Difference between revisions of "Disjoining Pressure"

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Entry by Kelly Miller
 
Entry by Kelly Miller
  
The disjoining pressure is due to an attractive interaction between two surfaces. It is a pressure due to the attractive force between two surfaces, divided by the area of the surfaces. For two flat, parallel surfaces the disjoining pressure can be calculated as the derivative of the Gibbs energy per unit area.
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The disjoining pressure is the distance dependence of the interaction between two surfaces, either attractive or repulsive. It is a pressure due to the attractive force between two surfaces, divided by the area of the surfaces. For two flat, parallel surfaces the disjoining pressure can be calculated as the derivative of the Gibbs energy per unit area.
  
 
In the case of a film on a substrate, deGennes defined the energy function P(e) as the excess energy of a film on a substrate as a function of film thickness (e). Derjaguin defined the disjoining pressure as the derivative of this energy P(e) as a function of e.  
 
In the case of a film on a substrate, deGennes defined the energy function P(e) as the excess energy of a film on a substrate as a function of film thickness (e). Derjaguin defined the disjoining pressure as the derivative of this energy P(e) as a function of e.  

Latest revision as of 01:46, 15 December 2011

Entry by Kelly Miller

The disjoining pressure is the distance dependence of the interaction between two surfaces, either attractive or repulsive. It is a pressure due to the attractive force between two surfaces, divided by the area of the surfaces. For two flat, parallel surfaces the disjoining pressure can be calculated as the derivative of the Gibbs energy per unit area.

In the case of a film on a substrate, deGennes defined the energy function P(e) as the excess energy of a film on a substrate as a function of film thickness (e). Derjaguin defined the disjoining pressure as the derivative of this energy P(e) as a function of e.

Disjoining 1.png


The disjoining pressure is related to the stability of films. When P(e) is a decreasing function of e (favoring a thick film), <math>\pi (e)</math> is positive and the film is considered to be stable.

Disjoining 2.png


d(e)= increase in thickness e by adding a number of molecules dn=de/Vo where Vo= volume/molecules

If <math>\mu</math> is the chemical potential of the liquid, the energy varies by <math>\mu</math> dn


Disjoining 3.png


The chemical potential is related to the disjoining pressure by:

Disjoining 4.png


Sheluelko devised a method to measure the disjoining pressure using a system under equilibrium. The system is a porous ring filled with the same liquid as in the bulk, in equilibrium with the thin film:


Disjoining 6.png


The ring is subjected to a hydrostatic pressure <math>\rho g H</math> where

p=density of the liquid g= acceleration due to gravity H= height of the column


The chemical potential of the column of water is equal to the chemical potential of the thin film:

Disjoining 5.png


See also:

Disjoining pressure in Surface Forces from Lectures for AP225.


Keyword in references:

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