\omega = \frac{\sigma \left ( k^2 a^2-1 \right )}{2a \mu_A} \frac{1}{k^2 a^2 + 1 - k^2 a^2 I_0^2 \left ( ka \right ) / I_1^2 \left ( ka \right )} .
Examples of when this case would apply are when almost any liquid undergoes thread/jet breakup in an air environment.