Like a droplet, bubbles are round because cohesive forces pull its molecules into the tightest possible grouping, a sphere. Due to the trapped air inside the bubble, it is impossible for the surface area to shrink to zero, hence the pressure inside the bubble is greater than outside, because if the pressures were equal, then the bubble would simply collapse. This pressure difference can be calculated from Laplace's pressure equation,
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For a soap bubble, there exists two boundary surfaces, internal and external, and therefore two contributions to the excess pressure and Laplace's formula doubles to
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The capillary length can then be worked out the same way except that the thickness of the film,  must be taken into account as the bubble has a hollow center, unlike the droplet which is a solid. Instead of thinking of a droplet where each side is  as in the above derivation, for a bubble  is now
with  and  the radius and thickness of the bubble respectively.
As above, the Laplace and hydrostatic pressure are equated resulting in
Thus the capillary length contributes to a physiochemical limit that dictates the maximum size a soap bubble can take.