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

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

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

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

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

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

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

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

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

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

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

Solution Louisiana Tech University, Ruston, LA 71272