Capillary Pressure in Fluids

Study Notes

Capillary pressure is influenced by interfacial tension, adhesion tension, wettability, and chemical properties of fluids and solids.

Interfacial tension (σ12) between two fluids signifies the force needed to create new surface area.
Measured in dynes/cm, it reflects specific surface energy.

Occurs when two immiscible fluids contact a solid surface.
The force balance equation is: σso = σsw + σwo cos θ, where θ is the contact angle.
Adhesion tension (AT) is defined as: AT = σso − σsw.

The wetting of a solid surface changes according to the contact angle (θ).
Smaller contact angles result in larger wetted areas by water, thus enhancing wettability.
Wettability is linked to the adhesion tension.

Molecular interactions at solid-fluid and fluid-fluid interfaces affect interfacial tensions and thus contact angles.
The chemical makeup of solids and fluids, particularly mineralogy and fluid types (oil and water), affect wettability.

In a vertical capillary tube submerged in water, a preferentially water-wet glass draws water up to a height (h).
The pressure at the free water level (h = 0) in the beaker is represented as pa.
Water pressure in the capillary at height h is calculated as pw = pa − ρwgh, with ρw being water density and g the gravitational constant.
Air pressure on the opposite side is pg = pa − ρggh, where ρg is the density of air.
The pressure difference across the interface is given by: pg − pw = (ρw − ρg)gh.