M2 Forming and Rheology of Ceramic Suspensions

Topic

This model focuses on the rheological behavior of the ceramic suspension prior to sintering; this behavior is described by either the Bingham model or the Herschel-Bulkley model. The Bingham model describes a suspension that behaves like a rigid solid until a specific yield stress is exceeded, after which it flows with constant viscosity; in contrast, the Herschel-Bulkley model describes a suspension that also requires exceeding that same threshold to begin flowing, but whose viscosity—once the threshold is passed—is not constant but varies with the rate of deformation. In both models, the fact that the suspension requires a yield stress to initiate flow means it behaves like a solid when at rest and like a fluid when in motion.

This rheological behavior determines the quality of the green body obtained during forming: if the suspension is too fluid, ceramic particles settle unevenly before forming, resulting in packing defects in the green body; conversely, if the suspension is too viscous, it fails to completely fill the mold, leaving trapped air bubbles in the green body. Only within an intermediate rheological range—neither too fluid nor too viscous—does the green body achieve the quality necessary to proceed with the remainder of the process.

Within this suitable rheological range, slip casting is one technique used to form the green body from the suspension: the suspension is poured into a porous mold that absorbs water via capillary action, and as the mold absorbs water, a solid wall layer builds up, growing from the mold walls toward the interior. As the wall thickness increases, the slip casting process becomes directly dependent on that growth: the longer the suspension remains in the mold, the thicker the resulting wall becomes—although this growth rate slows over time because the already-formed wall hinders the continued flow of water from the piece's interior into the mold.

Extrusion is the other technique used to form a green body from this same suspension—albeit using a viscous paste rather than a liquid slip—and it is modeled using the Hagen-Poiseuille equation. This equation establishes that the flow rate of the paste through the extrusion die depends directly on the applied pressure and inversely on the paste's viscosity and the length of the die. Higher applied pressure, or lower paste viscosity and die length, results in a higher extrusion flow rate; conversely, the opposite conditions lead to a lower flow rate.

Consequently, this model—based on the initial ceramic suspension rheology—enables both slip casting and extrusion (the two techniques that form the green body from that rheology) to supply the resulting green body to another model in the set: the one describing ceramic sintering. The densification described by that second model relies precisely on the green body formed by this first model, the quality of which is determined by the initial rheology.

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