Potential Honours Projects
The following list does not aim to be an exhaustive list of honours
projects that I am interested in supervising, it is a list of
things that are interesting to investigate. Don't worry if some of
these projects don't make to you, come and see me for more details 
the comments make sense to me.
Autothermal processes combine
exothermic reactions, which produce heat, and endothermic reactions,
which take heat out of the system.
The advantages of autothermal reactors include:
 In conventional reactors energy must be supplied for endothermic
reactions to proceed, typically through the use of external burners
or interstage heaters.
The exothermic reaction produces heat, increasing the temperature of
the reactor and increasing the rate at which the endothermal process
occurs.
In an autothermal reactor we get
the heating for free. The absence of an external burner and the
accompanying power supplies makes the system both simpler and less
expensive.
 The endothermal reaction controls the temperature of the system,
making it less likely that thermal runaway
will occur as it provides a source of cooling.
 If the system is correctly setup then the overall process is energy
neutral. The energy released by the exothermic reaction drives
the endothermic reaction. This is an autothermal reactor.
There is growing interest in the use of autothermal reactors to
efficiently produce hydrogen from natural gas, and other fuels such as
ethanol, for use in fuel cells.
Such technology has great potential as an energy supply for compact
mobile power supplies, which can be used in homes and cars of the future.
It can also be scaled up to provide a distributed supply of energy for
industrial markets.
The use of such reactors will contribute towards reducing
greenhouse gas emissions.
Hydrogen can be produced through the catalytic reforming of hydrocarbons.
This process
couples endothermic
steam reforming with exothermic oxidation to create hydrogenrich fuel
feeds.
In this project we will examine some simple
models for this process.
Many chemical engineering processes can be modelled as endothermic and
exothermic reactions either in parallel, or in series or in competition.
Such reaction schemes, modeled by relatively simple systems of
nonlinear differential equations, give raise to complicated
behaviour.
Generation of heat within the human body. References supplied by
Professor Brian Gray are:
Biological Applications of Combustion Theory, with N.A. Kirwan and P. Gray.
Combustion and Flame 18, 439, 1972.
Heat Generation in Tissues, Bulletin of Mathematical Biology, 42, 273 (1980).
Distribution of Heat Sources in the Human Head, Journal of Theoretical
Biology, 82, ???
Surface law and Metabolic Rate. J. Theoretical Biology, 2, 757, 1982.
Physical Theory of Enzyme Catalysis (with I. Gonda).
J. Theoretical biology, 94, 513 (1982).
The last one is quantum mechanics, so you might not want to know about
that.
Wet combustion. Build proper models for moisture transport,
evaporation, condensation into the model. Biology+chemistry.
ReactionEngineering Model.
 Panikov, N.S. Microbial Growth Kinetics. Chapman & Hall,
UK, 1995.
 Identification of ODE Models.
Ordinary differential equation (ODE) models have been widely used
to model physical phenomena, engineering systems, economic behaviour,
and biomedical processes. In particular, ODE models have recently
plyaed a prominent role in describing both the within host dynamics
and epidemics of infectious diseases and other complex biochemical
processes. Great attention has been paid to the socalled
forward problem or simulation problem, i.e.\ predicting and
simulating the results of measurements or output variables for a given
sustem with given parameters. However, less effort has been
devoted to the inverse problem, i.e., using the measurements of
some state or output variables to estimate the parameters that
characterises the system, especially for nonlinear ODE models
without closed form solutions.
H. Miao et al. SIAM Review 53(1),
339, 2011.
339, 2011.
Suppose that we have a mathematical that contains n ODEs.
We can measure m (m≤n) output variables. The model contains
p parameters. Can we estiamte the p parameters from measurements
on the m output variables?
Idea has been applied to Monod model (page 10). There are plenty
of other models to try.
 A system with two tanks, one aerobic, one anaerobic and one settler.
 Look at doublesubstrate inhibition models with constant yields.
(Follow up to Tim's advanced maths project with emphasis on stability
calculations).
(wusc:2007)
 Variable yield model with death. suzuki:1985.
 grieves:1968 Look at twotank model with variable volume distribution
and variable feed distribution.
 Hydrolysis of substrate (Contois) followed by Monod reaction.
Could be two bacteria or the same.
See papers by Gawande, Ramirez.
 Two microbial species competing for one substrate.
 What if the substrate follows a logistic equation so this is not
a chemostat?
(a good keyword). See sonmezisik:1998.
"Under certain conditions, the growth rate of an organism may be simultaneously
limited by two or more substrates" (69).
beyenal:2003 Double substrate kinetics that are both Tessier. (Standard is
to use monod for both).
yurt:2002 "It is wellknown that the microbial growth rate often depends
on more than one substrate (Machado et al 1989; Beyenal and Tanyolac, 1997;
Neeleman et al, 2001).
A fancy phrase of biodiesel production is
biotechnology oil production.
 Examine models for the production of ethanol through the growth
of Saccharomyces cerevisiae growing on ethanol.
(joneskd:1999)
 tyagi:1980 has a model with substrate and product inhibition
with a four reactor cascade.
 ghose:1979a recyle experiments (interesting to assume that all
product is extracted from the recycle process).
 ghose:1979b substrate limitation and product inhibition.
 dourado:1987 distributed feeding is a way of removing the negative
effect due to substrate inhibition... In a cascade reactor, part of
the fermentation is carrief out in a lowethanolconcentration
environment (the first reactors)... A cascade of reacors allows us
to distribute the global dilution rate and the input substrate
among several reactors. First, the substrate concentration in each
reactor can be adjusted in order to reduce substrate inhibition...
The advantage of a cascade reactor is that it allows a substantial
increase in ethanol productivity... The distributed feeding appears to be
interesting for two main reasons. First, it allows us to eliminate the
drawback of the washout state if one is interested in a low output
ethanol concentration. Second, if the output ethanol concentration is
high, distributed feeding is profitable when the model is strongly substrate
inhibitory.
 Substrate inhibition continued. Repeat Hill and Robertson (1989)
but consider multistream feed strategies.
 economou:2010: batch model for biodiesal production.
 M. Stamoszewski and S. Koter. Theoretical analysis of steady state for
ester hydrolysis in an enzymatic membrane reactor with production
retention. Desalination, 248 (2009) 224234.
 staniszewski:2009
ester hydrolysis when the maximum growth rate depends upon the
pH of the solution which in turn depends upon the product concentration.
 R. Suresh and M. Chidambaram. Periodic operation of well mixed
enzyme reactors with steady state multiplicites using relay feedback.
Bioprodess Eng, 16 (1997), 225227.
 P.Y. Ho and H.Y. Li. Determination of multiple steady states in
an enzyme kinetics involving two substrates in a CSTR. Bioprocess Eng.,
22 (2000) 557561.
 J. VasquezBahena, M.C. MontesHorcasitas, J. OregaLopez,
I. MaganaPlaza and L.B. FloresCortera. Multiple steadystates in a
continuous stirred tank reactor: an experimental case study for hydrolysis
of sucrose by invertase. Process Biochem., 39 (2004) 21792182.
justification purwadi:2008
 ADM1 model. See ramirez:2010.
Incomplete mixing
A simple model for the dynamics of an anaerobic wastewater treatment
system is to treat it as two reactions: acidogenesis and
methanogenesis.
aS > cA +X
dA > CH4 +M
S is the organic substeate, A is the volatile fatty acids,
X is acidogenesis bacteria, CH4 is methane and
M is methanogenesis bacteria.
In the first reaction, the acidogenic bacteria (X) consume the
organic substrate (S) and produce volatile fatty acids (A).
In the second reaction, the methanogenic bacteria (M) use the volatile
fatty acids as substrate for growth and produce methane. The anaerobic
digestion process must be operated such that the acidification
(accumulation of volatile fatty acids) of the reactor is avoided.
Apply ideas to blood coagulation model. pompano:2008.
AMT have developed a nanoparticulate membrane bioreactor (NMB)
which has been shown to work at various scales with gray water,
grease trap waste, sewage and many different industrial waste water
streams such as effluents from breweries, wineries and a
detergent factory. We will develop models from this process based
upon partial differential equations.
(See work folder for chemeca flyer).
(Note basic membrane reactor model also appears in yoonsc:2004).
Food processing wastewaters and slurries typically contain high
concentrations of biodegradable organic matter. Before the wastewater
can be discharged the pollutant concentration must be reduced. One way
to achieve this is through the use of a biological species
(`biomass') that consumes the organic matter (`substrate').
In this project we will examine what happens when competition is moved
up one level by investigating what happens if there is a predator that
grows by consuming the biomass. Our interest is in how this competition
influences the level of pollutant that is discharged from the reactor.
 diffusion models. "Predator inhibition models".
hsusu:1978 papers.
 What happens if there are two species competing for one food
source (Monod model, the `weaker' one must become extinct)
but the weaker species is also a predator?

A biological wastewater treatment process can be considered as an artificial
ecosystem, and activated sludge is an ideal habitat for
several organisms other than bacteria. One way to reduce sludge production
is to exploit higher organisms such as protozoa and metazoa in the
activated sludge processes that predate on the bacteria whilst decomposition
of substrate remains unaffected... In an activated sludge system the
grazing fauna mainly consists of protozoa and occasionally
metazoa. Protoa present <1% of the total dry weight of a wastewater
biomass, and 70\% of protozoa are ciliates [6,88]. The protozoa present
can be divided into four groups: ciliates (free swimming, crawling and
sessile),flagellates, amoeba, and heliozoa [89].
It is well known that the presence of protozoa and metazoa in
aerobic wastewater treatment processes plays an important role in keeping
the effluent clear by consuming dispersed bacteria... Recently, many
researchers have focused on sludge reduction induced by grazing on
bacteria [90107].
weiy:2003
 The Twostage system considered in weiy:2003 with predators only in
the second stage.
 Periodic forcing.
 COnsider the classic threestep food chain but allow the substrate
to be another animal species with a decay rate. How does this effect
the behaviour of the system?
 In a membrane reactor. Perhaps the membrane reactor only applies to
one of the species or perhaps it applies to both species?
 Predatorprey with variable yield.
 X > substrate + particulates and predators!
Another application is to reduce excess sludge production in
the activated sludge process  zhangb:1996
 Sludge disintegration inside a normal bioreactor. EB
Yasui and Shibata (weiy:2003, 31) developed a new process for
reducing sludge production in the activated sludge process. The
process consists of a sludge ozonation stage and a biodegradation
stage, in which a fraction of recycled sludge passes through the
ozonation unit and then the treated sludge is decomposed in the
subsequent biological treatment.
 Add a model for sludge disintegration.
Thomas' model should be extended from 3 ODE to 6 ODE. The
sludge disintegration unit should be treated as a second reactor.
EDB
 Easy project is to look at exact parametric sensitivity in the
yoon model using the exact steadystate values.
 EDB. Note that the usual model for sludge
disintegration assumes that μ_{m} and K_{S}
are the same for all soluble organic materials, whether they are
originated from influent or disintegrated liquor.
 The ultimate sludgedisintegration model is to use the bioreactor
model from yoonsh:2005 with simple kinetics.
 Should look at a disintegration unit inside a normal bioreactor.
Variation of MLSS in a cascade of reactors with sludge disintegration
units?
 grady:1980chap12 might be useful for background models with
nonviable cells.
 Reconsider the model with a variable yield coefficient and
nondimensionalise it correctly. Add death to the model.
 Determine performance of the optimised cascade and
the cascade with equal residence time for two and three
reactors.
 Reinvestigate membrane model. H21 bifurcation curve
in alphabetak_d plane.
(note basic membrane bioreactor model also appears in
yoonsc:2004)

 Model of a fixedbed biological process and a generalized
model of a fixedbed biological process
 The fixedbed reactor as two completely mixed compartments in
parallel (Escudie et al., 2005).
 Contois model with X_{0} not equal to zero. EB.
stress related death in a model with oxygen transfer (Rubayyi).
replace V*k*X by V*(k+a*KLA)*X where KLA is the oxygen mass
transfer coefficient. Idea is that the intense mixing needed for
oxygen transfer increases the stress on the biomass.
see cliffe:1988 (page 280)
 harmand:2006b looked at the standard model with recirculation and
bypass in a control session. Can this be extended to the contois
model?
 Investigate a model with a sludge disintegration system
(cf thomas' masters project)
 Ice cream in a series of membran reactors.
 Use Andrews solutions for a two and three reactor cascade.
Use the optimisation functions of Erickson and Fan (1968).
This is really an optimisation project, rather than a dynamical
systems project. Similarly can look at the paper by Grieves and Kao.
And the paper by Scuras (2001). And Hill and Robertson (1989).
Harmand et al (2003) is definitive for some systems.
Could reinvestigate the effect of death upon many of these systems.
It's interesting the in the paper with Andrew I observed that
at high residence times equalresidence times give a performance
that is very nearly optimal. Optimising the reactor design only
seems to bring improvements at low residence time. Is this a
function of death?
Investigate recycle.
Good
 grady:book page 640.
Step Aeration Activated Sludge (SAAS)
can be modeled as four CSTR's in series with feed
distribution to each tank
 Production of ethanol in multiple reactors including cellrecycle.
Use a simple product inhibition model. How do we estimate parameter values
from experimental data?
 Add recycle to current model.
 Optimisation of reactors, see Hill and Robertson (1989). Could compare
different product inhibition mechanisms.
 wall:1992 A good approximation to this phenomenon is the linear
inhibition model of Ghose and Tyagi (1979).
μ = μ_{m}S/(K_{S}+S)*(1P/K_{I})
where K_{I} now represents the maximum ethanol concentration
above which growth ceases. Optimisation in a sequence of tanks?
 zhangj:2009. Death
Ethanol is formed to not only inhibit the specific growth rate,
but also to acclerate death.
k = k_d +alpha*exp(D*[ethanol]).
 Hill function. See ramirez:2010.
 ishizaki:1995. The kinetic parameters for substrate/microorganism/product
(eg \mu_max, K_s, K_i) could be different.
 Reexamine models including direct product formation from the
substrate.
 models with nongrowth associated product formation
dinopoulou:1988
Extend Soji model to consider different kinetics: Monod, Contois, Andrews
and product inhibition.
(note basic membrane bioreactor model also appears in
yoonsc:2004)
 Add a model for hydrolysis of death biomass.
EDB
 Oxygen as a variable with oxygen transport.
stress related death in a model with oxygen transfer (Rubayyi).
replace V*k*X by V*(k+a*KLA)*X where KLA is the oxygen mass
transfer coefficient. Idea is that the intense mixing needed for
oxygen transfer increases the stress on the biomass.
see cliffe:1988 (page 280)
 Model wall growth.
 bungay:1968 "In our laboratories, some studies of competition have
shown that adherence to the walls of the vessel can be a key factor in
competition. A slower growing species can persist in appreciable
numbers in competition with rapidly growing organisms if the slow
grower is continually reinoculated from the wall growth into the main
liquid bulk".
 senn:1994 "It is wellknown that wall growth can affect
steadystate concentrations in chemostat cultures. This effect
should be most pronounced at low input substrate concentrations
in the medium feed where the proportion of biomass on the
wall is high compared to that in solution".
 canale:1973
"a massive protozoan lysis had occurred. This cell lysis caused
considerable amounts of debris to accumulate within the medium".
Two other continuous runs of short duration at low dilution rates
resulted in a similar breakdown of the Tetrahymena population.
See predatorprey notes for a simple model.
 Models in which both species produce a toxin for each other with a
variable yield coefficient.
 abulesz:1987 investigated time delay models. This leads to
a system of three, rather than two, equations. This opens up a large
avenue of potential problems!
"All unstructured models predict a response to stepchanges in
operating variables which is faster than experimentally observed (40).
This is a result of the inherent assumption of those models
that there is no time lag between changes in the substrate level and
adjustment of the growth rate at the appropriate level. To relax
this assumption, one may assume that the specific growth rate is a
function not only of the present substrate level but also of previous
levels in a weighted manner". See also their references (41 & 42)
and page 1062.

 beyenal:2003 "It was expected that at low agitation rates the growth of
microorganisms was limited by external mass transport. Therefore, when
the agitation rates increased, the mass transfer rate to the microorganisms
increased, along with the SOUR, which reached a maximum value.
Increasing the agitation rate beyond this maximum actually decreased the
SOUR, probably because the agitation was injuring the microorganisms."
 yurt:2002 At low agitation rates, Leptothrix discophora
SP6 aggregated, and at higher agitation rates it was mechanically
damaged.
 Is it possible to investigate a stochastic version of the standard
model and investigate the effect on washout conditions?
 Standard model with dead cells. See grady:1980 for background and
also link this to the sludge disintegration unit work.
 grady:1980. Basic CSTR model with nonviable cells.
 grady:1980. Recycle models.
There are four cases of particular interest, all of which will use equal
reactor volumes. In the first case, the system corresponds to a simple
chain, with all feed and all recycle going to reactor one. In case two,
the feed and recycle are distributed evenly amongst the four tanks.
In case three, the feed is distributed evenly among the four tanks and the
recycle is added to tank 1, whereas in case four, all
recycle is returned to tank 1 and all feed enters tanks 3.
 grady:1980. Extend the basic model to analyse oxygen demand. This
can then be used to determine waste stabilisation. (chapter 12).
This would make a good six creditpoint project.
 Velocity dependent death rate. Speak to John Kavanagh about
"shear intolerance".
 Asymptotics for membrane reactor cascade (contois). Compare
against conventional reactors.
 jostc:2000 has lots of interesting things to read.
The first approach to reconcile theory and experiment was to
introduce flexible models that contain both Monod's and Contois's
functions as special cases (Roques et al 1982, Borija et al. 1995).
μ(S,X) = μS/(K_{s}+S+cX)
This form was introduced independently in ecology by
DeAngelis et al (1975) and by Beddington (1975).
 incomplete mixing using the standard approach. First assume
no death.
 Incomplete mixing. Allow epsilon to be a function of delta.
epstein:1995
 roques:1982 proposed a general rate expression which includes
both the Monod and Contois expressions as special cases:
μ(S,X) = &mu_{max}S/(S+a+bX).
 Model recycle more realistically (if possible) by looking at
sludge thickness analysis. See references [62,65] on page 673 of
grady:book for starts. SIAM paper. two substrates and two microorganisms. How does
longterm behaviour depend upon parameter values?
 bush:1976 deathrate ``is assumed to be independent of the substarte
concentration''.
 substratedependent death. huangd:2011 is a cracker.
See also standard model.
 bajpai1980:
Hegewald and Ruckbeil (20) have proposed a substrateinhibition model
for product formation and aghve simulated product formation by
Streptomyces hygroscopicus in continuous culture.
 Systems with Tissiet kinetics. fug:2005
 Edwards kinetics (sonmezisik:1998 reference 17)
 Luong kinetics (sonmezisik:1998 reference 18)
 Tessier kinetics with substrate inhibition and product inhibition
annuar:2008. Need to check out the reference (Heinzle and Lafferty, 1980).
 Tessier kinetics with a sludge disintegration system.
 mazutti:2009 has a list of 19 (!) kinetic equations for biomass
growth.
This project will investigate models for the sterilisation of
canned food. It will involving solving PDEs numerically.
See mohamed:2003 for references.
Dong suggests the following as a good research problem for a strong
PhD student
My suggestion is to work in heat/mass transfer (in drying) coupled with
mechanics (stress strain analysis)...this can make a difference in
literature.
The ideal candidate is to look at how micron sized particles (functional
particles for medical or food purpose) formed during liquid removal.
So far heat and mass transfer have been investigated a great deal but the
formation of the shell and shell structure has not been touched which I feel
very very important.
Icecream is quite an interesting substance (as well as one that is nice
to eat!). This project will investigate PDE models for the manufacture
of icecream.
For orally administered live bacteria (probiotics) to function,
they must be protected from the high concentration of bile acids that are
found in the intestine. This is essential to ensure reproducible and
efficient live cell delivery.
This project will use reactiondiffusion models to investigate how the
incorporation of bile adsorbing resins into capsulated drug delivery
systems protects probiotic bacteria.
 This is a numerical PDE's project. You will model heattransfer
through the human skin in order to estimate how long an individual
can be exposed to a specified heatflux before the skins develops
burns of a specified intensity.
(The model already exists. The aim of this project is to code up
the model).
Extend CTM paper on heterogeneous catalysis from a single reaction to
a bimolecular reaction.
 2 predator1 prey model (hsusb:1978 papers) with diffrent forms
for the diffusion terms. Perhaps even the 1 predator model is of
interest?
 R.S. Cantrell and C. Cosner. Spatial Ecology via ReactionDiffusion
Equations. Wiley. 577.0151/3.
Malchow, S.V. Petrovskii, Venturino. Spatiotemporal Patterns in Ecology
and Epidemiology. 577.015118/2
S. Cantrell, C. Cosner and S. RUan. Spatial Ecology.
577.015118/5.
 Apply semianalytical technique to RD equations.
 jostc:2000 has lots to say about predator dependent
growthrates in mathematical ecology in analogy with
microbiology and provides good references.
 BrindleyTruscott model. Contois formulation? PDE formulation applying
semianalytical technique?
 tian:2011.
Turing patterns created by crossdiffusion for a {Holling II} and
{Leslie}{Gower} type three species food chain model
 Predatorprey models. Predators might diffuse up the prey gradient.
 Competition for nutrients and other resources is an interaction
common among microbial species growing together in the same
environment. Competition tends to eliminate species from the system.
The main question then is whether the competing microbial species
can coexit and under what conditions.
pavlou:2013
Followup on Dong's heattest method. Look for solutions to the
linear problem? HAM solutions?
 Spherical particles with concentric layers of inert and drug.
Can target timetorelease by design of layers.
 Maybe c(r)  internal concentration of drug as a function of
radius as a way to control drug delivery rate.
 Want to achieve a constant delivery of drug.
 Maybe we could design different biodegradable materials with
different k values. Then distribution of k values leads to a
different delivery profile.
The food industry offers a surprisingly rich variety of interesting
problems in applied mathematics. Here are a couple that I am interested
in.
 Drying of small particles
 We will investigate the composition and temperature of spraydried
particles using distributed drying kinetics. This model will be
used to investigate segregation, which has been observed experimentally
during the spray drying of milk.
(Model can also be applied to the rice swelling problem.)
 Drying of a French Fry
 This project involves modelling the frying of a french fry in
hot oils. The primary practical interest in this problem is to
drive vapour out of the fry and this is what we will seek to
model. The chicken pattie model may be useful for this problem...
 Volume increasing + decreasing. Fit data to wrong models?
EB?
 Spratt, P., Nicolella, C., Pyle, D.L. (2005) An engineering model
of the human colon. Trans IChemE, Part C, Food and Bioproducts
Processing 83 (C2), 147157.
 Develop a model for how the pH changes in the human stomach
following a meal. Combine this with a model for the delivery of
a particulate drug. How do certain gastrodisease effect the
delivery of the drug?
 Investigate how the diffusion of bile
(secreted into the small
intestine) into a tablet kills dried bacteria. Investigat
mechanisms for retarding the uptake of the bile by the bacteria.
You will need to learn numerical methods for solving PDEs!
Dong: I think if u can incorporate the detailed chemistry in the stomach and
also some dimensional effect such as the breakdown of the encapsulated
materials...that shoulod be meaty enough.
Contract Troy!
Many chemical engineering processes can be modelled as endothermic and
exothermic reactions either in parallel, or in series or in competition.
Such reaction schemes, modeled by relatively simple systems of
nonlinear differential equations, give raise to complicated
behaviour.
Classic firstorder nonisothermal reactor PLUS nonperfect mixing models.
This would be a jointproject with Professor T.R. Marchant.
 Problems with prescribed flow conditions. John Dold's talk at
the John Clark meeting.
 Biochemical Engineering Book. Chapter 7.3.
 GrayScott model. Extensions from citations to papers
by Lin.
 reactive flows. Dold's papers. Look for "vorticesflow".
 blood coagulation model from pompano:2008
 Aris books
 S.P. Hastings. Classical Methods in Ordinary Differential Equations.
American Mathematical Society. (maybe, need to look at it).
See also
Mathematical Ecology and Epidemiology
Dong's salt diffusion problem as a twolayer diffusion problem.
Apply the mean action time approach used by Hickson.
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Page Created: 27th October 2007.
Last Updated: 9th January 2014.