摘要
溶质-热毛细对流是流体界面的浓度和温度分布不均导致的表面张力梯度驱动的流动,它主要存在于空间微重力环境、小尺度流动等表面张力占主导的情况中,例如晶体生长、微流控、合金浇筑凝固、有机薄液膜生长等.对其流动进行稳定性分析具有重要意义.本文采用线性稳定性理论研究了双自由面溶质-热毛细液层对流的不稳定性,得到了两种负毛细力比(η)下的临界Marangoni数与Prandtl数(Pr)的函数关系,并分析了临界模态的流场和能量机制.研究发现:溶质-热毛细对流和纯热毛细对流的临界模态有较大的差别,前者是同向流向波、逆向流向波、展向稳态模态和逆向斜波,后者是逆向斜波和逆向流向波.在Pr较大时,Pr增加会降低流动稳定性;在其他参数下,Pr增加会增强流动稳定性.在中低Pr,溶质毛细力使流动更加不稳定;在大Pr时,溶质毛细力的出现可能使流动更加稳定;在其他参数下,溶质毛细力会减弱流动稳定性.流动稳定性不随η单调变化.在多数情况下,扰动浓度场与扰动温度场都是相似的.能量分析表明:扰动动能的主要能量来源是表面张力做功,但其中溶质毛细力和热毛细力做功的正负性与参数有关.
Solute-thermocapillary convection is a flow driven by a surface tension gradient caused by uneven concentration and temperature distribution at the fluid interface.It mainly appears in microgravity environment space or small-scale flow where the surface tension dominates,such as crystal growth,microfluidic,alloy pouring and solidification,organic thin liquid film growth,etc.The stability of this flow is of great significance of these applications.In the present work,the convective instability in the solutal-thermocapillary liquid layer with two free surfaces is examined by linear stability analysis.The relation between the critical Marangoni number and the Prandtl numbers(Pr)is obtained at different capillary ratio(η).The critical modes of solute-thermocapillary flow and pure thermocapillary flow are quite different.The former are downstream streamwise wave,upstream streamwise wave,spanwise stationary mode and upstream oblique waves,but the latter are upstream oblique waves and upstream streamwise wave.When Pr is larger,the flow stability will be weaker when Pr increases.At other parameters,the flow stability will be stronger when Pr increases.In the middle or low Pr,solute capillary force makes the flow more unstabler;at high Pr,solute capillary force may make the flow more stable.Flow stability does not change monotonously fromη.In most cases,the distributions of perturbation concentration field and temperature field are similar.The energy analysis shows the main energy source of perturbation kinetic energy is the surface capillary force,but the work done by solute capillary force and thermal capillary force may be either positive or negative.
作者
赵诚卓
胡开鑫
Zhao Chengzhuo;Hu Kaixin(School of Mechanical Engineering and Mechanics,Ningbo University,Ningbo 315211,Zhejiang,China)
出处
《力学学报》
EI
CAS
CSCD
北大核心
2022年第2期291-300,共10页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(11872032)
浙江省自然科学基金(LY21A020006)资助项目。
作者简介
胡开鑫,副教授,主要研究方向:非牛顿流体,流动稳定性,微重力流体.Email:hukaixin@nbu.edu.cn。
