Irodov Problem 2.177
Physics · mechanics · fluid-mechanics · thermodynamics
Problem
Find the lifetime of a soap bubble of radius R connected with the atmosphere through a capillary of length 1 and inside radius r. The surface tension is a, the viscosity coefficient of the gas is 11.Intuitive explanation
A soap bubble loses air through the capillary because the pressure inside exceeds atmospheric pressure due to surface tension. The key is balancing two rates: the pressure-driven flow of gas escaping through the capillary (governed by the Hagen–Poiseuille equation) against the shrinking bubble, whose internal pressure drops as decreases. By setting up the mass flow rate and tracking how changes with time, you can integrate to find when the bubble vanishes.
Intuitive explanation
A soap bubble loses air through the capillary because the pressure inside exceeds atmospheric pressure due to surface tension. The key is balancing two rates: the pressure-driven flow of gas escaping through the capillary (governed by the Hagen–Poiseuille equation) against the shrinking bubble, whose internal pressure drops as decreases. By setting up the mass flow rate and tracking how changes with time, you can integrate to find when the bubble vanishes.