Bingham Fluid Rheology and a Dimensionless Analysis of Wire Cutting in Fresh Cementitious Filaments

Bingham fluids combine a finite yield stress with an approximately linear post-yield relation between shear stress and shear rate. This compact model is widely used for pastes, slurries, drilling muds, cementitious materials and other viscoplastic media, yet its apparent simplicity conceals the free-boundary problem created by yielded and unyielded regions. This article reviews the constitutive basis of the Bingham model, analytical results for simple flows, and numerical strategies based on regularization, finite elements and the lattice Boltzmann method. The review emphasizes that yield surfaces are stress-defined rather than material interfaces and that regularization parameters must be checked against mesh and time-step sensitivity. A feasible research object is then developed: transverse wire cutting of a freshly extruded cementitious filament. The wire is treated as a translating cylinder in a low-Reynolds-number yield-stress medium. A dimensionless analysis based on the Bingham number separates viscous-dominated, mixed and yield-dominated cutting regimes, while a transparent resistance scale links yield stress, plastic viscosity, wire diameter and cutting speed. The analysis shows why slower cutting does not necessarily minimize resistance when structural rebuilding raises the yield stress. A combined rheometry, force-measurement and regularized-flow simulation protocol is proposed. The Bingham model is suitable as a baseline for process design, but thixotropy, elasticity, wall slip, particle size and fracture must be added when they control the observed cutting response.