreactor design, it is possible to ensure a
sufficient mass transfer capacity so that photosynthetically generated oxygen does not over-
accumulate. Energy required to attain the proper mass transfer coefficient in flat plate, bubble
column, and tubular photobioreactors is presented. It was found that the mass transfer capacity in
the flat panel photobioreactor could be attained with 53W/m3 power supply. To attain the same
mass transfer capacity, 40W/m3 are required in bubble columns, and 2400–3200W/m
3 in tubular
photobioreactors. So it would seem that the flat plate bioreactor, at least from a mixing
standpoint is a good candidate for design (Sierra, et al.). These results compare nicely with the
findings of Chisti outlined in his previously mentioned book Airlift Bioreactors (Chisti, 1989).
Geometry will play an even more important role later, when discussing light exposure to the
19
system. The mass transfer of gas into liquid by virtue of the hydrodynamics of the system was
also studied by (Acien, et al.). They found that although the increase in superficial gas velocity
increased the mass transfer, there would be issues of scale up due to induced turbulence.
Turbulence is harmful simply because it can add enough stress to burst the cellular wall of the
micro-algae, thus killing them (Fernandez, et. al).Through each of these studies, the investigators
have reported methodologies for the optimization of specific systems. These methodologies can
be used later in the design of efficient photobioreactors who use known hydrodynamic
phenomena to increase system efficiency.
Optimizing these systems does not stop at interaction between the gas and the fluid; care
must be taken in the nutrients provided to the algae. Studies have been conducted on the proper
rationing of nutrient levels, in an effort to optimize the lipid content of the cell. To have a high
yield of fuel to biomass ratio, you must have a high lipid to biomass ratio. Muller-Feuga reported
that in order to obtain optimum lipid content, algae should be grown in a nitrogen deficient
environment. The author goes on to propose a model for growth as it relates to rationing (Muller-
Fuega, 1999). The concept of rationing is not new, and has been applied throughout biology in
various ways.
Optimization of all life support structures is necessary for algae to reproduce most
efficiently. For photosynthesis in photoautotrophic algae however, light exposure is seemingly
the most important. Without the energy given by light in the visible spectrum, photosynthesis
would not be possible. The following will overview some of the efforts in the field to this end.
3.2 Light Distribution Modeling
The study of photoautrophic micro-algal production under outdoor conditions has been
used to determine the effects of culture conditions, nutrient supply, biomass concentration,
temperature control, and incident radiation. Light availability, the most important factor affecting
cellular growth is difficult to control outside of a lab. This is due to the variation in solar
irradiance throughout the day/year, as well as, variability due to attenuation or absorption.
Despite the importance of light energy for the growth of photosynthetic cells, the
20
characterization and utilization of light energy has been underestimated in the field of
photobioreactor engineering. Light energy is readily absorbed but cannot be stored in a
photobioreactor, and any light energy not absorbed or not used for photosynthesis is dissipated as
thermal energy. The exposure of cells to excess light leads to a decline in their growth which is
of particular concern for industrial-scale cultivation (Nobel, 1991). Therefore, light energy must
be supplied continuously at an appropriate level, and the light energy supplied should be utilized
at the highest possible efficiency.
Beer-Lambert’s law is simple yet robust enough to estimate light distribution within any
of previously mentioned reactor vessels. Measured deviations from the law are acceptable and
can usually be handled by empirically derived attenuation coefficients or calibration curves. The
aforementioned deviations are due to biomass absorption and light scattering effects in all
directions (Aiba, 1982; Coronet, Dussap, & Dubertret, 2004). Selective light absorption has also
been referenced as a source of deviations from Beer-Lambert’s Law when working with average
coefficients (Rabe & Benoit, 1962).
3.3 Photobioreactor Productivity
Design and scale-up methodologies for photobioreactors are still in the developing stages.
This could be in part because physical parameters necessary for efficient scale-up are either
assumed or neglected. For instance, further increase in irradiance will inhibit growth. This
decrease in photosynthetic production is known as photo-inhibition. Although photo-inhibition is
well documented in the Phycology field, it has often been disregarded in mathematical models.
For example, Equations (12), (14)-(16) in Table 3 do not take photo-inhibition in to account. In
the table, only Equations (13) and (17) consider the inhibitory effects of excessive light.
Table 3: Growth Rate Models
Equation Reference
12. � = ��9:;<�9:;=�< (Tamiya, et al., 1976)
13. � = <�9:;<9:;
01 − e$ >>9:;1 (Steele, 1977)
21
14. � = �9:;<?@A9=<9�9 (Bannister, 1979)
15. � = �9:;<0@B=<=>6CA1 (Aiba, 1982)
16. � = �9:;<D?<ED=<D�
(Molina Grima, Garcia Camacho, Sanchez Perez,
Fernandez Sevilla, Acien Fernandez, & Contreras
Gomez, 1994)
17. � = �9:;<:FG0HI J>K1L<EM%=0>KCA1:NHI J>K=<:FGHI J>KO
(Acien, Garcia, Sanchez, Fernandez, & Molina, 1997)
Each of the equations in Table 3 use different experimentally determined coefficients.
Generally though, µ is considered to be the growth rate, µmax the maximum growth rate, Iavg
average intensity in the photobioreactor, I0 initial intensity, Imax is the maximum light intensity
dictated by photo-inhibition. The productivity of a photobioreactor system depends on its ability
to closely monitor, and adjust all life support structures. Each algal strain has different, albeit
similar, life support needs. Some environmental factors include temperature, mineral/nutrients
supply, pH, light intensity, dissolved CO2, and in some cases mixing. Each of the previously
mentioned life support structures can be individually monitored; however, some are more
difficult than others. Controlling the supply of light in a lab for instance is not as difficult as is
controlling the supply of solar radiation, which is dependent on the solar irradiance of the area,
cloud cover, etc. The productivity of the system is determined by the growth rate, which is a
function of the light profile within the reactor and the spectral distribution to which the cells are
exposed. In dense micro-algal cultures, light penetration is impeded by self-shading and light
absorption. These effects affect the radiation profile inside the culture. Consequently, within any
photobioreactor design, there exist zones of different levels of illumination. These zones may
have different volumes. How long the cells reside in each zone of different illumination plays a
major role in the productivity of the system.
22
3.4 How Does Light Effect Productivity
Availability and intensity of light are the major factors controlling productivity of
photosynthetic cultures. According to Acien, et al (1997) in continuous culture as typically
practiced for microalgae, the biomass productivity (µ) is a function of the cell concentration (Cb)
in the culture medium and the dilution rate (D):
μ = DCS ����
At steady state, the dilution rate equals the specific growth rate (�), which is governed by
the amount of light. The dependence of � on the average irradiance has been expressed variously
as summarized in Table 3. Generally, � increases with increasing irradiance, reaching a
maximum value, µmax.
T = TUVW'VXY�Z= [\K]^'_ M1 + �'(̀a]VNZ= [\K + 'VXYZ= [\Kb
���
The above expression presented by Acien, et al (1997) accounts for photo-inhibition and
the fact that the dependence of the growth rate (�) on the average irradiance (Iavg) varies with the
initial intensity incident to the photobioreactor (Io).
In order to describe the average light intensity within the photobioreactor, it sometimes
becomes necessary to overcome the deviations from Beer-Lambert’s law. In the past, two
approaches have been explored. One involves incorporating the light scattering effects neglected
in the Beer-Lambert’s law into the model (Aiba, 1982; Coronet, Dussap, & Dubertret, 2004).
The other approach involves the use of an empirical model. The light distribution within a
photobioreactor can be affected by scattering, reflection, and refraction of the light caused by the
cells, culture medium, bubbles, reactor surface, and other geometric components of the
photobioreactor. Thus, it is extremely difficult to consider all of these effects in one model. On
the other hand, light attenuation by cells (Acien, Garcia, Sanchez, Fernandez, & Molina, 1997);
(Iehana, 1987), (Iehana, 1990) or by the light path-length (Katsuda, et al., 2000; Suh & Lee,
2002) has been successfully described using hyperbolic equations. In this study, we observed
23
however that was not necessary due to the data’s linear nature. The use of nonlinear regression
curve fits is only necessary when the representation of absorbance vs. concentration or the
absorbance vs. length deviate from the linearity of Beer-Lambert’s law. If the empirical approach
was necessary, the light path-length causes similar effects on light attenuation as cell
concentration, since longer light path-lengths may likewise increase light scattering. Using this
assumption, the light scattering effect by cells and the light path-length can be formulated as the
product of two hyperbolic equations:
'c�, 2, 3d = '(e fghcifjKdcklIhd?kiIi� (Suh & Lee, 2002) �����
The variables �, KC, and KL are coefficients of maximal light absorption, light scattering
by cells, and light scattering by light path-length. The parameter values above are directly
influenced by the wavelength of light; however, in the case that the same type of light sources
are used throughout the photobioreactor, the wavelength dependent parameters can be regarded
as constant. If the cell concentration is very low (C<<KC) and the light path-length very short
(L<<KL), then the above expression reduces to Beer- Lambert’s Law:
'c�, 2, 3d = '(e$)+c*$m(d (Suh & Lee, 2002) ����
The availability of the light is determined by the light attenuation within the system. The
light attenuation of the system depends on a few factors that include, but are not limited to, the
material of the tubing or plate, concentration level of the algae, the intensity of the light entering
the system at each wavelength, the geometry of the system, and the type of algae. In chapter 5 a
proposed mathematical model of light distribution which assesses the light conditions inside an
internally radiating photobioreactor in terms of light distribution profile and average light
intensity is presented. The validity of the model was examined by comparing the measured light
intensities to the predicted light intensities.
24
CHAPTER FOUR
MATERIALS AND METHODS
This chapter discusses the materials and methods used in the evaluation of the extinction
coefficient and or experimentally determined calibration curve. Section 4.1 discusses equipment
used in the gathering and evaluation of data for each of the experiments described in section 4.2-
4.5. Section 4.2 describes the process of cell counting, where the algal strain Nannochloropsis
Oculata is counted. Section 4.3 introduces an experiment wherein light passes 1-dimensionally
through a rectangular cuvette and is measured. By measuring the light intensity before and after
the absorbing medium, the light extinction coefficient can be evaluated using Beer-Lambert’s
Law. In this section, the concentration of the absorbing medium will be changed, and
measurements recorded. Section 4.4 re-introduces the same concept as mentioned before, only in
this circumstance instead of changing the absorbing medium’s concentration, the light path
length is varied. Section 4.5 measures the light absorbed by a medium when neither
concentration, nor light path length is varied. In this case, temperature is varied in order to see
the role that temperature can play in an absorption event.
4.1 Instrumentation
Determining the relationship of the parameters involved in Beer-Lambert Law requires
the count of the number of cells per volume of solution, or the amount of dried biomass per
volume of solution. In all experimentation, cell count per volume (mL) is used, not a dry
biomass. Cell counting is performed using ruled slide called a Hemocytometer. The ruling of a
Hemocytometer describes the layout and spacing of the grids etched into the surface of the slide.
Figure 10 shows the ruling of the Improved Neubauer Hemocytometer. The disposable
hemocytometer in Figure 10 has two counting grids onto which the sample is placed. The
hemocytometer used for this experiment is an Improved Neubauer ruling. Figure 11 shows the
layout of the grids that will be used for cell counting. The Improved Neubauer grid has nine
squares, each 1 mm along a side, and is further divided into 20 to 25 smaller squares. The
chamber is 0.1 mm deep; therefore each grid (9 mm2) holds 0.009mL of sample.
25
4.2 Cell Counting of the Algal Strain Nannochloropsis Oculata
In this section, the algal strain Nannochloropsis Oculata is counted using the Improved
Neubauer hemocytometer. Nannochloropsis Oculata is used because of its ability to grow
quickly under varying conditions. Once the count is completed, the cell concentration can be
determined.
Instruments Used:
• Celestron Professional Biological Microscope
• Disposable Improved Neubauer Hemocytometer
• Pipetman Fixed Volume 10�L pipette
• 3.5mL Cuvette
• ImageJ Software
Procedure:
1. While using a sterile technique, a well-mixed sample was taken from the 3.5 mL cuvette
used in the measurement of the absorption spectra. A drop of Lugol’s solution (mixture
of Potassium Iodide, Iodine, and distilled water) was used to kill the algae cells. It is
Figure 10: Improved Neubauer Hemocytometer
26
important to kill the algae prior to counting to make them immobile. Algae can move
from cell to cell while counting, thus adding error to the count.
2. The sample was extracted using a 10�L micro-pipette and placed in one of the two
counting grids.
3. First, the grid was scanned using a low power in order to aide in the location of the
counting grids. It is important to magnify the sample as much as possible in order to
distinguish actual cells from detritus. Detritus is non-living organic material.
4. There is quite a bit of discretion necessary in cell counting. It is important to decide
whether the cells that fall on the line are “in” or “out”, whether or not to count dead cells,
etc. In all the cell counts that were performed, any visible cells were counted.
5. The counting portion of cell counting is where a considerable amount of operator error
can occur. To minimize this error, the program ImageJ was used. The use of ImageJ gave
a visual way to keep track of the counted cells, thus minimizing over or under counting a
sample. Shown in Figure 12 is an example of a cell count made using ImageJ.
6. The mean number of cells/volume is calculated in the following manner:
o Mean number of cells/unit area X area of entire grid/unit area counted =
number of cells/grid
o Number of cells/grid X mL/volume of sample on the grid = number of
cells/mL
Figure 11: ImageJ Screen Capture of a Cell Count
27
4.3 Light Absorption Coefficient with Varying Cell Concentration
Section 4.3 introduces an experiment wherein light passes 1-dimensionally through a
rectangular cuvette and is measured. By measuring the light intensity before and after the
absorbing medium, the light extinction coefficient can be evaluated using Beer-Lambert’s Law.
In this section, the concentration of the absorbing medium is changed, and measurements
recorded.
Instruments Used:
• Celestron Professional Biological Microscope
• Disposable Improved Neubauer Hemocytometer
• Pipetman Fixed Volume 10�L pipette
• 3.5mL Cuvette
• ImageJ Software
• Vernier SpectroVis Spectrophotometer
• Vernier Logger Pro 3.6 Software (Figure 17)
Procedure:
1. Samples of Nannochloropsis Oculata were taken during the peak of the logarithmic
growth phase (maximum possible cell concentration).
2. Samples were diluted in the following fashion:
a. 1 cuvette 3mL maximum concentration
b. 1 cuvette 2.5mL maximum concentration .5mL distilled water
c. 1 cuvette 2.0mL maximum concentration 1.0mL distilled water
d. 1 cuvette 1.5mL maximum concentration 1.5mL distilled water
e. 1 cuvette 1.0mL maximum concentration 2.0mL distilled water
3. The Vernier SpectroVis Spectrophotometer was calibrated using a cuvette filled with
distilled water. Once calibration was complete, the samples could be loaded for analysis.
28
4. During the measurement of absorption, the data tends to fluctuate initially. In order to
make an adequate measurement a five seconds were given to allow the sample to
stabilize.
5. After the first sample was recorded, the process was repeated for each of the diluted
samples.
6. Once all of the samples were recorded, the next step was to perform the cell counts for
each sample. This is necessary in order to find the extinction coefficient �.
7. The cell counts were completed as outlined in section 4.2
8. After the cell counts were calculated and recorded, the linear Absorption vs.
Concentration plot could be completed using the Logger Pro software. In Figure 12, the
use of the logger pro software in plotting absorption vs. concentration is shown. This plot
will be discussed further in Chapter 6.
4.4 Light Absorption Coefficient with Varying Light Path Length
Section 4.4 introduces an experiment wherein light passes 1-dimensionally through a
glass cylinder and is measured. By measuring the light intensity before and after the absorbing
medium is in place, the light extinction coefficient can be evaluated using Beer-Lambert’s Law.
Figure 12: Absorbance vs. Wavelength for Various Concentrations
29
In this section, the light path length was varied by varying the diameter of glass cylinders from 2-
10cm.
Instruments Used:
• Celestron Professional Biological Microscope
• Disposable Improved Neubauer Hemocytometer
• Pipetman Fixed Volume 10�L pipette
• ImageJ Software
• Vernier SpectroVis Spectrophotometer
• Vernier SpectroVis Optical Fiber
• Custom Glass Cylindrical Vessels
Procedure:
1. As in section 4.3, samples of Nannochloropsis Oculata were taken during the peak of the
logarithmic growth phase (maximum possible cell concentration).
2. In order to vary the path length, cylindrical vessels were constructed in the approximate
sizes;
a. 2cm
b. 4cm
c. 6cm
d. 8cm
e. 10cm
3. Note: These cylindrical vessels were constructed out of blown glass. As such, their
diameters are not constant throughout their height.
4. Each cylindrical vessel was calibrated with distilled water as in section 4.3 using the
Logger Pro software to minimize any changes in light scattering between the different
diameters.
5. Once calibrated, each vessel was filled with the Nannochloropsis Oculata from the
growth vessel and absorption was measured.
6. As in section 4.3 each recorded value was allowed to “settle” prior to being recorded to
maintain consistency in the methodology.
30
7. Once recorded, a sample was taken from each vessel to verify the cell concentration. This
was accomplished by doing the procedure outlined in section 4.2 cell counting.
8. After cell concentrations were calculated and recorded, it was possible to produce the
linear absorbance vs. path length plot, which will be shown in discussed in Chapter 6.
4.5 Light Absorption Coefficient with Varying Temperature
Section 4.5 discusses an experiment carried out in order to determine the role temperature
plays in an absorbance reading. In order to minimize the change in cell concentration due to
algae growth, the preceding experiment was conducted over a period of 48 hours. Also, as
previously stated, samples were taken from the ending phase of the logarithmic growth period.
During such time minimal growth and change in concentration can be assumed. Figure 12 shows
the temperature test set-up. The sample is contained in a constant temperature bath. Samples are
taken incrementally from 72-90oF. Figure 13 shows a sample contained in a ice bath. Figure 14
shows a sample being heated on a hot plate.
Figure 13: Temperature Test Setup
31
Figure 14: 31.4oF Extreme Temperature Test
Figure 15: 144.7oF Extreme Temperature Test
Instruments Used:
o Celestron Professional Biological Microscope
o Disposable Improved Neubauer Hemocytometer
o Pipetman Fixed Volume 10�L pipette
32
o ImageJ Software
o Vernier SpectroVis Spectrophotometer
o 3.5mL Cuvette
o Water Bath
o Temperature Regulators
o Digital Thermometer
o Air Circulation Pump
Procedure:
1. Samples of Nannochloropsis Oculata were taken during the peak of the logarithmic
growth phase (maximum possible cell concentration).
2. In order to vary the temperature, the in tank temperature regulator’s output was adjusted
such that the desired temperatures could be reached (Figure 13). For this experiment, the
desired temperatures were range of values acceptable for a relative optimum algae
growth. The effects on absorption for the following temperatures were observed;
a. 72oF or 22.2
oC
b. 74oF or 23.3
oC
c. 76oF or 24.4
oC
d. 78oF or 25.5
oC
e. 80oF or 26.6
oC
f. 82oF or 27.8
oC
g. 84oF or 28.9
oC
h. 86oF or 30.0
oC
i. 88oF or 31.1
oC
j. 90oF or 32.2
oC
3. As each temperature was incrementally reached, 5 samples were taken and measured
using a 3.5mL rectangular cuvette.
4. Before each grouping of samples was recorded, the SpectroVis spectrophotometer was
calibrated with distilled water in a 3.5 mL rectangular cuvette.
5. As in previous sections the samples were allowed to settle before the data was recorded.
33
6. After the data was recorded in the logger pro software, the samples were capped and
stored for later cell counting.
7. In an attempt to test the extremes of this phenomena, additional temperature tests were
conducted at approximately 31.1oF (0
oC) and 150
oF (65.6
oC).
8. The 31.4oF (0
oC) test was conducted by creating an ice bath which is shown in Figure 14.
9. The 144.7oF was conducted using a hot plate as shown in Figure 15.
10. For each of the above two extreme tests, 5 samples were taken.
11. Each was analyzed using the SpectroVis spectrophotometer, and stored for later cell
counting.
34
CHAPTER FIVE
MODEL DEVELOPMENT
Chapter 5 presents a model that has been created using the experimental data from
chapter 4.
5.1 Cell Cultivation
The unicellular micro-algal culture Nannochloropsis Oculata was selected for the
experiment, and cultured in a photobioreactor. Cells were cultivated in an externally radiated
glass vessel shown below. All experiments of light distribution analysis were completed in a 48
hr period to minimize the differences in cell concentrations between experiments. Samples of
Nannochloropsis Oculata were taken during the peak of the logarithmic growth phase (maximum
possible cell concentration).To determine the cell concentration, individual cells counts were
done per sample using a hemocytometer as explained section 4.2. Light measurements were
performed using a Vernier SpectroVis Spectrophotometer in the visible spectrum (400.2 nm-
724.3nm). Figure 16 shows the growth progression of Nannochloropsis Oculata over a 5 day
period. The sample on the left is Nannochloropsis Oculata; the sample on the right is
Botryococcus Braunii. It is clear that the sample on the left is growing much faster based on the
dramatic change in color (optical density). Typically growth started to stabilize at around day 21
and hold constant until day 35. If left unattended past day 35, the culture begins to die off and
fall out of suspension. Images past day 7 are not shown because they do not illustrate much of a
change from day 7 on, even though growth is still occurring. It is important to eliminate the
possibility for growth during testing as much as possible. Growth represents a change in cell
concentration, and can be a source of error if not properly accounted for.
35
5.2 External Light Source
In developing the present light distribution model for an externally radiating
photobioreactor, modeling was completed in 2-dimensions to simplify the expressions. Beer-
Lambert’s requires a light path length.. The following considers a cylindrical photobioreactor
that receives light from an external source illustrated in Figure 17. The assumptions of the model
are as follows:
• The light source is constant on the top surface of the cylinder.
• The attenuation of light depends only on the cell concentration (C) and the light path
length (L)
Figure 17: Vector Description of Light Path Length for External Radiation
Day 2 Day 4 Day 7
Figure 16: Growth Progression of Nannochloropsis Oculata
36
5.2.1 Light Intensity
Using a vector representation shown in Figure 17, the following relationship for the light
path length can be derived:
L?rp,�p� = qY − rp sin�pq [22]
Y?rp,�p� = tR5 − rpcos?�p�5 [23]
Using the light path length L (rp, �p) in Beer-Lambert’s Law yields the following
expression;
I?rp,�p� = I(10$�yzt{6$|} ~���}6$|} ����}z [24]
Where R is the radius of the cylindrical photobioreactor, �, the extinction coefficient, C is
the cell concentration in cells/mL, rp and �p are the coordinates for any point within the
cylindrical photobioreactor. Equation 24 describes the light intensity at any point (rp, �p) inside
the photobioreactor whenever the initial intensity I0,
5.2.2 Average Light Intensity
The average light intensity within the cylindrical photobioreactor can be found by
integrating I(rp, �p) between 0 ≤ �� ≤ 2� and 0 ≤ �� ≤ � as shown below.
'VXY?rp,�p� = 1��5 � � ��'(10$�yzt{6$|} ~���}6$|} ����}z�(
5�( ������
[25]
With equation 25, the average light intensity of an externally radiated photobioreactor
can be calculated with the experimentally determined values presented in chapter 6.
5.3 Internally Radiated Light Source(s)
In developing the present light distribution model for an internally radiating
photobioreactor, modeling will be completed in 2-dimensions in adherence to Beer-Lambert’s
Law. The following considers a cylindrical photobioreactor that receives light from internal
sources illustrated in Figure 24. The assumptions of the model are as follows:
37
• The light source is constant from the surface of the light source.
• The attenuation of light depends only on the cell concentration and the light path length
L.
• Beer-Lambert’s Law is applicable
5.3.1 Light Intensity
Figure 18 illustrates the horizontal cross-section of the cylindrical photobioreactor, with a
light source located at an arbitrary distance away from the origin. The local light intensity can be
obtained by integrating with respect to the radius from the surface of the light source S1, where
the light intensity is I0, to an arbitrary position P inside the photobioreactor.
Equation 18 represents the relationship between the diameter of the light source and it’s
radius. Equation 19 represents the light path length L1 from the light source S1. The radius of the
light source is incorporated in equation 19. Equation 19 presents Beer-Lambert’s Law with the
light path length as the difference between equation 18 and r0 .The radius r0 is subtracted from
the light path Length L1 because the light is assumed to be radiating from the surface of the light
source, and not the center of the light source.
Figure 18: Single Source not centered at the origin
38
�( = �(2 [26]
L% = t�r�% cos ��% + rp cos �p]5 + ?r�% sin��% + rpsin�p�5
[27]
Icr�%,��%d = I(10$�yc�4$|Kd [28]
If the photobioreactor is equipped with multiple light sources (figure 16), the total light
intensity can be expressed as the sum of the light intensities from all light sources relative to the
distance from each source. This assumption is valid when internal reflection is considered
negligible. For convenience, the distance from an individual source will be expressed as Lk/n,
where n is the number of light sources, and k is an index number ranging from 1 to n. Neglecting
internal reflection the total light intensity at an arbitrary position is the sum of all light
intensities, Equation 28 can be expressed as follows:
I�cr�%,��%d = � I(10$�y?�E/D$|K����%
[29]
Where;
L� �� = t�r� �� cos �� �� + rp cos �p]5 + �r� �� sin�� �� + rpsin�p]5
[30]
39
5.3.2 Average Light Intensity
The average value of a light distribution profile inside the cylindrical photobioreactor can
be calculated in a similar manner as discussed in section 5.2.2. The methodology presented in
this section was originally presented by (Suh & Lee, 2002) for the unicellular cyanobacterium
Synechococcus sp. Figure 19 represents the 4 sections inside a photobioreactor with one light
source. In Section 3, no biomass exists and thus no photosynthetic activity occurs. Therefore, the
light source (Section 3) is excluded from the average.
The average light intensity of Section 1 can be obtained by integrating over 0 ≤ � ≤ � and � + ��% ≤ � ≤ 2� + ��% − � where;
� = tan$% 0r�%r( 1 [31]
Figure 19: Multiple Sources not centered at Origin
40
To evaluate the average light intensity of the remaining sections, the wedge in Figure 27
is divided into three regions. If (r, �) is an arbitrary point on the surface boundary of the radiator
Section 3, as illustrated in Figure 25, the following relationships are valid for the boundary
Section 3:
r(5 = r5 − 2rr(cosc� − ��%d + r�%5 [32]
Figure 20: Integrating Areas
Equation 20 represents the equation of a circle not centered at the origin. Manipulation of
equation 32 yields equation 33 after the application of the quadratic equation.
r = r�%cosc� − ��%d ± �2�2r(5 − r�%5 + r�%5cosc2� − 2��%d2 [33]
Equation 32 is the representation of the light source in polar coordinates. In order to have
a surface to integrate from, equation 32 will be broken down into its individual parts which
represent the top and bottom arcs of the lights source.
41
� = r�%cosc�− ��%d − �2�2r(5 − r�%5 + r�%5cosc2� − 2��%d2 [34]
� = r�%cosc�− ��%d + �2�2r(5 − r�%5 + r�%5cosc2� − 2��%d2 [35]
Now, the average light intensity inside the photobioreactor with a single internal radiator
can be calculated using the following set of equations:
I%,���cr�%, ��%d = 1A% �� � rI%cr�%, ��%ddrdθ{K(
5�=¡¢4$££=¡¢4 + 2 � � rI%cr�%, ��%ddrdθ�
(£=¡¢4
¡¢4+ 2 � � rI%cr�% , ��%ddrdθ{
�
£=¡¢4¡¢4 ¤
[36]
A% = π?R(5 − r(5� [37]
The first, second, and third terms on the right hand side of the equation indicates the
integral of light intensity in Sections 1, 2 and 4. Equation 35 can be expanded to a cylindrical
photobioreactor with multiple internal light sources using the same methodology.
The equations presented in sections 5.2-5.4 were solved using Wolfram Mathematica 7.0
and the results are shown for local light intensity by plotting the light distribution profiles on a
contour plot. Discussion of the results is found in section 6.4
42
CHAPTER SIX
RESULTS AND DISCUSSION
Chapter 6 presents the results of the individual tests, and discusses the potential meaning
of those results. Section 6.1 presents the cell counts for the tests that involved varying the
concentration of the absorbing medium, while holding the light path length constant. Section 6.1
also presents the absorbance vs. concentration data in order to empirically discern either the
extinction coefficient �, or in the non-linear case, a suitable curve fit. Section 6.2 presents the
absorbance vs. light path length data for the experiment that involved keeping the concentration
of the absorbing medium constant, while varying the light path length. As in section 6.1, the data
is presented and analyzed to empirically determine either the light extinction coefficient � or a
suitable curve fit. Section 6.3 presents a test that represents a relationship between light
absorbance and temperature for the algal culture Nannochloropsis Oculata. Section 6.4 provides
the results of applying the empirically determined light extinction coefficient � (or curve fit) to
the model presented in section 5.1-5.3.
6.1 Cell Counting and the Extinction Coefficient with Varying Concentration
Table 4 shows an example of a cell count tally. Cell counts in all experiments were
completed manually. There are other methodologies that can be used to approximate cell density
in a solution; however, the instrumentation necessary was outside of the budget for this project.
As described in chapter 4, the hemocytometer is divided into many chambers. Each corner is
comprised of 16 chambers. Each of the four corners is counted and added together to give a
number of cells/mL. It should be noted that the cell count shown corresponds to the dilution used
for the experiments, not the dilution shown in figures 28 and 29.
43
Table 4: Spectrometer Data/ Cell Counts
Spectrometer Data/ Cell Counts
Sample
(Algae/
Water) Corner 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Cell
Count
cells/mL
1 500mL / 0mL 1 23 19 24 9 19 10 7 21 9 16 14 16 9 12 6 20
2.43E+06 2 20 9 11 18 20 10 15 20 14 27 27 15 15 11 12 9
3 5 27 10 16 21 9 23 24 28 12 6 6 19 8 17 18
4 13 18 10 10 15 16 18 9 12 25 5 7 35 19 4 21
The general case of absorbance vs. concentration is shown for Nannochloropsis Oculata.
Absorbance values were recorded for the 5 concentrations shown and plotted in figure 21. Figure
29 represents the absorbance vs. concentrations levels at ~400.2nm wavelength. The data at
400.2nm was selected because it represents the “highest” level of absorbance. The highest level
of absorbance is usually recommended by spectroscopists due to its inherent stability. Beer-
Lambert Law also requires that light values used are monochromatic. Figure 21 illustrates the
linear behavior predicted by the Beer-Lambert Law.
Figure 21: Absorption vs. wavelength w/varying concentrations
44
Figure 22: Absorbance vs. concentration at 400.2nm
Using the calibration curve extracted from figure 22, figure 23 shows what the predicted
values for cell concentration based on absorbance values. Figure 23 exhibits an almost one-to-
one relationship between predicted values, and the measured values.
Figure 23: Predicted cell concentration vs. measured cell concentration
45
During the process of experimentation and validation of the mathematical model, an
important lesson was learned. In the first test, concentration was varied, and light path length and
initial light intensity were kept constant. Based on the manner by which data is collected for the
other experiments, it was not considered that the light source (initial light intensity) must be the
same across all wavelengths. To illustrate this further, figures 24 show the radiant power vs.
wavelength for a cool white fluorescent bulb and an incandescent bulb. It can be seen that the
distribution of power by wavelength is vastly different. Not understanding this can lead to
erroneous results. This experiment varied length to see if the same linear relationship can be
seen. For this experiment, the SpectroVis spectrophotometer was used in a less than traditional
fashion.
Figure 24: Radiant Power vs. Wavelength Cool White Fluorescent (left) Incandescent (right)
In figures 25 and 26 the effect of changing light sources, on otherwise identical setups is
shown.
46
Figure 25: Incandescent Light Source
Figure 26: LED Light Source
Using the same methodology as before, an attempt to extract the relationship between
absorbance and cell concentration was made. It can be seen that the data does not represent a
linear relationship as it did previously. This non-linearity can be interpreted by going back to the
requirements of the Beer-Lambert law. The first case was shown on a small system where
47
keeping the requirements of the Beer-Lambert Law are easier. As the system grows in size, this
becomes more difficult. It will be shown that the easiest way to handle this fact is a calibration
curve. Data from figure 26 was extracted at 550nm from the data-set represented by figure 27.
Figure 27: Absorbance vs. Concentration
Figure 28: Predicted vs. Measured
In order to accommodate the non-linearity exhibited by the data set, a power curve fit can
be used to better fit the data. Using the curve fit equation and the Beer-Lambert Law, error in
predicted values can be reduced. Depending on the application, better curve fitting techniques
48
can be used to increase accuracy between predicted and measured results. Applying a power
curve fit as shown in Figure 27, yield a more linear relationship between your predicted and
measured values shown in Figure 28 (by comparison to Figure 26).
Figure 29: Absorbance vs. Concentration Power Curve Fit
Figure 30: Predicted vs. Measured with using Power Curve Fit
49
6.2 Extinction Coefficient with Varying Light Path Length
Figure 29 shows the absorbance vs. wavelength for the cylindrical vessels which vary in
diameter from 2, 4...10cm. Each measurement was calibrated to the vessel being used.
Calibration consists of filling each vessel with distilled water and measuring I0�. Calibration is
done to minimize the losses to scattering by attempting to calibrate with some scattering induced
by the distilled water. It is important to note that the vessel that was 2 cm in diameter continually
measured no light absorbance. Re-calibration and re-measurement did nothing to change this
fact. In this case, there are many factors that could contribute to reading no light absorption. The
first possible consideration can simply be that the radiator was larger than the vessel itself, thus
allowing some of the light circumvent the cylinder. Another likely explanation is the amount of
light scattered or absorbed was equivalent to the calibrated value. This doesn’t mean that no light
was absorbed or scattered, it just means that it was proportionally equivalent to that of the
calibrated value. Light path lengths L2, L3, L4, and L5 all registered readable values.
Figure 31: Absorbance vs. wavelength externally radiated with varying length
50
In each of the aforementioned tests, the light absorbance seemed to deviate slightly from
Beer-Lambert’s law based on the vessel geometry. It seemed pertinent to understand the case
where the light would be radiating outward from within the vessel, as opposed to outside the
vessel radiating inward. Figure 32 shows the case where light is contained within the vessel and
its position from the optical fiber varies in equal increments of .635cm or .25”. L4 represents the
farthest distance that could be attained from the optical fiber within the vessel (~8cm). Further
measurements were not taken any closer then L1 because the spectrophotometer started to
register no light absorbance in the 530-600nm wavelengths. Figure 36 shows that in this case the
relationship between absorbance and light path length does not exhibit a linear relationship
predicted by Beer-Lambert’s Law. By comparison to the previously mentioned case, it can be
seen that the vessel geometry contributes to some of the deviation from the linearity described by
the law.
Figure 32: Absorbance vs. light path length externally radiated
51
Figure 33: Absorbance vs. wavelength with internal radiator with varying light path length
Figure 34: Absorbance vs. light path length for internal radiator
Figure 35 below shows the predicted values for light path length vs. the measured values.
The predicted values were calculated using the experimentally determined calibration curve
shown in Figure 34. The data shows a fairly close one-to-one relationship between the predicted
values and the measured values.
52
Figure 35: Predicted Length vs. Measured Length
6.3 Variation in Absorbance as a Function of Temperature
As explained in the background, light absorption, reflection, and scattering depends on
many different properties. In the case of a gas, light absorption varies with pressure, temperature,
and molecular makeup. Since water is considered to be incompressible, pressure does not play a
large role in how light attenuates through water. Temperature, however, causes a density change
in water thus changing its optical density (OD). Therefore, it can be inferred that anything mixed
with water (such as an algal culture) is subject to similar effects. The following test was
performed to determine the role of temperature in the absorbance of water in the 72oF-90
oF
range. This range was selected due to the fact that it is a good representation of the average water
temperatures that can be found in Florida. In Figure 31, the top curve is representative of the
31oF measurement, and the other measurements shown are in the 72
oF-90
oF range falling linearly
with temperature. When running absorbance tests two effects can be seen as the temperature is
varied. The first effect is shown clearly in Figure 36 by the large absorbance change at the lower
temperatures. This effect is due to the density change of homogenous water mixtures. The other
effect that the can be seen elsewhere is called a “red-shift”. The explanation of red-shift is
53
however, outside the scope of this work. Red-shift only seems to occur at very low temperatures,
which are not conducive to optimum algae growth.
Figure 36: Absorbance vs. Wavelength Varying Temperature
Figure 37:Absorbance Temperature Trend
54
It is now clear that temperature is something that must be controlled in photobioreactors
due to its absorption numbers being somewhat misleading. When calculating cell concentration
C based on absorbance A, it can easily be seen that this would lead to two very different cell
concentrations when in the extrema of the plot. It is for this reason that knowing how the selected
medium, whether it be water or some organic nutrient mixture, reacts to temperature is extremely
important.
6.4 Verification of the Model Using Experimental Values
The model presented above is now verified using the experimentally measured values
presented in sections 6.1-6.3. It is important to note that the model is being verified using
absorbance values as opposed to intensity values. Absorbance values are described as the log of a
ratio of two intensities. Section 5.1 and 5.2 presented the case where light is radiated from an
external source through a cylindrical vessel. Section 6.2 presented an experiment to investigate
such a scenario. Figure 38 below is a contour plot which shows the distribution of absorbance as
a function of light path length described in section 5.1-5.2. In accordance with Beer-Lambert’s
Law light is absorbed as it passes through the medium. Due to the size of the cylinders tested; it
was not possible to get a light sensor inside the vessel to verify the light distribution profile.
Table 5 shows the values the model predicts, and the values measured experimentally.
Table 5: Predicted vs. Measured Values
Diameter Predicted Predicted Measured Measured
2cm .098 79.80 0.0000 100
4cm .196 63.68 0.20961 61.72
6cm .280 52.48 0.29109 51.16
8cm .380 41.69 0.38301 41.40
10cm .480 31.11 0.56837 27.02
In section 6.2, the case of the 2cm radius was discussed. The model predicts that some
light would be absorbed; however, no absorbance was measured. There are a few things that can
cause such an outcome. In the case of the 1cm rectangular cuvette shown in section 6.1, it can be
seen that the light path length of 1 cm is still “capable” of absorbing some light. So, in the above
55
scenario with a light path length of 2cm, it can be inferred that some light would be absorbed as
well. The following are possible reasons for this measurement.
1. The light value of 0.01 absorbance is outside of the range of values that the
spectrophotometer can measure.
2. Stray light was incident on the sensor
Regardless of the 2cm diameter cylinder, it can be seen that the other predicted values are
within +/- 5% of the measured values.
Section 5.2 presents a methodology for calculating the average light intensity within a
cylindrical vessel. Direct calculation of the average light intensity is not possible due to the
inability of the spectrophotometer to give light intensity values that are not relative. If the initial
light intensity is assumed, then the calculation of the average light intensities for the above cases
is outlined in Table 6.
Table 6: Predicted Average Light Intensity
Diameter Initial Assumed Light Intensity (W/m2) Average Light Intensity (W/m
2)
2cm 10 9.58
4cm 10 9.42
6cm 10 8.80
8cm 10 8.45
10cm 10 8.11
Section 6.2 also presents the scenario of an internally radiated vessel. In this test,
absorbance values were taken at 4 light path lengths each .25” or .635 cm intervals starting at an
approximate distance of 5 cm from the light source. Figure 47 shows the predicted transmittance
distribution profile. Due to the nature of the contour plot, it is somewhat difficult to discern the
accuracy of the model just by sight alone. Values of absorbance were calculated at the positions
where the light was measured.
56
As shown in Table 7, the predicted values are within +/- 7% of the measured values.
Greater accuracy could be attained if the model took into account internal light reflection.
Internal reflection could account for the measured values being higher than the predicted values.
As with any model that is based on an experimental calibration curve, more accurate results can
be attained with more experimental results. In the above experiment, the vessel size limited the
number of values that could be taken.
Table 7: Predicted and Measured Absorbance Internal Light Source
Distance from Light
Source (cm)
Predicted
Absorbance
Predicted
Transmittance %
Measured
Absorbance
Measured
Transmittance %
5.08 0.12 75.86 0.083212 82.56
5.72 0.17 67.61 0.16610 68.22
6.35 0.23 58.61 0.24621 56.73
7.62 0.39 40.18 0.33422 46.32
Figure 38:Absorbance Distribution Profile for Externally Radiated 6” Diameter Cylinder
57
CHAPTER SEVEN
CONCLUSION AND SUGGESTED FUTURE WORK
7.1 Conclusions
The following work presented an analysis of the distribution of the light absorbance
profile. The proper identification of conditions that maximize the growth efficiency of
photosynthetic algae is necessary to optimize the productivity as a whole of the photobioreactor.
In an effort to understand light as it interacts with an absorbing species such as algae, various
tests were completed to extrapolate calibration curves based that were combined with Beer-
Lamberts Law to make predictions about the physical makeup of the solution. To characterize
the absorbance conditions in a photobioreactor, a light distribution model was developed. From
the basis of an external radiated light system, a single-source system was developed.
Mathematical expressions for the local light intensity and the average light intensity were
derived for a cylindrical photobioreactor with external sources, single internal sources, and
multiple internal sources. The proposed model was used to predict the light absorbance values
inside an externally and internally radiated photobioreactor using Nannochloropsis Oculata. The
effects of cell density and light path length were interpreted through experimental and model
simulation studies. The predicted light intensity values were found to be within +/- 7% to those
obtained experimentally. This level of accuracy could be improved with more testing and more
precise instrumentation, as well as, better approximations of data trends. Due to the simplicity
and flexibility of the proposed model, it was also possible to predict the light conditions in other
complex multiple light source photobioreactors.
7.2 Suggested Future Work
The goal of the preceding work was to provide a methodology for determining the light
distribution profile of an algal photobioreactor. This was accomplished through experimentation
to find the light extinction coefficient, or in some cases, the calibration curve relevant to the
individual setup. The next relevant step is to apply the knowledge gleaned from this work to the
optimization of light for an algal photobioreactor. Using the above techniques, as well as refining
58
them to maximize their accuracy could potentially lead to the discovery of optimum growth
conditions for an algal mono-culture. The continuation of work should go as follows:
• Select algal strain optimum for growth of lipids for biofuels
• Culture the strain to its peak concentration in the growth vessel
• Characterize the strain to identify the light extinction coefficient
• Build lab-scale airlift bioreactor
• Verify that no calibration curve is necessary for the vessel, if one is necessary create it
using methodology mentioned previously
• Test various lighting conditions focusing on the peak absorbance wavelengths (blue-
violet and red)
• Attempt to develop experimental optimum based on holding temperature, pH, and
nutrient level constant while varying lighting conditions.
Figure 39: Disposable Hemo
Vernier SpectroVis Sp
• Portable: 15 cm
• One-step calibra
• Measures absor
• 100 wavelengths
• Powered by com
• Software used L
Figur
Pipetman F fixed volum
• Fixed volume 10�
59
APPENDIX A
ocytometer
Figure 40: Improved Neubauer
pectrophotometer (Figure 12)
m x 9 cm x 4 cm
ration
orbance over a 400 – 725 nm range
ths, ~3 nm between reported values
mputer USB
Logger Pro 3.6
ure 41: SpectroVis Spectrophotometer
me Micro-pipette (Figure 13)
10�L
er Grid Layout
60
• Suitable for Hemocytometer internal volume
• Disposable tips
Figure 42: Pipetman F fixed volume micro-pipette
SpectroVis Optical Fiber (Figure 14)
• Useful for varied length absorption testing
Figure 43: SpectroVis Optical Fiber
Celestron Profession Biological Microscope (Figure 15)
• 1500x Power Biological Microscope
• Binocular Head - 360° Rotatable
• Two of 10x and two of 15x Wide Field Eyepieces
• 4x, 10x, 40x, and 100x Objective Lenses
• Fully Coated Glass Optics
• Metal Body with 360° Rotatable Monocular Head
• Built-in Halogen Illumination
• Mechanical Stage
61
• Five Prepared Slides
• Abbe Condenser
• Iris Diaphragm
• Powers Available 40x, 60x, 100x, 150x, 400x, 600x, 1000x, 1500x
• Coaxial Focus with Coarse and Fine Focus Knobs
Figure 44: Celestron Biological Microscope
62
APPENDIX B
63
APPENDIX C
MATHEMATICA CODE
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
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BIOGRAPHICAL SKETCH