# little engineering/little calc

• Mar 7th 2009, 04:54 AM
dolphin1384
little engineering/little calc
In dealing with metal surfaces that undergo oxidation, the thickness of the oxide film has been found to increase exponentially with time, such that d=dmax (1-e^(-kt)), t>2000 where d=thickness of oxide film and t=time.
This expression is the result of integrating an ordinary differential equation.

I'm trying to derive the Ordinary differential equation and the associated initial condition needed that produces d=dmax (1-e^(-kt))

Any help for how to approach this is much appreciated!
• Mar 7th 2009, 11:17 PM
CaptainBlack
Quote:

Originally Posted by dolphin1384
In dealing with metal surfaces that undergo oxidation, the thickness of the oxide film has been found to increase exponentially with time, such that d=dmax (1-e^(-kt)), t>2000 where d=thickness of oxide film and t=time.
This expression is the result of integrating an ordinary differential equation.

I'm trying to derive the Ordinary differential equation and the associated initial condition needed that produces d=dmax (1-e^(-kt))

Any help for how to approach this is much appreciated!

If:

\$\displaystyle d(t)=d_{max} (1-e^{-kt})\$

Then differentiating:

\$\displaystyle d'(t)=d_{max} k e^{-kt}\$

and \$\displaystyle d(0)=0\$.

CB