Unsteady Diffusion into a Sphere

1. Unsteady Diffusion into a Sphere Steven A. Jones BIEN 501 Wednesday, May 16, 2007 Louisiana Tech University, Ruston, LA 71272

2. Diffusion into a Cell Outside: How does the concentration inside the cell change with time? Louisiana Tech University, Ruston, LA 71272

3. Equations Mass conservation Initial Conditions Boundary Conditions Louisiana Tech University, Ruston, LA 71272

4. Non-Dimensional Variables Radial Coordinate Normalized Concentration Time coordinate Louisiana Tech University, Ruston, LA 71272

5. Non-Dimensional Equations Mass conservation Becomes Initial Condition Becomes Boundary Conditions Become Louisiana Tech University, Ruston, LA 71272

6. Separation of Variables Becomes Louisiana Tech University, Ruston, LA 71272

7. Difference from Bessel Because of the factor of 2 in the second term this is not the standard Bessel equation. Louisiana Tech University, Ruston, LA 71272

8. Solution BC at h = 0 Louisiana Tech University, Ruston, LA 71272

9. Boundary Condition at 0 So B = 0 Louisiana Tech University, Ruston, LA 71272

10. BC at Cell Wall So Substitute back: Louisiana Tech University, Ruston, LA 71272

11. Initial Condition in Gives Louisiana Tech University, Ruston, LA 71272

12. Solution Louisiana Tech University, Ruston, LA 71272