Stretching of viscous threads at low Reynolds numbers

We investigate the classical problem of the extension of an axisymmetric viscous thread by a fixed applied force with small initial inertia and small initial surface tension forces. We show that inertia is fundamental in controlling the dynamics of the stretching process. Under a long-wavelength approximation, we derive leading-order asymptotic expressions for the solution of the full initial-boundary value problem for arbitrary initial shape. If inertia is completely neglected, the total extension of the thread tends to infinity as the time of pinching is approached. On the other hand, the solution exhibits pinching with finite extension for any non-zero Reynolds number. The solution also has the property that inertia eventually must become important, and pinching must occur at the pulled end. In particular, pinching cannot occur in the interior as can happen when inertia is neglected. Moreover, we derive an asymptotic expression for the extension.