# Creating small bubbles of soap!

A soap bubble of initial radius $r_1$ is blown at the end of a capillary tube of length $\ell$ and cross sectional radius $a$. It is then left so that the size of the air bubble gradually reduces and the new radius is $r_2$. If the surface tension of the soap bubble is $T$ and the coefficient of viscosity of air is $\eta$, then the time taken by the bubble to reduce to radius $r_2$ can be represented as

$t = \dfrac{6 \eta \ell}{T a^4 x} \left( {r_1}^4 - {r_2}^4 \right),$

where all quantities are in SI units and $x$ is a positive integer. Viscosity of air and surface tension of soap solution is independent of temperature.

Evaluate the value of $x$.

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