Rheology of Dendrite-Like Particles in Suspension

During solidification of metals, millions of tinny snowflake-like crystals form. Like in a snowstorm, these crystals can move, pile up in front of an obstacle, whirl around and even form avalanches. The law for describing the motion of a single snowflake-like crystal in a liquid is known quite a while. However, for the collective motion of ensemble of snowflake-like crystals in a liquid the laws of motion are questionable. Collisions and interlocking of individual crystals or crystal ensembles are becoming more and more signif- icant when the crystal number density increases. By using a modern 3D printer, we plan to produce over 100.000 crystals that are only micrometres in size and resemble snowflakes. A suspension containing these particles will be stirred under well-defined con- ditions. From the measured forces, conclusions will be drawn about the laws that govern the collective motion. Such investigations using different spherical particles are well known. However, snowflake-like particles will definitely behave different and thus new insights into the dynamic of their collective motion are to be expected. Additionally to the experimental work, computer simulations will help to interpret the measurements. Here, new modelling approaches will be necessary to describe phenomena that are characteristic for the motion of ensembles of snowflake-like particles. Those modelling approaches will finally enable to improve computer simulations of solidification process and with that a quality improvement of cast products will be possible.

During the solidification of alloys, snowflake-like crystals, known as dendrites, form. They swirl around, interact, and eventually settle. Understanding the flow behaviour and viscosity of a mixture consisting of melt/liquid and dendritic particles is therefore crucial, particularly at increasing solid fractions. To date, no studies addressing this problem have been reported. Building on insights from suspensions of small spherical particles, an apparatus was constructed consisting of a cylindrical container with a rotating, partially permeable lid. By prescribing force and torque, a defined position and rotational speed are established, from which the suspension viscosity can be inferred. Dendritic particles were produced in large quantities (>100,000) using a modern 3D printing technique ("photopolymer multi-jet technology") from a specialised polymer. Three different types of dendritic particles were fabricated, namely star-shaped structures with six arms of varying lengths. To minimise buoyancy effects, the fluid and the particles ideally should have identical material densities. This posed a challenge, as the fluid used in previous experiments is now banned in the European Union due to extreme toxicity. Alternative fluids were therefore sought, and glycerol and PEG-PPG were ultimately employed. Glycerol has a density approximately 10% higher, and PEG-PPG about 9% lower, than the density of the 3D-printed particles. Consequently, positive and negative buoyancy forces arose and had to be taken into account in the measurements. Additional complications appeared from particles lodging in the gap between the container and rotating lid, distorting the measurements. A slightly larger lid was fabricated, requiring extremely precise alignment of the lid and numerous control measurements to ensure a truly frictionless setup. Ultimately, reliable measurements were successfully obtained, and the results can be summarised as follows: (i) The friction coefficient increases with decreasing solid fraction and is comparable for all three types of dendritic particles, provided that the respective maximum packing densities are taken into account. The theoretical framework used to describe the friction coefficient remains essentially the same as that applied to suspensions of spherical particles, albeit with modified parameters. (ii) Particle pressure and rotational velocity can be described using the determined friction coefficient. However, the shear rate is significantly lower than for spherical particles, indicating that the linear velocity profile assumption valid for spheres is no longer justified for dendritic particles using the present configuration. In addition to the experimental work, a numerical model was developed and successfully validated that accounts for particle pressure at high solid fractions. This extends simulations of solidification processes by incorporating a previously unconsidered aspect of significant importance in certain regimes.