A soap bubble is blown at the end of a capillary tube of radius a and length L. When the other end is left open, the bubble begins to deflate. Write the radius of the bubble as a function of time if the initial radius of the bubble was `R_(0)`. Surface tension of soap solution is T. It is known that volume flow rate through a tube of radius a and length L is given by Poiseuille’s equation- `Q=(pia^(4)DeltaP)/(8ne L)`

Where `DeltaP` is pressure difference at the two ends of the tube and `ne` is coefficient of viscosity. Assume that the bubble remains spherical.

Answer

`R=R_(0)[1-(a^(4)Tt)/(2neLR_(0)^(4))]^(1//4)`