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University of Birmingham Research Archive
e-theses repository
This unpublished thesis/dissertation is copyright of the author and/or third
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as modified by any successor legislation.
Any use made of information contained in this thesis/dissertation must be in
accordance with that legislation and must be properly acknowledged. Further
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Acknowledgements
Firstly, I would like to show my deepest gratitude to my supervisors Prof. Mike Adams and
Prof. Zhibing Zhang for their outstanding guidance and constant support. It is their valuable
advice and inspiration that made certain that my work was to maintain a consistent standard
and it is their remarkable patience that kept me motivated and encouraged when facing
challenges.
I give my great thanks to Dr. James Bowen for his excellent technical supports and useful
discussions which I benefit a lot, and who is always being an excellent example of a scientific
researcher to me.
I would also like to give my sincere thanks to Dr. Shiping Zhu and Dr. Guoping Lian from
Unilever for giving me an unforgettable industrial experience, and my gratitude extends to
The School of Chemical Engineering at The University of Birmingham, Unilever, Colworth,
China Scholarship Council who have provided me the precious opportunity and financial
support.
I give my great thanks to Dr. Ruben Mercade-Prieto, my fellow members of my research
group and the excellent staff in The School of Chemical Engineering including Hazel
Jennings, Elaine Mitchell, Lynn Draper, and Kathleen Hynes for their countless help and
efforts.
I would thank for my dear grandma and my parents for always being understanding and
encouraging throughout my difficult time in my studies. I would also thank my boyfriend Kai
Lee for his constant encouragement and his help on the MATLAB, who himself is an
excellent PhD student.
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function xdot=membrane(t,x);
xdot = zeros(1,1);
cd0=1.51; % intial conc in donor mg/ml
va=0.6; % acceptor volume, ml
A=3.1416/4*0.008^2; % membrane area, m^2.
vd=0.1; % donor volume, ml
mm0=29.52*10^(-3); % initial caffeine in membarne, mg
Kvm=0.02952/1.46572; % product of equilibrium constant and membrane volume,
ml
Km=11.49*10^(-6); % permeability in cm/s
%x(2)=(cd0*vd+mm0-x(1)/2*Kvm-x(1)*va)/(vd+Kvm/2) % concentration in donor
chamber at time t, mg/ml
%xdot(2)=(-xdot(1)/2*Kvm-xdot(1)*va)/(vd+Kvm/2)
%Mt=Kvm/2*(cd+x(1))*10^(-2.7552)/(7.62*10^-3)*(t/60)^0.2126; % mg
if t<600
P2=2.653*10^-3/600/(7.62*10^-3)*Kvm/2*((cd0*vd+mm0-x(1)/2*Kvmx(1)*va)/(vd+Kvm/2)+x(1))% initial two points, mg/s
end
if t>=600
P2=Kvm/2*((cd0*vd+mm0-x(1)/2*Kvm-x(1)*va)/(vd+Kvm/2)+x(1))*10^(1.0153)*0.2126*(t)^(-0.7874)
end
xdot(1)=P2/va/2+Km*A/va*((cd0*vd+mm0-x(1)/2*Kvm-x(1)*va)/(vd+Kvm/2)x(1))*10^4;
t0=0;tf=18000;
x0=[0]'
[t x]=ode23('membranefinal',t0,tf,x0);
plot(t,x)
legend('x(1)')
title('C in the acceptor')
xlabel('t')
ylabel('Ca')
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