Mechanism of effect of stable cavitation on dendrite growth in ultrasonic field

Zhang Ying; Wu Wen-Hua; Wang Jian-Yuan; Zhai Wei

doi:10.7498/aps.71.20221101

Abstract

Ultrasonic waves used in liquid alloys can produce refined grain structures, which mainly contributes to ultrasonic cavitation and acoustic streaming. According to the bubble lifetime and whether they are fragmented into “daughter” bubbles, acoustic cavitation can be divided into transient cavitation and stable cavitation. Compared with the transient cavitation, the interaction between stable cavitation bubbles and solidifying alloys have been rarely investigated previously . In this work, the effect of stable cavitation on the dendritic growth of succinonitrile (SCN)-8.3% (mole fraction) water organic transparent alloy is systematically investigated by high-speed digital image technique and numerical simulation. It is found that when the bubble migration direction is consistent with that of dendritic growth, the periodic high pressure generated in bubble oscillation process increases the local undercooling, speeding up the dendrites growth effectively. Meanwhile, the concentrated stress inside dendrites induced by the linearly oscillation of cavitation bubble can break up dendrites into fragments. Specifically, if there exist stable cavitation bubbles suspended around the liquid-solid interface, periodically alternating flow field and high shear force in their surrounding liquid phase is produced. As a result, the nearby dendritic fragments will be attracted to those bubbles and then transformed into spherical grains.

Keywords:

Authors and contacts

School of Physical Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China

Corresponding author: Wang Jian-Yuan, wangjy@nwpu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 52088101, 51922089, 52130405, 51727803), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2021JCW-09), and the Key Industrial Chain Project of Shaanxi Provincial Key Research and Development Plan, China (Grant No. 2020ZDLGY13-03).

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References

[1]	Eskin G I, Eskin D G 2014 Ultrasonic Treatment of Light Alloy Melts (2nd Ed.) (London: CRC Press) pp32–43
[2]	Hu Y J, Wang X, Wang J Y, Zhai W, Wei B 2021 Metall. Mater. Trans. A 52 3097 Google Scholar
[3]	Feng X H, Zhao F Z, Jia H M, Zhou J X, Li Y D, Li W R, Yang Y S 2017 Int. J. Cast Metal. Res. 30 341 Google Scholar
[4]	Yasui K 2018 Acoustic cavitation and bubble dynamics (Switzerland: Springer International) pp14, 15
[5]	Gielen B, Jordens J, Janssen J, Pfeiffer H, Wevers M, Thomassen L C J, Braeken L, Van Gerven T 2015 Ultrason. Sonochem. 25 31 Google Scholar
[6]	吴文华, 翟薇, 胡海豹, 魏炳波 2017 66 194303 Google Scholar Wu W H, Zhai W, Hu H B, Wei B B 2017 Acta Phys. Sin. 66 194303 Google Scholar
[7]	Koukouvinis P, Gavaises M, Supponen O, Farhat M 2016 Phys. Fluids 28 052103 Google Scholar
[8]	Feng X H, Zhao F Z, Jia H M, Li Y J, Yang Y S 2018 Ultrason. Sonochem. 40 113 Google Scholar
[9]	Chow R, Blindt R, Chivers R, Povey M 2005 Ultrasonics 43 227 Google Scholar
[10]	Zhao Y, Zheng Q L, Liu Z W 2020 Mater. Lett. 274 128030 Google Scholar
[11]	Shu D, Sun B D, Mi J W, Grant P S 2012 Metall. Mater. Trans. A 43 3755 Google Scholar
[12]	Tan D Y, Mi J W 2013 Mater. Sci. Forum 765 230 Google Scholar
[13]	Wang F, Eskin D, Mi J W, Wang C N, Koe B, King Andrew, Reinhard C, Connolley T 2017 Acta Mater. 141 142 Google Scholar
[14]	Wang B, Tan D Y, Lee T L, Khong J C, Wang F, Eskin D, Connolley T, Fezzaa K, Mi J W 2018 Acta Mater. 144 505 Google Scholar
[15]	Todaro C J, Easton M A, Qiu D, Zhang D, Bermingharm M J, Lui E W, Brandt M, Stjohn D H, Qian M 2020 Nat. Commun. 11 142 Google Scholar
[16]	徐珂, 许龙, 周光平 2021 70 194301 Google Scholar Xu K, Xu L, Zhou G P 2021 Acta Phys. Sin. 70 194301 Google Scholar
[17]	Omoteso K A, Roy-Layinde T O, Laoye J A, Vincent U E, McClintock P V E 2021 Ultrason. Sonochem. 70 105346 Google Scholar
[18]	Lofstedt R, Barber B P, Putterman S J 1993 Phys. Fluids A 5 2911 Google Scholar
[19]	Lin H, Storey B D, Szeri A J, Andrew J S 2002 J. Fluid Mech. 452 145 Google Scholar
[20]	Murakami K, Yamakawa Y, Zhao J Y, Johnsen E, Ando K 2021 J. Fluid Mech. 924 A38 Google Scholar
[21]	Wang S, Guo Z P, Zhang X P, Zhang A, Kang J W 2019 Ultrason. Sonochem. 51 160 Google Scholar
[22]	Koss M B, LaCombe J C, Tennenhouse L A, Glicksman M E, Winsa E A 1999 Metall. Mater. Trans. A 30 3177 Google Scholar
[23]	Shang S, Han Z Q 2019 J. Mater. Sci. 54 3111 Google Scholar
[24]	Cattaneo C A, Evequoz O P E, Bertorello H R 1994 Scripta Metall. Mater. 31 461 Google Scholar
[25]	Cain J B, Clunie J C, Baird J K 1995 Int. J. Thermophys. 16 1225 Google Scholar
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图 1 SCN-H₂O溶液的超声凝固观测实验以及数值模型示意图　(a) 单轴超声凝固原位观测装置示意图; (b) SCN-8.3%H₂O溶液在SCN-H₂O平衡相图中的位置, 图中S表示固态, L表示液态; (c) 气泡稳态振荡作用下枝晶内部应力分布的数值模型示意图

Figure 1. Schematic of experiment and numerical model: (a) In situ observation experiment setup of uniaxial ultrasonic solidification; (b) position of SCN-8.3% H₂O solution in equilibrium phase diagram; (c) numerical model of stress distribution inside dendrite under a stable bubble oscillation. a stable bubble oscillation.

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图 2 稳态空化气泡作用下枝晶生长过程　(a) t = 0 s; (b) t = 1.02 s; (c) t = 2.96 s; (d) t = 5.94 s

Figure 2. In situ observation of dendritic growth under the action of stable cavitation: (a) t = 0 s; (b) t = 1.02 s; (c) t = 2.96 s; (d) t = 5.94 s.

DownLoad: Full-Size Img PowerPoint

图 3 气泡稳态振荡过程中枝晶生长速率的变化规律　(a) 枝晶主干长度L随时间t的变化; (b) 一个振荡周期内过冷度随时间的变化; (c) LKT模型拟合的枝晶生长速率与过冷度的关系

Figure 3. Influence of dendritic growth velocity induced by a stable cavitation bubble: (a) Evolution of primary dendritic length with time; (b) variation of local undercooling in one oscillation period; (c) relationship between dendritic growth velocity and undercooling by LKT model.

DownLoad: Full-Size Img PowerPoint

图 4 向固相内部迁移的气泡与枝晶生长的相互作用　(a) t = 0 s; (b) t = 0.24 s; (c) t = 0.82 s; (d) t = 5.04 s; (e) t = 7.42 s; (f) t = 11.26 s

Figure 4. Images of the interaction between the stable bubble migrating into solid phase and growing dendrites: (a) t = 0 s; (b) t = 0.24 s; (c) t = 0.82 s; (d) t = 5.04 s; (e) t = 7.42 s; (f) t = 11.26 s.

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图 5 空化气泡稳态振荡导致与其接触的二次枝晶臂根部弯曲、断裂的动态过程　(a) t = 0 ms; (b) t = 2.34 ms; (c) t = 4.68 ms; (d) t = 8.19 ms; (e) t = 9.36 ms; (f) t = 10.11 ms

Figure 5. Continuous bending until fragmentation of the secondary dendritic arm induced by the stable oscillation bubble: (a) t = 0 ms; (b) t = 2.34 ms; (c) t = 4.68 ms; (d) t = 8.19 ms; (e) t = 9.36 ms; (f) t = 10.11 ms.

DownLoad: Full-Size Img PowerPoint

图 6 稳态空化气泡对枝晶臂弯曲角度及内部应力-应变影响　(a) 二次枝晶臂弯曲角度随时间的变化规律; (b) 一个周期内初始半径为35 μm的气泡振荡过程中半径及压强随时间的变化; (c) 二次枝晶臂内部不同位置的应力分布

Figure 6. Effect of a stable oscillation bubble on stress-strain distribution inside the secondary dendritic arm: (a) Bending angle of the secondary dendritic arm changing over time; (b) radius and pressure calculated by Rayleigh-Plesset equation in one period with an initial bubble radius of 35 μm; (c) stress distribution at different positions inside the secondary dendritic arm.

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图 7 液-固界面处的游离碎片被邻近的稳态空化气泡吸引并形成球状晶的演化过程, 其中(a) t = 0 s, (b) t = 2.42 s, (c) t = 5.20 s, (d) t = 6.08 s, (e) t = 8.40 s; (f) 气泡振荡过程中半径及吸附层厚度随时间的变化规律

Figure 7. Evolution process of the free fragments attracted by a neighboring stable bubble at liquid-solid interface with a transformation into spherical grains: (a)–(e) Images of real-time observation at t = (a) 0 s, (b) 2.42 s, (c) 5.20 s, (d) 6.08 s, (e) 8.40 s. (f) The bubble radius and adsorbed layer thickness over time.

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图 8 气泡稳态振荡吸引枝晶碎片并形成球状晶的原理　(a) 超声波作用下气泡的稳态振荡过程; (b) 枝晶碎片被气泡吸引并形成球状晶的示意图

Figure 8. Principle of dendritic fragments attracted to a stable cavitation bubble with transformation into spherical grains: (a) Linearly oscillation of a steady-state bubble under the ultrasonic wave; (b) dendritic fragments attracted to a bubble and transformed into spherical grains.

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表 1 数值模拟中用到的物理量数值

Table 1. Values of parameters in numerical simulation.

物理量	数值	单位
气泡初始半径 R₀	45	μm
液体介质密度 ρ₀	970^[21]	kg/m³
饱和蒸汽压 P_v	2330^[20]	Pa
表面张力 σ	3.85×10^{–2 [21]}	N/m
液体介质黏度 μ	2.66×10^{–3 [21]}	Pa·s
液体介质静压力 P₀	1.013×10^{5 [20]}	Pa
声压幅值 P_a	6.59×10⁴	Pa
超声频率 f	20	kHz
气体比热系数 γ	1.4^[20]	/
液体介质声速 c₀	1500^[4]	m/s
液体介质熔点 T_L	316	K
凝固潜热 ∆H_f	3700^[23]	J/mol
体积变化 ∆V	2.23×10^{–6 [22]}	m³/mol
熔化熵 ∆S	11.67^[23]	J/(m^–3·K^–1)
液相比热容 C_p	188.1^[22]	J/(mol^–1·K^–1)
热扩散系数 D_T	1.134×10^{–7 [22]}	m²/s
平衡液相线斜率 m	1.42	K/at.%
溶质浓度 C₀	8.3	at.%
溶质分配系数 k_e	0.65^[24]	/
溶质扩散系数 D_L	8.33×10^{–10 [25]}	m²/s
液-固界面能 σ_SL	8.94×10^{–3 [22]}	J/m²
Gibbs-Thomson系数 Γ	6×10^–8	m·K

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map

[1]	Eskin G I, Eskin D G 2014 Ultrasonic Treatment of Light Alloy Melts (2nd Ed.) (London: CRC Press) pp32–43
[2]	Hu Y J, Wang X, Wang J Y, Zhai W, Wei B 2021 Metall. Mater. Trans. A 52 3097 Google Scholar
[3]	Feng X H, Zhao F Z, Jia H M, Zhou J X, Li Y D, Li W R, Yang Y S 2017 Int. J. Cast Metal. Res. 30 341 Google Scholar
[4]	Yasui K 2018 Acoustic cavitation and bubble dynamics (Switzerland: Springer International) pp14, 15
[5]	Gielen B, Jordens J, Janssen J, Pfeiffer H, Wevers M, Thomassen L C J, Braeken L, Van Gerven T 2015 Ultrason. Sonochem. 25 31 Google Scholar
[6]	吴文华, 翟薇, 胡海豹, 魏炳波 2017 66 194303 Google Scholar Wu W H, Zhai W, Hu H B, Wei B B 2017 Acta Phys. Sin. 66 194303 Google Scholar
[7]	Koukouvinis P, Gavaises M, Supponen O, Farhat M 2016 Phys. Fluids 28 052103 Google Scholar
[8]	Feng X H, Zhao F Z, Jia H M, Li Y J, Yang Y S 2018 Ultrason. Sonochem. 40 113 Google Scholar
[9]	Chow R, Blindt R, Chivers R, Povey M 2005 Ultrasonics 43 227 Google Scholar
[10]	Zhao Y, Zheng Q L, Liu Z W 2020 Mater. Lett. 274 128030 Google Scholar
[11]	Shu D, Sun B D, Mi J W, Grant P S 2012 Metall. Mater. Trans. A 43 3755 Google Scholar
[12]	Tan D Y, Mi J W 2013 Mater. Sci. Forum 765 230 Google Scholar
[13]	Wang F, Eskin D, Mi J W, Wang C N, Koe B, King Andrew, Reinhard C, Connolley T 2017 Acta Mater. 141 142 Google Scholar
[14]	Wang B, Tan D Y, Lee T L, Khong J C, Wang F, Eskin D, Connolley T, Fezzaa K, Mi J W 2018 Acta Mater. 144 505 Google Scholar
[15]	Todaro C J, Easton M A, Qiu D, Zhang D, Bermingharm M J, Lui E W, Brandt M, Stjohn D H, Qian M 2020 Nat. Commun. 11 142 Google Scholar
[16]	徐珂, 许龙, 周光平 2021 70 194301 Google Scholar Xu K, Xu L, Zhou G P 2021 Acta Phys. Sin. 70 194301 Google Scholar
[17]	Omoteso K A, Roy-Layinde T O, Laoye J A, Vincent U E, McClintock P V E 2021 Ultrason. Sonochem. 70 105346 Google Scholar
[18]	Lofstedt R, Barber B P, Putterman S J 1993 Phys. Fluids A 5 2911 Google Scholar
[19]	Lin H, Storey B D, Szeri A J, Andrew J S 2002 J. Fluid Mech. 452 145 Google Scholar
[20]	Murakami K, Yamakawa Y, Zhao J Y, Johnsen E, Ando K 2021 J. Fluid Mech. 924 A38 Google Scholar
[21]	Wang S, Guo Z P, Zhang X P, Zhang A, Kang J W 2019 Ultrason. Sonochem. 51 160 Google Scholar
[22]	Koss M B, LaCombe J C, Tennenhouse L A, Glicksman M E, Winsa E A 1999 Metall. Mater. Trans. A 30 3177 Google Scholar
[23]	Shang S, Han Z Q 2019 J. Mater. Sci. 54 3111 Google Scholar
[24]	Cattaneo C A, Evequoz O P E, Bertorello H R 1994 Scripta Metall. Mater. 31 461 Google Scholar
[25]	Cain J B, Clunie J C, Baird J K 1995 Int. J. Thermophys. 16 1225 Google Scholar
[26]	高学鹏, 李新涛, 郄喜望, 吴亚萍, 李喜孟, 李廷举 2007 56 1188 Google Scholar Gao X P, Li X T, Qie X W, Wu Y P, Li X M, Li T J 2007 Acta Phys. Sin. 56 1188 Google Scholar
[27]	Trivedi R, Lipton J, Kurz W 1987 Acta Metall. 35 965 Google Scholar
[28]	Lipton J, Kurz W, Trivedi R 1987 Acta Metall. 35 957 Google Scholar
[29]	Longuet-Higgins M S 1998 P. Roy. Soc. A-Math. Phy. 454 725 Google Scholar

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