Creating small bubbles of soap!

A soap bubble of initial radius r1r_1 is blown at the end of a capillary tube of length \ell and cross sectional radius aa. It is then left so that the size of the air bubble gradually reduces and the new radius is r2r_2. If the surface tension of the soap bubble is TT and the coefficient of viscosity of air is η\eta, then the time taken by the bubble to reduce to radius r2r_2 can be represented as

t=6ηTa4x(r14r24),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 xx is a positive integer. Viscosity of air and surface tension of soap solution is independent of temperature.

Evaluate the value of xx.

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