= Localized-neck and uniform-thread stretching exponents
{title2=$L\propto(t^*-t)^{-1/2}\text{ or }(t^*-t)^{-1}$}
A constant-tension <slender viscous thread> loses the same cross-sectional area along each material element: $A=A_0-Ft/(3\mu)$. Volume conservation gives material stretch $A_0/A$. Near an isolated quadratic minimum of $A_0$, integration over a shrinking material width proportional to $(t^*-t)^{1/2}$ gives total extension exponent $-1/2$. A uniformly thin thread has the same divergent stretch everywhere and exponent $-1$. The localized coefficient is independent of remote endpoints.
Back to article page
