Meaning
A fluid dynamics principle that describes the laminar movement of a viscous liquid through a cylindrical pipe or parallel channel under a pressure gradient. Engineers apply poiseuille flow formulas to estimate the behavior of polymers in extrusion dies.
Velocity Profile
Friction against the boundary walls reduces the fluid speed to zero at the solid surface. This condition creates a parabolic distribution where the velocity is highest at the center of the channel. The resulting velocity distribution influences the residence time of the material in the heated die.
Pressure Drop
Flow resistance causes the pressure to decrease along the length of the conduit. The magnitude of this drop is inversely proportional to the fourth power of the channel radius. Small reductions in the die opening therefore require much higher pressures to maintain a constant throughput.
If the pressure exceeds safe operating limits, the extruder must slow down to prevent mechanical failure. When viscous heating occurs due to high shear, the local viscosity drops and changes the flow characteristics.
Shear Rate
Velocity gradients within the moving liquid generate mechanical shear stresses. This shear rate reaches its maximum value at the channel walls and is zero at the center. Understanding this distribution helps prevent polymer degradation from excessive localized heating.