Die swell

In fluid dynamics and polymer science, die swell (also called extrudate swell or the Barus effect) is what happens when a polymer melt comes out of an extrusion die wider than the opening it just passed through. It sounds counterintuitive. The material was forced through a narrow channel, so you might expect it to stay narrow. Instead it expands, sometimes dramatically. The Barus effect is named after physicist Carl Barus, who described it in 1893.^[1]

For anyone designing a die or trying to hold tight tolerances on an extruded pipe or film, die swell is not an academic curiosity. It is a practical problem that has to be designed around every time.^[2]

Quantification

The die-swell ratio B is the standard way to put a number on the effect:

B = D ex D 0 {\displaystyle B={\frac {D_{\text{ex}}}{D_{0}}}}

where D_ex is the diameter of the extrudate after it exits and D₀ is the diameter of the die opening.^[2] A simple Newtonian fluid swells a little just from velocity profile rearrangement, giving B somewhere around 1.1 to 1.2. Polymer melts are another matter entirely. Because they are viscoelastic, the elastic recovery dominates, and B typically lands between 2 and 3, meaning the cross-sectional area can increase by 50 to 300 percent.^[3]

Physical explanation

The reason comes down to memory. Polymer chains are long, tangled molecules, and they remember their former shape. Before the die, they sit in a relaxed, roughly spherical conformation that maximises entropy. Inside the die, the sudden acceleration and constriction stretches and aligns them along the flow direction. Elastic energy builds up. Chain entanglements that have not had time to slip act like temporary crosslinks, keeping that stored stress locked in.^[4]

When the chains clear the die and the walls are gone, that stored energy releases and the material recoils outward. The longer the chains and the faster they are pushed through, the less time there is for entanglements to relax inside the die, and the more spring-loaded the melt is when it exits. A very long die at a slow throughput gives the chains time to disentangle and settle; swell is reduced. A short die running fast gives them almost no time at all; swell is at its worst.

Factors affecting die swell

Several variables move the needle:

• Molecular weight and molecular weight distributionː longer chains and a broader distribution mean more elasticity and more swell.^[2]
• Die length-to-diameter ratio (L/D)ː a longer die is a longer residence time, which means more relaxation and less swell.
• Flow rateː pushing harder stores more elastic energy and increases swell, right up to the point where melt fracture sets in.
• Temperatureː hotter melts relax faster, so swell tends to decrease as temperature rises.
• Die entry angleː a sharp, abrupt entry creates more extensional deformation than a gradual taper, loading the melt with more stored stress before it even reaches the land.^[2]
• Fillers and nanocompositesː solid particles and nanocomposite reinforcements restrict chain mobility and generally bring swell down compared to the unfilled material.^[5]

Measurement

The standard approach is capillary rheometry. The polymer is melted and forced through a cylindrical capillary at a known shear rate, and the extrudate diameter is measured just after the exit, usually with a laser micrometer or imaging system. From those two numbers you get B directly.^[6]

Measuring it sounds simple. In practice it is fiddly, because the extrudate continues to swell and sag after exit, and the point at which you measure matters.

Industrial significance

Die swell is why extrusion dies are never made exactly to the final product dimensions. The die opening has to be undersized so that after swell the extrudate ends up at the right size. Getting B wrong means pipe walls that are too thick or thin, films that are out of gauge, and profiles that will not fit their intended application. Process engineers control it by adjusting die L/D, melt temperature, and screw speed, and by building in draw-down after the die to pull the extrudate back toward the target dimensions.^[2]

See also

• Polymer extrusion
• Melt fracture
• Wall slip
• Viscoelasticity
• Normal stress differences
• Weissenberg effect

References