Pore Formation from Bubble Entrapment by a Solidification Front

Abstract

Mechanism of the pore shape in solid resulted from a tiny bubble captured by a solidification front is theoretically and generally investigated. Pore formation and its shape in solid are one of the most critical factors affecting properties, microstructure, and stresses in materials, and biosciences, global warming, etc. This work is an extension of the previous original work (Wei and Hsiao, 2012) to reveal additional mechanisms. For simplicity without loss of generality, the tiny bubble beyond the solidification front is considered to have a spherical cap, whose contact angle is identical to inclination angle of the pore at the solidification front. The contact angle of the bubble cap is thus governed by the Abel’s equation of the first kind in terms of displacement of the solidification front. The controlling parameter is the bubble growth ratesolidification rate ratio. It is found that inclination angle of the pore in the upper region depends on the bubble growth rate-to-solidification rate ratio. Isolated pore cannot occur, provided that contact angle of the bubble cap cannot reach 90 0 . The predicted pore shape and contact angle agree with predictions and observations. Manipulating either bubble growth rate or solidification rate can control pore formation in solid.