Claire McIlroy

Modelling capillary break-up of particulate suspensions

We have constructed a simple one-dimensional model of capillary break-up to demonstrate the thinning behaviour of particulate suspensions previously observed in experiments. The presence of particles increases the bulk viscosity of a fluid and so is expected to retard thinning and consequently delay the time to break-up. However, experimental measurements suggest that once the filament thins to approximately five particle diameters, the thinning no longer follows the behaviour predicted by the bulk viscosity; instead thinning is “accelerated” due to the effects of finite particle size. Our model shows that accelerated thinning arises from variations in local particle density. As the filament thins, fluctuations in the local volume fraction are amplified, leading ultimately to particle-free sections in the filament. The local viscosity of the fluid is determined from the local particle density, which is found by tracking individual particles within the suspension. In regions of low particle density, the fluid is less viscous and can therefore thin more easily. Thus, we are able to model the accelerated thinning regime found in experiments. Furthermore, we observe a final thinning regime in which the thinning is no longer affected by particle dynamics but follows the behaviour of the solvent.

Deformation of an amorphous polymer during the fused-filament-fabrication method for additive manufacturing

Three-dimensional (3D) printing is rapidly becoming an effective means of prototyping and creating custom consumer goods. The most common method for printing a polymer melt is fused filament fabrication (FFF) and involves extrusion of a thermoplastic material through a heated nozzle; the material is then built up layer-by-layer to fabricate a 3D object. Under typical printing conditions, the melt experiences high strain rates within the FFF nozzle, which are able to significantly stretch and orient the polymer molecules. In this paper, we model the deformation of an amorphous polymer melt during the extrusion process, where the fluid must make a 90° turn. The melt is described by a modified version of the Rolie–Poly model, which allows for flow-induced changes in the entanglement density. The complex polymer configurations in the cross section of a printed layer are quantified and visualized. The deposition process involving the corner flow geometry dominates the deformation and significantly disentangles the melt.

Capillary breakup of suspensions near pinch-off

We present new findings on how the presence of particles alters the pinch-off dynamics of a liquid bridge. For moderate concentrations, suspensions initially behave as a viscous liquid with dynamics determined by the bulk viscosity of the suspension. Close to breakup, however, the filament loses its homogeneous shape and localised accelerated breakup is observed. This paper focuses on quantifying these final thinning dynamics for different sized particles with radii between 3 μm and 20 μm in a Newtonian matrix with volume fractions ranging from 0.02 to 0.40. The dynamics of these capillary breakup experiments are very well described by a one-dimensional model that correlates changes in thinning dynamics with the particle distribution in the filament. For all samples, the accelerated dynamics are initiated by increasing particle-density fluctuations that generate locally diluted zones. The onset of these concentration fluctuations is described by a transition radius, which scales with the particle radius and volume fraction. The thinning rate continues to increase and reaches a maximum when the interstitial fluid is thinning between two particle clusters. Contrary to previous experimental studies, we observe that the final thinning dynamics are dominated by a deceleration, where the interstitial fluid appears not to be disturbed by the presence of the particles. By rescaling the experimental filament profiles, it is shown that the pinching dynamics return to the self-similar scaling of a viscous Newtonian liquid bridge in the final moments preceding breakup.

CaBER vs ROJER—Different time scales for the thinning of a weakly elastic jet

In this paper, we demonstrate that the capillary thinning dynamics of a weakly viscoelastic jet follow a different timescale than a liquid bridge of the same fluid between two stationary surfaces for similar geometrical scales. The thinning in the latter case observed with capillary breakup extensional rheometry (or CaBER) follows a well established scaling of the radius with time for an elasto-capillary (EC) balance of R ∼ exp ⁡ ( − t / 3 λ ) . However, for the thinning of the filaments between droplets in a jet, it was so far just assumed that the same scaling law holds. In this paper, we experimentally demonstrate that the jet thinning in a Rayleigh–Ohnesorge jetting extensional rheometer (or ROJER) follows a different scaling of R ∼ exp ⁡ ( − t / 2 λ ) . This is demonstrated by a direct comparison of the thinning dynamics of weakly viscoelastic ( O h < 0.01 ) aqueous solutions of polyethylene oxide in the two experimental setups, covering a wide range of jetting velocities or Weber numbers of 1–70. We demonstrate outgoing from a momentum balance that includes inertia and elasticity that this difference in scaling is due to a constant axial tension in the jet arising from the constant creation rate of new surface at the nozzle. Numerical simulations using the FENE-P model support this theory and demonstrate that in the exponential thinning regime of the jet the elastic stresses are indeed balanced by the axial tension (rather than by capillary pressure as in the EC balance regime of the CaBER experiment). It is readily shown from the reduced stress balance that this axial-elastic balance regime in the ROJER experiment leads to a faster exponential thinning, following the new scaling of R ∼ exp ⁡ ( − t / 2 λ ) that was experimentally observed. Furthermore, we observe both in experiment and simulation that a jet thinning does not exhibit a self-similar structure of the corner region where the thinning filament connects to the drop as it is generally observed for a filament with an axial tension decaying with the filament radius as in the CaBER. The resulting difference of 50% in extensional relaxation time λ extracted from ROJER experiments might require one to revisit previously reported ROJER experiments and is required for the correct evaluation of future jetting rheometry experiments.In this paper, we demonstrate that the capillary thinning dynamics of a weakly viscoelastic jet follow a different timescale than a liquid bridge of the same fluid between two stationary surfaces for similar geometrical scales. The thinning in the latter case observed with capillary breakup extensional rheometry (or CaBER) follows a well established scaling of the radius with time for an elasto-capillary (EC) balance of R ∼ exp ⁡ ( − t / 3 λ ) . However, for the thinning of the filaments between droplets in a jet, it was so far just assumed that the same scaling law holds. In this paper, we experimentally demonstrate that the jet thinning in a Rayleigh–Ohnesorge jetting extensional rheometer (or ROJER) follows a different scaling of R ∼ exp ⁡ ( − t / 2 λ ) . This is demonstrated by a direct comparison of the thinning dynamics of weakly viscoelastic ( O h < 0.01 ) aqueous solutions of polyethylene oxide in the two ...