This preview shows pages 1–3. Sign up to view the full content.
x
C
D
J
∂
∂

=
Diffusion
is defined as the movement of solute molecules from a higher to
a lower concentration gradient
occurs by a “
random walk
” mechanism in which molecules are continually colliding
with each other while moving “on average” towards a particular direction
brownie in motion – “
random walk
” – random movement of a molecule by its energy
state – molecules colliding with each other
And gradually diffuse out as it goes on
The
diffusive flux
Where dC/dx is the
concentration gradient
in the direction of solute movement
And D is the constant of proportionality and is defined as the
Diffusion constant
or Diffusion coefficient
Fick's First Law
Fick's First Law is used in steady state
diffusion
, when the
concentration within the diffusion volume
does not change with respect to time (Jin=Jout).
∙
J
is the diffusion flux in dimensions of [(
amount of
substance
) length2 time1], [mol m2 s1]
∙
D
is the diffusion coefficient or
diffusivity
in dimensions
of [length2 time1], [m2 s1]
∙ is the concentration in dimensions of [(amount of
φ
substance) length3], [mol m3]
∙
x
is the position [length], [m]
Movement of a solute in a random manner.
Diffusive flux = mass per unit time
Mathematically proportional to the concentration gradient
Concentration gradient in the direction of the solute movement
J is proportional to the concentration gradient, d = diffusion constant
Diffusion constant depends on what the solute is, where it is (liquid, water, oil)
A property of the solute, but depends on what the solute is
Depends on temperature
Diffusion prop. To energy you give it
Provide heat energy, collides more, moves more
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Documentz
y
x
t
C
a
y
x
J
J
z
x
J
J
z
y
J
J
z
z
z
y
y
y
x
x
x
∆
∆
∆
∂
∂
=
+
∆
∆


∆
∆


∆
∆


∆
+
∆
+
∆
+
)
(
]
[
]
[
]
[
ψ
Negative sign in front? By convention, if movement is high to low, direction of solute
movement, the concentration decreases
You can find out what D is for a particular solvent, using this equation.
You use microscopy techniques to follow its random movement over time.
The root mean square displacement
Square each, take the mean, and square root the answer
If diffusion coeff. Is high > diffuse much more distance
If diffusion coeff. Is low
diffuse much less
Flux proportional to conc. Gradient
What is missing from first law? What is not in the equation?
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '08
 Frey
 Biomedical Engineering

Click to edit the document details