Convection effects are of fundamental importance in controlling pattern formation of interface microstructures. A great number of experimental and simulation works have shown the effect of solute convection, external forced flows on interface microstructures[1-3]. The external forced flow imposed in the undercooled melt will strongly change the solidification dynamics and then pattern formation of interface microstructures. The upstream flow imposed on the growing crystal enhances the growth velocity of the interface growing in the opposite direction to the flow[4]. The uniform streaming flow results in higher local growth rate near the surface where the flow is incoming[5]. Due to the melt convection, the crystal directly nucleates from the convective undercooled melt and grows up to a large scale[6]. In the uniform streaming flow, an initially spherical particle evolve into a peach-like shape[7]. Lan et al.[8,9] experimentally and numerically investigated the convective effects driven by accelerated crucible rotation on the segregation, interface shape, and morphological instability during crystal growth. Jung et al.[10] investigated the effect of an external time-dependent flow to simulate the industrial Czochralski process for growing silicon crystals. In recent years, these phase selection and grain refinement have been investigated for the perspective of applications. It has provided strong motivation for the direct calculation of interface morphologies and evolution of particle growth. In the paper, we study the effect of the shear flow on particle growth in the undercooled melt[11]. When a flow is exerted on the melt, the fully coupled problem of the heat transfer and the fluid flow is hard to solve with numerical and analytical approaches accurately. However, the fluid velocity near the particle can be decomposed into the superposition of the uniform streaming flow and the linear flow. By using the multi-variable expansion method, we find the asymptotic solution temperature field and shape of the particle in the fully coupled problem. With the analytical solution, we show the temperature field, interface evolution and growth of the particle. We calculate the interface shape of iron particles in Cu-Fe alloys in convective solidification, and the result shows that the shear flow significantly deforms the interface of the particle. Due to the competition between the shear flow effect and the anisotropy effect of surface tension, the particle rapidly splits into more fine particles and refines the interface microstructure. The result is in good agreement with the experimental results.

References

[1] D. Medvedev, T. Fischaleck, K. Kassner, Journal of Crystal Growth 303, 69(2007).

[2] C. W. Lan, M. H. Lee, M. H. Chuang, C. J. Shih, Journal of Crystal Growth 295, 202(2006).

[3] M. Asta, C. Beckermann, A. Karma, W. Kurz, R. Napolitano, M. Plapp, G. Purdy, M. Rappaz, R. Trivedi, Acta Materialia 57 941(2009).

[4] P. K. Galenko, O. Funke, J. Wang, D. M. Herlach, Materials Science and Engineering A 375–377, 488(2004).

[5] D. S. Noh, Y. Koh, I. S. Kang, Journal of Crystal Growth, 183, 427 (1998).

[6] T. Li, X. Lin, W. D. Huang, Acta Materialia 54, 4815(2006).

[7] M. W. Chen, Y. L. Wang, H. Zhang, L. Y. Wu and Z. D. Wang, Journal of Applied Physics 109, 103517 (2011).

[8] Y. C. Liu, B. Roux, C. W. Lan, Journal of Crystal Growth 304, 236 (2007).

[9] L. C. Wang, Y. C. Liu, W. C. Yu, B. Roux, T. P. Lyubimova, C. W. Lan, Journal of Crystal Growth 311, 684(2009).

[10] T. Jung, J. Seebeck, J. Friedrich, Journal of Crystal Growth 368, 72(2013).

[11] Z. D. Wang, X. W. Wang, Q. S. Wang, I. Shih, J. J. Xu, Nanotechnology 20, 075605(2009).

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