Mechanics of Interfaces Lecture notes

Chapter 4 Surface tension and gravity

This chapter is dedicated to phenomena where surface tension and gravity govern the dynamics. The balance between these two forces generally leads to a static configuration and the object of interest is the geometric shape of the interface.

4.1 Dimensional analysis

Gravity is characterized by the specific weight of the liquid ρg\rho g, where ρ\rho is the liquid density and gg is the acceleration due to gravity. The dimensions of specific gravity are F/L3F/L^{3}, where FF denotes the dimensions of force and LL those of length. Since the dimensions of surface tension σ\sigma are F/LF/L, a balance of surface tension and gravity invariably yields the ratio (σ/ρg)(\sigma/\rho g), which has the dimensions L2L^{2}. Based on this arises the capillary length defined as c=(σ/ρg)1/2\ell_{\text{c}}=(\sigma/\rho g)^{1/2}. For a fluid like water, with σ=72×10-3\sigma=72\times 10^{-3} N/m and ρg=9800\rho g=9800 N/m3{}^{3}, the capillary length is c=2.7\ell_{\text{c}}=2.7 mm.

4.2 Planar capillary meniscus

Figure 4.1: Shape of the planar meniscus. Based on the solution shown in LABEL:eqn:MeniscusSolution.