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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