ME 125NT
Intro to Nanotechnology
Due: 4/8/2008
1
Problem 1:
You just put 5mL of heavy cream into your 16 oz. coffee and instead of mixing them
together, you just wait for all the cream to diffuse with the coffee. What is the time
scale for this mixing? (You may want to try it out just to make sure you have the right
order of magnitude). What are the parameters that affect this mixing? What are the
relevant Equations?.
Now for the obvious question – how many times faster will this diffusion occur for a
10nL volume of flourescein dye in a 1uL microfluidic channel? What equations are
different? What are the relevant parameters, and how does this differ than at the
macroscale?
Hints: diffusion coefficient is measured in units of m^2/s
ANSWER
For the first three questions we have to look at what is affecting the diffusion. The
variables that have to be considered are the concentration c, diffusion constant D
(this is the coefficient of MASS diffusivity, completely analogous to the coefficient of
THERMAL diffusivity,
α
), time t and distance x. The equation that controls the
diffusion is a second order differential equation and is as follows.
2
2
x
c
D
t
c
∂
∂
=
∂
∂
What this says is that the concentration over a certain time will follow the second
derivative of the concentration multiplied by a constant D. This means that the
higher the concentration the faster it will diffuse. The Diffusion equation is
completely analogous to the heat equation you used in ME 151b, c and you can learn
how to solve this in 140b.
2
2
x
T
t
T
∂
∂
=
∂
∂
α
The diffusion constant D =
υ
*R*T with the units is in m^2/s, where
υ
is a material
constant, R is the universal constant and T is temperature.
Using the coffee cup and milk, we see that the time scale is on the order of minutes
(or even hours if you want it to be completely diffused). From this time, we can solve
for the actual diffusion constant, using the solution to the above equation, and
noting that the solution predicts:
Dt
x
2
=
(in one dimension)
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View Full DocumentME 125NT
Intro to Nanotechnology
Due: 4/8/2008
2
Where x is the one dimension we are looking at, D is the diffusion coefficient, and t
is time.
When scaling down to the smaller dimension, we will first ASSUME that D remains
constant, since it is a property of the fluid. If this is the case, then we can use the
relation above to look at the time scale given a much smaller x. Obviously, all the
D’s calculated will be a different number, so the actual number doesn’t matter, just
the order of magnitude.
Assume we calculated a D = 10
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 Spring '08
 PENNATHUR
 Electron, Photon, Light, metal work function, PHOTOELECTRIC EFFECT DATA

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