A dynamic model for the interaction between a solid particle and an advancing solid/liquid interface
- PDF / 557,149 Bytes
- 10 Pages / 612 x 792 pts (letter) Page_size
- 7 Downloads / 195 Views
I. INTRODUCTION
PARTICLE distribution in ceramic particle reinforced metal matrix composites, inclusion or porosity management in castings, segregation of flux pinning particles in hightemperature superconductors, and growth of monotectics involve the interaction of a solid/liquid interface (SLI) with second-phase particles. These particles may be solid, liquid, or gaseous. When a liquid containing an insoluble particle is solidified, three distinct interaction phenomena have been observed: instantaneous engulfment of particles, continuous pushing, and particle pushing followed by engulfment.[1] For a given particle size, there is a critical velocity above which a particle is engulfed. This velocity is a function of solidification velocity and some materials parameters. All models that describe this transition analyze the forces exercised on a particle positioned in the vicinity of the SLI. These models[2–7] solve the steady-state balance between the engulfing drag force applied by the liquid on the particle and the repulsive interfacial force between the particle and the SLI. The weakness of the steady-state models is that the force balance can be satisfied for any subcritical solidification velocity and therefore additional assumptions must be introduced to predict the critical velocity for engulfment. For example, Po´tschke and Rogge[6] in their steady-state analytical model and Sasikumar et al.[8] in their steady-state numerical model assume that the critical velocity is the maximum of the function particle velocity–interface distance. This is clearly a weak assumption, since it produces a minimum particle–interface distance equal to the atomic size.[6,7] On the other hand, Hadgi[9] in his steady-state asymptotic analysis of particle engulfment calculates the minimum gap thickness by minimizing the expression of the gap thickness. This value is then used to calculate the critical velocity. The present article proposes a non-steady-state model for ADRIAN V. CATALINA, Research Scientist, is with the Universities Space Research Association, NASA/Marshall Space Flight Center, Huntsville, AL 35182. SUNDEEP MUKHERJEE. Graduate Research Assistant, and DORU M. STEFANESCU, University Research Professor and Director, are with the Solidification Laboratory, The University of Alabama, Tuscaloosa, AL 35487. Manuscript submitted August 9, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
the interaction between an insoluble particle and the advancing SLI. The non-steady-state approach is based on the fact that a particle, initially at rest, must have an accelerated motion in order to reach the steady-state velocity, which is the solidification velocity. Moreover, as we will show in this article, steady state cannot be achieved for the case of particle engulfment. It is only a terminal condition when the solidification is conducted at subcritical velocities. II. BACKGROUND The transient nature of the interaction between the SLI and the particle has been discussed recently in two models.[10,11] These models numerically solve th
Data Loading...
