Meaning
A fluid mechanics metric scales the elasticity of a viscoelastic solution by comparing its polymer relaxation time to the characteristic shear rate of the flow. The Weissenberg Number Expansion describes the transition of a fluid from simple viscous behavior to highly elastic flow regimes during high-stress industrial processes. This non-dimensional parameter is used to predict the onset of flow instabilities in extrusion and coating.
Fluid Flow
Non-Newtonian liquids exhibit dramatic changes in flow profile when subjected to rapid deformation within narrow channels. Under high shear conditions, the Weissenberg Number Expansion becomes critical for identifying when elastic forces start to dominate the flow field. This transition can lead to swelling at the exit of extrusion dies, an effect that must be carefully calculated to maintain dimensional accuracy in manufactured parts.
Elastic Response
Polymeric chains align and stretch along flow lines, storing mechanical energy that is released when the flow path changes. This elastic response is characterized by a high value in the Weissenberg Number Expansion, which indicates that the rate of deformation is faster than the rate of molecular relaxation. The stored elastic stress can cause self-sustaining flow oscillations, causing surface irregularities and mechanical defects in the coated film.
Structural Instability
Flow instability occurs in high-speed coating and polymer processing when the elastic forces exceed the dampening capacity of the fluid viscosity. The structural instability associated with a large Weissenberg Number Expansion leads to melt fracture or sharkskin defects on the surface of extruded plastics. This defect can be mitigated by adjusting the operating temperature or reducing the processing speed to allow the polymer chains more time to relax during flow.
Such process changes effectively reduce the characteristic shear rate, shifting the system back into a stable operating regime where viscous forces dominate.
