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Review of Mass Transfer

Fick’s First Law (one dimensional diffusion) J flux (moles/area/time) At steady-state or any instant in time. Fick’s Second Law When concentration changes with time. Review of Mass Transfer. Example – Fick’s First Law. Determine amount of drug to pass through membrane in one hour

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Review of Mass Transfer

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  1. Fick’s First Law (one dimensional diffusion) J flux (moles/area/time) At steady-state or any instant in time Fick’s Second Law When concentration changes with time Review of Mass Transfer

  2. Example – Fick’s First Law • Determine amount of drug to pass through membrane in one hour • D = 1 x 10-10 cm2/s • h = 2 x 10-3 cm • A = 10 cm2 • C1 = 0.5 mol/L • C2 = 0 membrane C1 • SS valid if a high C1 is maintained and • C2 remains << C1 by removal of drug or large volume C2 h

  3. Example Fick’s First Law

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

  5. Partition Coefficient • A measure of relative concentrations in membrane vs. solution at equilibrium • If both solvents (1 and 2) are the same, then • Flux becomes • The term [DKm/h] is the Permeability

  6. C1 C1 C2 C2 h h high Km low Km C1 C2=0 h Partition Coefficient • Sketch the profiles for a high Km and a low Km • Sketch the profile for C2=0 • Common situation: body acts as a sink to remove the drug

  7. Digitoxin (used for heart failure; ointment) How much digitoxin can be delivered transdermally in one day Membrane control – skin acts as barrier membrane (stratum corneum, outermost layer) Km1 = 0.014 Between ointment and s.c. D = 5.2 x 10-10 cm2/s Through the s.c. h = 2x10-3 cm Typical thickness of s.c. A = 10cm2 Covered by ointment C1 = 0.01 mg/cm3 Saturation C of drug in ointment Example – Transdermal Delivery

  8. Solution

  9. Some K values Reported by Sundaram and Kincl [93] in Kydonieus, Treatise in CDD

  10. Fick’s Second Law • For one-dimensional unsteady-state diffusion • How many IC’s and BC’s are needed?

  11. Finite source • IC • At t=0, C=C0 • BC1 • x=L, C=0 • BC2 • X=0, dC/dx = 0 (symmetric) Sink (large volume) X=L Diffusion X=0 X=-L Polymer containing drug

  12. Finite source, reflective boundary • IC • At t=0, C=C0 • BC1 • x=L, C=0 • BC2 • X=0, dC/dx = 0 (symmetric) Sink (large volume) X=L Diffusion X=0 Polymer containing drug Impermeable boundary at x=0

  13. Solution method • For cartesian (planar) systems • Separation of variables or Laplace Transforms • Error function solution • We will investigate this later!

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