Module 3: "Thin Film Hydrodynamics"
  Lecture 11: ""
 

 

If the film thickness is very small , the potential energy due to interaction between the substrate and film needs to be taken into account. Electrostatic interactions can also be important.

where accounts for the other interaction potentials. It is a function of and hence, of

(3.9)

 

 

This is a non-linear PDE of 4th order, which can generally be solved only using numerical techniques.