X-ray particle tracking velocimetry for steady-state rheological characterization: Case study of a complex polymer melt flow in material extrusion additive manufacturing

TL;DR

This paper introduces X-ray Particle Tracking Velocimetry (XPTV) to quantify velocity fields and local rheology of opaque polymer melts inside a fused filament fabrication nozzle. By embedding tungsten tracers in a PS filament and imaging with a custom aluminum nozzle inside a µ-CT setup, the authors extract axial velocity fields, infer the radial component via continuity, and compute the full strain-rate tensor, revealing predominantly shear-dominated, nonisothermal flow that deviates from Newtonian predictions. The measurements are corroborated by non-isothermal CFD simulations with melting physics (enthalpy-porosity, VOF), which reproduce the observed trends and support the interpretation of incomplete heating inside the nozzle as a driver of non-Newtonian behavior. The work demonstrates, for the first time, that XPTV can quantify both velocity fields and rheological properties in opaque polymer melts, offering a powerful tool for investigating additive manufacturing processes and other opaque polymer flows where optical methods fail.

Abstract

We introduce X-ray Particle Tracking Velocimetry (XPTV) as a promising method to quantitatively resolve the velocity field and associated rheological information of polymer melt flow within the nozzle of a fused filament fabrication (FFF) printer. Employing tungsten powder as tracer particles embedded within a polymer filament, we investigate melt flow dynamics through an aluminum nozzle in a custom setup comparable to commercial printers. The velocity profiles obtained via XPTV reveal significant deviations from classical Newtonian flow, highlighting complex heterogeneous and non-isothermal behavior within the melt. From these measurements, we determine the local infinitesimal strain rate tensor and correlate flow-induced non-Newtonian effects to spatially varying temperature distributions, reflecting incomplete thermal homogenization within the nozzle. We complement the experiments with computational fluid dynamics simulations of the flow inside the printing nozzle, incorporating filament melting through an enthalpy-porosity formulation and treating the air-polymer melt interface using a two-phase approach. The simulated velocity profiles agree closely with the XPTV measurements across the investigated operating conditions, supporting the experimental interpretation. Our findings demonstrate the capability of XPTV to quantify both velocity fields and rheological properties, underscoring its potential as a tool for investigating opaque polymer melt flows in additive manufacturing, industrial processing, and rheology. To our knowledge, this is the first application of XPTV to polymer melt rheology. It enables measurements that are inaccessible to conventional optical methods.

Figures (12)

• Figure 1: Schematic illustrating (a) the FFF process, (b) the design of a typical nozzle and its connection to components such as the heater block, heat break, and heat sink.
• Figure 2: Master curves comparing complex viscosity as a function of shear rate for particle-laden and particle-free filaments.
• Figure 3: Differential Scanning Calorimetry (DSC) results for particle-laden and particle-free filaments, demonstrating that the addition of tungsten particles has no measurable effect on the glass transition temperature.
• Figure 4: Schematic of the polymer extrusion setup and the X-ray imaging principle for circular flow with tracer particles. (a) Overview of the extrusion setup, based on a previous version described in Ref. kattinger2023analysis, adapted for integration with the X-ray system. (b) Sectional view of the manufactured nozzles, showing dimensions and orientation relative to the cone beam and detector. (c) Top view of the nozzle. (d) Cropped raw image stack of the region of interest (ROI), showing low particle contrast. (e) Background-subtracted image stack with enhanced contrast. (f) Particle tracking results with velocity-coded tracks. (g) Schematic representation of particles positioned at $y = r$ and $y = -r$.
• Figure 5: Particle size distribution obtained by laser diffraction, showing particle diameter on the x-axis and corresponding volume fraction and cumulative distribution on the y-axis.