Capillarity and Surface Forces (Liquids) - Surface and Colloid Chemistry: Principles and Applications - page 13

real-world situations where γ of both liquids and solids is needed in order to describe
the physics of the surfaces.

2.3 laPlace equatIon (lIquId curvature and PreSSure)
Let us consider aspects in the field of wettability. Surely everybody has noticed that
water tends to rise near the walls of a glass container. This happens because the mol-
ecules of this liquid have a strong tendency to adhere to glass. Liquids that wet the
walls make concave surfaces (e.g., water/glass), and those that do not wet them make
convex surfaces (e.g., mercury/glass). Inside tubes with internal diameter smaller
than 2 mm, called capillary tubes, a wettable liquid forms a concave meniscus in
its upper surface and tends to go up along the tube. On the contrary, a nonwettable
liquid forms a convex meniscus and its level tends to go down. The amount of liquid
attracted by the capillary rises until the forces that attract it balance the weight of the
fluid column. The rising or lowering of the level of liquids into thin tubes is named
capillarity ( capillary force ). Further, capillarity is driven by the forces of cohesion
and adhesion already mentioned.
One notices that a liquid inside a large beaker is almost lat at the surface.
However, the same liquid inside a fine tubing will be found to be curved (Figure 2.3).
This behavior is of much importance in everyday life. The physical nature of this
phenomena will be the subject of this section.
The surface tension, γ, and the mechanical equilibrium at interfaces have been
described in the literature in detail (Adamson and Gast, 1997; Chattoraj and Birdi,
1984; Birdi, 1989, 2002, 2008). The surface has been considered as a hypothetical
stretched membrane , which is termed as the surface tension. In a real system under-
going an infinitesimal process, it can be written that

d W = p d V + p ′ d V ′ − γ d A (2.10)

where d W is the work done by the systems when a change in volume d V and d V ′,
occurs; p and p ′ are pressures in the two phases α and β, respectively, at equilibrium;
and d A is the change in the interfacial area. The sign of the interfacial work is des-
ignated as negative by convention (Chattoraj and Birdi, 1984).

Tube

Beaker

FIGure 2.3 Surface of water inside a large beaker and in a narrow tubing.