4.1 Disjoining Pressure
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Here is the problem: the liquid in the wetting film does not drain out to the
surrounding bulk liquid despite its greater mechanical pressure than the pressure in
the adjacent bulk liquid. To the contrary, one will need to apply even more pressure
to squeeze the trapped liquid film out. How can this be?
The reason why one needs to apply an excess mechanical pressure to squeeze out
a wetting liquid film from between the solid wall and the approaching bubble, which
already has a higher pressure than the surroundings, is that the liquid film wets the
solid surface and resists being removed. The thin liquid film has a positive disjoining
pressure (negative chemical potential) which would keep pulling the liquid in from its
surroundings. As the liquid film thins due to the compression, the negative gradient
in the disjoining pressure steepens (the chemical potential differential broadens) and
the film will pull even more liquid in from its surrounding bulk liquid.
The external mechanical pressure applied to the thin liquid film will increase
the mechanical pressure and consequently raise the chemical potential of the liquid
molecules trapped inside the film. In order to squeeze the trapped liquid film out,
the mechanical pressure must exceed the threshold that corresponds to the chemical
potential increment that matches the negative chemical potential due to the disjoining
pressure. Thus, if one can measure the tipping point when the film first starts to drain,
one can deduce what the disjoining pressure inside the film has been at the tipping
point.
The above considerations apply equally to negative disjoining pressures. The
liquid in a non-wetting film (negative disjoining pressure) would easily collapse or
drain out with little or even no compression at all, because it has a higher chemical potential than the surroundings. Here the positive excess pressure inside an
approaching bubble is sufficient to easily displace the liquid between the wall and
the bubble.
4.1.3 The Origin of the Disjoining Pressure
We showed the definition and phenomenological descriptions of the disjoining pressure to provide the readers with the conceptual ideas behind the disjoining pressure.
But what is the physical origin of the disjoining pressure? When Derjaguin and
Obuchov originally studied the attachment of a bubble onto a glass wall that was
immersed inside a liquid, they observed that a thin liquid film separated the glass
wall from the bubble. The force in the thin liquid film that held the bubble downward
against the buoyancy was named disjoining pressure because it “dis-joined” (separated) the solid wall from the gas phase. Such a system can be described schematically
in Fig. 4.4 in which one semi-infinite medium is denoted as 1, the other semi-infinite
medium as 2 and the thin film in between as 3.
Consider a common case in which the medium 1 is a gas (g), the medium 2 is a
solid substrate (s), and the medium 3 is a thin liquid film (l). The Gibbs free energy
per unit area of a single-component system of this setting can be written as,
87
Here is the problem: the liquid in the wetting film does not drain out to the
surrounding bulk liquid despite its greater mechanical pressure than the pressure in
the adjacent bulk liquid. To the contrary, one will need to apply even more pressure
to squeeze the trapped liquid film out. How can this be?
The reason why one needs to apply an excess mechanical pressure to squeeze out
a wetting liquid film from between the solid wall and the approaching bubble, which
already has a higher pressure than the surroundings, is that the liquid film wets the
solid surface and resists being removed. The thin liquid film has a positive disjoining
pressure (negative chemical potential) which would keep pulling the liquid in from its
surroundings. As the liquid film thins due to the compression, the negative gradient
in the disjoining pressure steepens (the chemical potential differential broadens) and
the film will pull even more liquid in from its surrounding bulk liquid.
The external mechanical pressure applied to the thin liquid film will increase
the mechanical pressure and consequently raise the chemical potential of the liquid
molecules trapped inside the film. In order to squeeze the trapped liquid film out,
the mechanical pressure must exceed the threshold that corresponds to the chemical
potential increment that matches the negative chemical potential due to the disjoining
pressure. Thus, if one can measure the tipping point when the film first starts to drain,
one can deduce what the disjoining pressure inside the film has been at the tipping
point.
The above considerations apply equally to negative disjoining pressures. The
liquid in a non-wetting film (negative disjoining pressure) would easily collapse or
drain out with little or even no compression at all, because it has a higher chemical potential than the surroundings. Here the positive excess pressure inside an
approaching bubble is sufficient to easily displace the liquid between the wall and
the bubble.
4.1.3 The Origin of the Disjoining Pressure
We showed the definition and phenomenological descriptions of the disjoining pressure to provide the readers with the conceptual ideas behind the disjoining pressure.
But what is the physical origin of the disjoining pressure? When Derjaguin and
Obuchov originally studied the attachment of a bubble onto a glass wall that was
immersed inside a liquid, they observed that a thin liquid film separated the glass
wall from the bubble. The force in the thin liquid film that held the bubble downward
against the buoyancy was named disjoining pressure because it “dis-joined” (separated) the solid wall from the gas phase. Such a system can be described schematically
in Fig. 4.4 in which one semi-infinite medium is denoted as 1, the other semi-infinite
medium as 2 and the thin film in between as 3.
Consider a common case in which the medium 1 is a gas (g), the medium 2 is a
solid substrate (s), and the medium 3 is a thin liquid film (l). The Gibbs free energy
per unit area of a single-component system of this setting can be written as,