FIG. 11 A bubble forming at a conical projection (a, on the left) or in a conical cavity (b on the right). The half angle of the cone is β in each case.

Using Young’s equation, γLV cos θ=γSV−γSL, and geometrically evaluating the areas, AA and AB, and volumes, VA and VB, together with the condition for equality of chemical potential at the critical size:

At the critical size, r=r*, the terms can be expanded in a Taylor series. Taking the leading two terms in the Taylor series leads to the full equation for the nucleation rate, J, in a conical pit of half angle, β:

(19)

It will be seen that both preexponential and exponential terms are affected, but as noted earlier, changes in the preexponential are relatively unimportant. The main result is that

the function appears as a multiplier in the exponential, and that in turn depends on both the contact angle, θ and the cone half angle, β. Wilt [32] showed that with a contact angle of 94°, a cone of half angle 4.7° would produce nucleation in a carbonated beverage with a saturation ratio of 5. None of these values is physically unrealistic, although one could argue about how common such sites might be. However, fizziness in Coca Cola appears to be universal.