APPENDIX A
LANGMUIR MODEL DERIVATION
The approach used to develop a closed-form analytical solution for the fractional
coverage of an adsorbed surface film in tribological contact uses a Langmuir adsorption
model. The model development offered here is minimally described and written as
compactly as possible.
dO
- = v'(1-9)
dt
dO = Jv'dt
(1-0)
-ln(1-0)=v't+c
ln(1 -0) = -v't + c
Boundary Conditions:
at t=O
In(l 0.,) = -v'(0) + c
c = In(l- o.,)
ln(1 -9) = -v 't + ln(1 9.,)
(1-9)= exp[-v't +ln(1 Ot)]
(1-0) = exp(-v't)exp[ln(1- Ou,)]