When a drop of liquid with interfacial tension

is placed on a non-wetting solid surface, the drop assumes a shape that is determined by the contact angle

that the liquid makes at the three-phase contact line, in accordance with the Young–Dupré equation (see [1]). Under static conditions, the drop shape must also satisfy the Young–Laplace equation of capillarity, which describes the mechanical equilibrium for two homogeneous fluids separated by an interface:

,

where

and 1/

are the two principal curvatures of the drop and

is a reference curvature at the drop apex (

).

In this Demonstration the shape of an axisymmetric sessile drop is computed for given

,

, and contact angle

. The liquid is taken to be water and the surrounding fluid is air. For computational purposes it is convenient to work with arc length

along the curve and the turning angle

, which is defined in terms of the local slope by

. Introducing

and the arc length

(i.e.,

) as new variables along the interface allows the Young–Laplace equation to be expressed as

where

is the volume and

the surface area of the drop. Thus for a given

and

, specifying the reference curvature

is equivalent to specifying the volume or surface area of the drop.

(or

) decreases monotonically with increasing

.

The sliders let you investigate how the shape of the drop depends on the surface tension

(to simulate the effect of temperature or the presence of a surfactant), the contact angle

, and the radius of curvature

at the drop apex. Either the shape of the drop (a 3D rendition, or its cross sectional profile) can be selected. The button "family of nodoids" displays the nodoid shape family from which the sessile drop belongs (see the blue portion of the curve). The characteristic feature of the nodoid family is that it does not have an inflection point.