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