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




                                                                1
    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




                                                                        2
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)

                                                                     7
Solution




           8
Some K values
  Steroid                      K
  Cortisol                     5.5e-3
  Estradiol                    2e-1
  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
    unsteady-state
    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)


                                                         11
   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)


                                                            12
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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posted:3/17/2014
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