Creating small bubbles of soap!

The pressure inside the bubble is at time t when the radius of the bubble is reduced to r will be ${P_{bubble}} = {P_0} + \frac{{4T}}{r}$ . Now, through the capillary of length l, the air is flowing and we can use Poiseuillie's equation for it. That is, $Q = - \frac{{dV}}{{dt}} = \frac{{\pi \Delta p{a^4}}}{{8\eta l}}$ $V = \frac{4}{3}\pi {r^3}$ $\Delta p = \frac{{4T}}{r}$ Putting these values in the equation, $\begin{gathered} - 4\pi {r^2}\frac{{dr}}{{dt}} = \frac{{4\pi T{a^4}}}{{8\eta rl}} \\ - \int_{{r_1}}^{{r_2}} {{r^3}dr} = \frac{{T{a^4}}}{{8\eta l}}\int_0^t {dt} \\ t = \frac{{2\eta l}}{{T{a^4}}}(r_1^4 - r_2^4) = \frac{{6\eta l}}{{T{a^4}x}}(r_1^4 - r_2^4) \\ x = 3 \\ \end{gathered}$