Scaling analysis and self-similarity near breakup of elasto-viscoplastic liquid threads under creeping flow

We investigate theoretically the breakup dynamics of an elasto-visco-plastic filament surrounded by an inert gas. The filament is initially placed between two coaxial disks, and the upper disk is suddenly pulled away, inducing deformation due to both constant stretching and capillary forces. We model the rheological response of the material with the Saramito–Herschel–Bulkley (SHB) model. Assuming axial symmetry, the mass and momentum balance equations, along with the constitutive equation, are solved using the finite element framework PEGAFEM-V, enhanced with adaptive mesh refinement with an underlying elliptic mesh generation algorithm. As the minimum radius decreases, the breakup dynamics accelerates significantly. We demonstrate that the evolution of the minimum radius, velocity and axial stress follow a power-law scaling, with the corresponding exponent depending on the SHB shear-thinning parameter, $n$ . The scaling exponents obtained from our axisymmetric simulations under creeping flow are verified through asymptotic analysis of the slender filament equations. Our findings reveal three distinct breakup regimes: ( a ) elasto-plastic, ( b ) elasto-plasto-capillary, both with finite-time breakup for $n\lt 1$ , and ( c ) elasto-plasto-capillary with no finite-time breakup for $n=1$ . We show that self-similar solutions close to filament breakup can be achieved by appropriate rescaling of length, velocity and stress. Notably, the effect of the yield stress becomes negligible in the late stages of breakup due to the local dominance of high elastic stresses. Moreover, the scaling exponents are independent of elasticity, resembling the breakup behaviour of finite extensible viscoelastic materials.