Viscous-thread drawing

In steady viscous-thread drawing the conserved volume flux $Aw=Q$ couples thinning directly to acceleration. The axial tensile stress is $3\mu w_z$, so solutions with larger positive $w_z$ thin more rapidly.

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 $(t^{\ast }-t{)}^{1/2}$ 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.