# Review of Mass Transfer - Rowan.ppt

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```					Review of Mass Transfer

n   Fick’s First Law (one          n   Fick’s Second Law
dimensional diffusion)             q   When concentration
q   J flux (moles/area/time)           changes with time
q   At steady-state or any
instant in time

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Example – Fick’s First Law
membrane                          n   Determine amount of
C1                                             drug to pass through
membrane in one hour

C2              n   D    = 1 x 10-10 cm2/s
n   h    = 2 x 10-3 cm
h
n   A    = 10 cm2
SS valid if a high C1 is maintained
n
and
n   C1   = 0.5 mol/L
n    C2 remains << C1 by removal of        n   C2   =0
drug or large volume

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Example Fick’s First Law

3
membrane C <C
Partitioning                                 Cm1
1   m1
the drug
C1              “prefers”
the
polymer
n   So far we have
assumed the drug has                      Cm2
C2
equal affinity for                         h
solution and              n   Flux across membrane
membrane. This is
unlikely.
n   Preference is indicated   n   Cannot measure Cm
by partitioning
n   Partition Coefficient
relates Cm to C

4
Partition Coefficient

n   A measure of relative concentrations in membrane
vs. solution at equilibrium
n   If both solvents (1 and 2) are the same, then

n   Flux becomes

n   The term [DKm/h] is the Permeability

5
Partition Coefficient
n   Sketch the profiles for a high Km and a low Km

C1                               C1

C2                          C2
h                          h
high Km                     low Km

n   Sketch the profile for C2=0
q    Common situation: body acts as a sink to remove the drug

C1

C2=0
h                                          6
Example – Transdermal Delivery

n   Digitoxin (used for heart   n   Km1 = 0.014
failure; ointment)              q    Between ointment and s.c.
D      = 5.2 x 10-10 cm2/s
n   How much digitoxin can      n

Through the s.c.
be delivered                    q

h      = 2x10-3 cm
transdermally in one        n

Typical thickness of s.c.
day
q

n   A      = 10cm2
n   Membrane control –              q    Covered by ointment
skin acts as barrier        n   C1     = 0.01 mg/cm3
membrane (stratum               q    Saturation C of drug in
corneum, outermost                   ointment
layer)

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Solution

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Some K values
Steroid                      K
Cortisol                     5.5e-3
Melengstiol acetate          18.87
Norethindrone                1.22
Norgestrel                   3.19
19-Norprogesterone           33.3
Megesterol acetate           35.7
Mestranol                    100
Progesterone                 22.7
Testosterone                 4.31

Reported by Sundaram and Kincl [93] in Kydonieus, Treatise in CDD

9
Fick’s Second Law

n   For one-dimensional
diffusion

n   How many IC’s and
BC’s are needed?

10
Finite source

Sink                 • IC
(large volume)
• At t=0, C=C0
X=L
• BC1
Diffusion

X=0
• x=L, C=0
X=-L
Polymer               • BC2
containing drug
• X=0, dC/dx = 0
(symmetric)

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Finite source, reflective boundary

Sink              • IC
(large volume)
• At t=0, C=C0
X=L
• BC1
Diffusion

• x=L, C=0
X=0
Polymer                  • BC2
containing drug
Impermeable                 • X=0, dC/dx = 0
boundary at x=0                (symmetric)

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Solution method

n   For cartesian (planar) systems
q   Separation of variables or Laplace Transforms
q   Error function solution
n   We will investigate this later!

13

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