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Flux 1
We establish a steady-state concentration
gradient across a 3D gel of length L by
fixing the concentration at one side at CA1
and the other side at CA2. What is the flux
of A?
Flux 2
•  Cells grown on the surface of a Petri dish
produce species A at constant rate ω. Atop
the cells is a collagen gel of height h, and
above that is medium where CA is kept at 0.
What is the steady-state flux at the surface?
Flux 3
Consider phosphorous doping of a silicon
wafer.
In a 1-D system, how does the flux of POCl3
(species A) relate to the flux of Cl2 (B)?
Si + 2POCl3 (g) "
"k → SiO 2 (s)+ 3Cl2 + 2P(s)
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Flux 4
Species A diffues to a surface where it reacts to
form species B. What needs to be true about the
relative diffusive flux and reaction rate in order
for the boundary condition at the surface to be
CA
x =0
=0 ?
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Flux 5
In an Arnold cell, liquid A evaporates into gas
B, and gas B is insoluble in liquid A. How
does NA compare to NB at the liquid surface?
Flux 6
(2 min) Consider again phosphorous doping
of a silicon wafer where POCl3 is delivered
in the bulk. In a 1-D system, assuming
instantaneous reaction, write an expression
for the total flux NA of POCl3 as a function
only of POCl3 (species A).
Si + 2POCl3 (g) "
"k → SiO 2 (s)+ 3Cl2 + 2P(s)
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Flux 7
•  In a drug-eluting stent with drug
concentration CAo, blood flows with a core
velocity vcore and a certain mass is delivered
per unit time. It is now desired to deliver
twice the dosage total to the blood. What
should the new CAo be?
Flux 8
•  In a drug-eluting stent with drug
concentration CAo, blood flows with a core
velocity vcore and a certain mass is delivered
per unit time. If blood flow rate increases by
50% (v’ = 1.5 vcore), how is the total drug
delivery changed ?
Diffusion confusion 1
•  Does salt diffuse faster in a low-viscosity or
high viscosity oil?
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Diffusion confusion 2
•  Does oxygen diffuse faster in cold air (0°C)
or in hot water (99°C)?
Diffusion confusion 3
•  How does the diffusion of a 1 nm particle in
water differ from that of a 10 nm particle?
Diffusion confusion 4
•  Which diffuses faster: a 1 nm particle in a
1.0 cp oil at 298K, or a 2 nm particle in 0.5
cp oil at 310 K?
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Diffusion confusion 5
If we know DAB at temperature T1 = DAB
does
T
DAB T 2 = DAB T1 2
T1
T1
?
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Diffusion confusion 6
•  Name three things that affect the diffusion
coefficient of one gas in another gas.
Diffusion confusion 7
kT
,
6πµB rA
what do the top and bottom terms of the ratio refer to?
In other words what is this a ratio of?
In the Stokes-Einstein equation DAB =
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Boundary Confoundry 1
•  A spherical capsule of radius R is releasing
drug A into a large tissue space. The capsule
maintains constant concentration for short
time periods. List two boundary conditions.
Boundary Confoundry 2
•  A spherical capsule of radius R is releasing
drug A into a large tissue space, where it is
consumed by cells according to rate
RA=kCA. The capsule maintains constant
concentration for short time periods. List
two boundary conditions.
Boundary Confoundry 3
•  A water-filled gel sphere is placed into a
solution of chemical A with CAo. A diffuses
into the sphere. List two boundary
conditions and an initial condition.
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Boundary Confoundry 4
•  Species A reacts instantaneously at the
surface to form species B. What is the
boundary condition at the surface (a) for A,
and (b) for B?
Boundary Confoundry 5
•  Cells grown on the surface of a Petri dish
(x=0) consume species A at a rate
proportional to CA. What is the boundary
condition for A at x=0?
Boundary Confoundry 6
•  Cells grown on the surface of a Petri dish
(x=0) secrete species A at a constant rate ω,
which bind to protein B (inert) in the
medium to form AB* according to a rate k:
A+ B "
"k → AB *
•  What is the boundary condition for B at
x=0?€
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The 5th Dimension(less) 1
•  What dimensionless number compares the
relative contributions of convection and
diffusion?
The 5th Dimension(less) 2
•  What dominates over what when Reynolds
number Re << 1?
The 5th Dimension(less) 3
•  A water-filled gel microsphere (radius =10
µm) is placed in a solution of A (CAo) whose
diffusion coefficient in water is 100 µm2/s.
What is the order-of-magnitude time it takes
for the microsphere to have the same
concentration CAo as in the solution?
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The 5th Dimension(less) 4
•  What number relates DAB with kinematic
viscosity ν?
The 5th Dimension(less) 5
•  The convection coefficient kc depends on
which two dimensionless numbers?
The 5th Dimension(less) 6
•  What dimensionless number compares the
concentration gradient at the surface with
the global gradient into a bulk fluid?
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The 5th Dimension(less) 7
•  How exactly is the Sherwood number
defined?
The 5th Dimension(less) 8
•  How does the Schmidt number relate to the
mass transfer boundary layer thickness δ?
Totally Unassuming 1
•  What assumption needs to be valid
concerning DAB for the following equation to
be true?
∂CA
= DAB ∇ 2CA − v ⋅ ∇CA + RA
∂t
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Totally Unassuming 2
•  Does species A have to be dilute (yA <<1)
for the following equation to be valid?
∂CA
= DAB ∇ 2CA − v ⋅ ∇CA + RA
∂t
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Totally Unassuming 3
•  After what time frame (t >> ?) is it generally
safe to assume steady-state for a diffusion
within a chamber?
Totally Unassuming 4
•  When can a surface reaction be assumed to be
instantaneous?
• 
• 
• 
• 
A.
B.
C.
D.
when reaction rate << diffusive flux
when reaction rate >> diffusive flux
when reaction rate is infinity
when CAs = 0
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Totally Unassuming 5
•  In diffusion into a falling film, if texp is the
exposure time of fluid exposed to gas in the length
of the column and δ = distance into the fluid where
velocity ~ constant, what needs to be true (in terms
of texp and δ) in order for penetration theory
(diffusion into a semi-infinite medium assumption)
to be valid?
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