High-speed printing processes are a leading technology for the large-scale manufacture of a new generation of nanoscale and microscale devices. Central to all printing processes is the transfer of liquid from one surface to another, a seemingly simple operation that is still not well understood. A useful idealization of liquid transfer is a liquid bridge with moving contact lines being deformed between two separating surfaces. The fluid mechanics of such bridges are relevant not only to printing, but also to other important applications, such as adhesion, tribology, biology, oil recovery, and microfluidics.

Liquid Transfer in Printing Processes: Liquid Bridges with Moving Contact Lines

Article de synthese des methodes permettant de simuler des images de defauts observes par topographie RX, par informatique. Etude theorique, et ses limitations. Exemple dans le cas de dislocations et de defauts plans

Simulation of X-ray topographs

This article describes the initial development of fluid flow and heat transfer in a planar flow casting (PFC) process for amorphous ribbon formation using a two-dimensional (2-D) model of fluid flow with free surface and surface tension, and heat transfer with phase transformation. The heat transfer in the rotating copper roller is incorporated into the model. A coupled fluid-solid (the puddle/roller surface) solution is employed for identifying the ideal interfacial heat transfer. The initial developments of puddle shape and flow and temperature distribution, including the air and the melt in the puddle zone, over time are presented. The time-dependent theoretical interfacial heat-transfer-coefficient and temperature profiles in the rotating roller are investigated. The effect of the varying roller speed, the PFC configurations (slit width and gap distance), and the roller parameters (roller radius and roller layer thickness) on the development of the melt flow and heat transfer in a PFC process are discussed. Numerical results show that a stable puddle shape can be formed within a very short period of time (on the order of milliseconds). The time evolution of the upstream meniscus is different from that of the downstream meniscus. The recirculation flows both in the surrounding air and in the melt of the puddle zone can be observed at a quasi-steady-state condition, but show different flow and thermal behaviors. The interfacial heat-transfer coefficient and temperature distribution of the rotating roller change with different cycles of the roller revolution until the heat-flux balance is reached. The varying parameters associated with the roller speed, slit width, gap distance, roller radius, and roller layer thickness affect the time evolution of the flow and thermal behavior in the puddle and the temperature distribution in the rotating roller.

Numerical Simulation of Initial Development of Fluid Flow and Heat Transfer in Planar Flow Casting Process

The effect of planar flow melt spinning (PFMS) parameters on the continuity, surface quality, and structure of 10-mm-wide Fe68.5Si18.5B9Nb3Cu1 ribbons has been investigated. The change in shape and stability of the melt puddle as a function of the processing parameter was studied using a high-speed imaging system and was correlated to ribbon formation. A window of process parameters for obtaining continuous ribbons with good surface quality has been evaluated. It has been observed that thinner ribbons are found to be more continuous because of higher ductility. The higher melt temperature leads to the formation of crystalline phase in as-spun ribbons, and this deteriorates the soft magnetic properties on annealing. The experimental results are corroborated with the numerical estimates, which suggest that the critical thickness for amorphous phase formation decreases with increasing initial melt temperature.

Effect of Planar Flow Melt Spinning Parameters on Ribbon Formation in Soft Magnetic Fe 68.5 Si 18.5 B 9 Nb 3 Cu 1 Alloy

Surface tension acting at a cylindrical interface holds an underlying liquid in motionless equilibrium. This static base state is subject to dynamic capillary instability, including Plateau―Rayleigh breakup. If the interface is partially supported by a cylindrical cup-like solid, the extent of the wetting contact can significantly influence the dynamics and the stability of the configuration. The equation for the motion of small disturbances is formulated as an eigenvalue equation on linear operators. A solution is constructed on a constrained function space using a Rayleigh―Ritz procedure. The influence of the extent-of-constraint on the dispersion relation and on modal structures is reported. In the extreme, the support reduces to a wire, aligned axially, and just touching the interface. From prior work, this constraint is known to stabilize the Plateau―Rayleigh limit by some 13 %. We report the wavenumber of maximum growth and estimate the time to breakup. The constraint is then bent in-plane to add a weak secondary curvature to the now nearly cylindrical base state. This is referred to as the torus lift of the cylinder. The static stability of these toroidal equilibria, calculated using a perturbation approach, shows that the position of constraint is crucial ― constraint can stabilize (outside) or destabilize (inside). The combined influence of secondary curvature and wire constraint on the Plateau-Rayleigh limit is tracked. Finally, attention is restricted to constraints that yield a lens-like cylindrical meniscus. For these lenses, the torus lift is used as apparatus along with a symmetrization procedure to prove a large-amplitude static stability result. Our study is conveniently framed by a classic paper on rivulets by Davis (J. Fluid Mech., vol. 98, 1980, p. 225).

Stability of constrained cylindrical interfaces and the torus lift of Plateau–Rayleigh

Planar-flow melt spinning (PFMS) is a single-stage rapid manufacturing/solidification technique for producing thin metal sheets or ribbons. Molten metal is forced through a nozzle onto the substrate where it freezes and is spun as ribbon product. A puddle of molten metal held by surface tension (capillarity) forms between the nozzle and substrate. An important measure of product quality is the uniformity of thickness along and across the ribbon. At small length scales, local thickness changes or surface defects are present that are undesirable. This work examines the cross wave, a well-defined periodic surface defect, seen when casting aluminum-silicon alloys. The presence of the defect is related to processing conditions and puddle dynamics. Motions of the puddle menisci are captured using high-speed video and analyzed for frequency content. A high frequency vibration of both menisci corresponds to the observed frequency of the surface defect. A scaling analysis reveals these motions to be capillary in nature and comparisons are made with two model problems of vibrating capillary liquids.

Capillary puddle vibrations linked to casting-defect formation in planar-flow melt spinning

Capillary stability limits for liquid metal in melt spinning

Planar-flow melt spinning (PFMS) is a single stage rapid manufacturing/solidification technique for producing thin metallic sheet or foil. A new technology, envisioned to allow real-time manipulation of the local cooling rates and properties in melt-spun ribbon, has been tested successfully when casting Al–7%Si. Pulsed laser heating, directed low on the upstream meniscus, or on the substrate, leaves patterns of ‘dimples’ in the ribbon. Typical cooling rates of 10 4  K/s have been measured using a control-volume approach. Secondary dendrite arm spacing (SDAS) has been measured through the thickness of ribbons showing areas both affected by the laser heating and unaffected by the laser. Through a correlation of cooling rates and SDAS, it is shown that the unmodified ribbon has an average cooling rate similar to that measured macroscopically. The cooling rate underneath a laser dimple is estimated to be six times slower near the contact surface. It is envisioned that the technology described may bring the concept of ‘casting-by-design’ one step closer to realization.

In situ manipulation of cooling rates during planar-flow melt spinning processing

A system and method for controlling and manipulating solidification of a molten material includes a substrate on which at least a portion of the molten material is dispensed and a first pressure adjustment system at least partially upstream of a location where the molten material is deposited on the substrate. The first pressure adjustment system imposes a first pressure at the upstream location which is different from a second pressure at a location downstream from where the molten material is dispensed.

Cormac J. Byrne

Papers

Capillary puddle vibrations linked to casting-defect formation in planar-flow melt spinning

Capillary stability limits for liquid metal in melt spinning

In situ manipulation of cooling rates during planar-flow melt spinning processing

Planar flow melt spinning systems with pressure adjustment and methods thereof