Extrudate Swelling: Physics, Models, and Computations

Viscous, viscoelastic, or elastic normal stresses are superimposed to pressure within flowing fluids. These stresses act normal to the boundaries of the flow that may deform depending on their modulus or viscosity. At absolutely rigid boundaries of infinite modulus of elasticity any boundary deformation and therefore any fluid expansion or swelling is surpressed (eg, flow in rigid pipes, annuli, channels). Elastic boundaries (eg, flow in veins and arteries, flow by membranes, around inflating/deflating balloons) deform under the action of normal stresses, allowing expansion or swelling of fluid. The same mechanism prevails in lubrication, where pressure and superimposed normal viscoelastic stresses keep surfaces in relative motion apart, with simultaneous increase in load capacity. Viscous boundaries (eg, liquid jet in air or in immiscible liquid, slow extrusion of viscoelastic liquids from dies, expanding/collapsing air-bubbles or liquid-droplets) are displaced by flowing adjacent immiscible fluids, allowing swelling or imposing contraction depending on relative rheological characteristics. Thus, the kind of swelling examined here is independent of density, ie, incompressible, and is due to the action of normal stresses against the boundary that is imposed either by adjacent deformable obstacles or else by surface tension. The resulting swelling is dynamic (ie, it initiates, changes and ceases with the flow) and can be made permanent by solidification, crystallization or glassification. The most profound form of incompressible swelling is the extrude swelling that controls the ultimate shape of extruded parts. Incompressible swelling is enhanced by the ability of macromolecules to deform and recover (eg, viscoelastic) and by the design of flow conduits to impose sharp transitions of deformation modes (eg, singular exit flows). The same swelling is reduced by the ability of molecules (or fibers in fiber-suspensions) to align with the flow streamines, as well as any tendency of solid-like structure formulation (eg, viscoplastic).