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Brenton L Cox Current Research

Research Focus

Stability and dynamics of fluid mechanics and heat transfer in planar-flow spin casting.

Planar-flow spin casting process dynamics and defect formation

Planar-flow spin casting is an energy-efficient rapid manufacturing technique. Molten metal is forced through a nozzle onto a rotating chill wheel where it forms a liquid puddle. Underneath this puddle forms the solid metal, which leaves the puddle as a ribbon and eventually departs from the substrate (as shown above). 

Variations in the final thickness of the ribbon product are typically undesirable in manufacturing and are considered defects. Two similar periodic defects which appear in the ribbon product are studied and compared. The defect with wavelength of order 1 mm appears at lower pressures. In higher pressure casts, the defect with wavelength of order 10 mm appears. While the defect frequencies differ, they are found to scale with the same capillary/inertial time scale. It is observed experimentally that pinning/depinning on the upstream meniscus of the puddle determines which of the two defects will appear. When the upstream meniscus is pinned at the inlet aperture (constrained), the shorter wavelength defect appears. When the meniscus unpinned (free to move), the longer wavelength defect appears in the ribbon product. Instances in which the upstream meniscus may only partially pin due to imposed geometry of the inlet aperture result in coincidence of the two defects.

Variation in thickness also occurs on a larger scale due to thermal expansion of the substrate. This expansion decreases the gap between the nozzle and the substrate and constricts the flow into the puddle region. In the feed-limited regime, this results in a decreased solidification velocity. Elaborating on previous studies, phenomenon is modeled using solid mechanics and heat transfer allowing the prediction of the dynamics of the gap and subsequent ribbon thickness based on the parameters set prior to a cast.

Finite-amplitude dynamics of cylindrical menisci.

Inspired by the liquid metal interface in planar-flow spin casting, we studied the stability and dynamics of coupled cylindrical menisci. A meniscus is pinned at either end of a rectangular slot, and these interfaces communicate through the inviscid liquid in the slot between. Capillary forces are assumed dominant and the menisci are assumed circular in cross-section. The response to infinitesimal and finite disturbances is studied using linear and weakly-nonlinear stability analyses and simulations. The resulting model has a Hamiltonian structure, showing dynamical behavior like the Duffing-oscillator. The energy landscape has a single- and double-welled potential depending on the total liquid volume (a bifurcation parameter). For large volumes, previously known stability criteria are applied to find the limit at which translational symmetry is lost, and comparison is made to the Plateau-Rayleigh stability limit for cylindrically shaped menisci. The addition of an axial constraint results in stability beyond the Plateau-Rayleigh limit, and is further stabilized by a second constraint.