Energy Method for Stability of Superposed Fluids

Example 5.5 Energy Method for Stability of Superposed Fluids 

Use Equation 5.127 to determine the stability condition for superposed fluids. Solution 

This result agrees with that obtained by the general analysis above (see remark following Equation 5.61). 

In systrans where A is a thin Uqtttd film in gas, the effect of gravity in Equation 5.126 is replaced by that of disjoining presstrre. As Eqttation 5.104 indicates for an equilibrium film having a tmiform value of 1), taken as zmr for converrience. Pa is given by -( )y + )e), which, in tirm, is V(H -i- H ). Recogrrizing that 

Manipulations similar to those above for a single interface yield the same expression for as in Equation 5.119. For a thin liquid film on a solid surface, only the fluid interface is deformed and the faetor of 2 disappears from the term multiplying (dll/dh) in Equation 5.128. 

---