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李祥伟, 郝浩浩, 谭唤书. 溶质梯度诱导悬浮液滴自驱动的数值模拟研究. 力学学报, 2024, 56(5): 1-10. DOI: 10.6052/0459-1879-24-011
引用本文: 李祥伟, 郝浩浩, 谭唤书. 溶质梯度诱导悬浮液滴自驱动的数值模拟研究. 力学学报, 2024, 56(5): 1-10. DOI: 10.6052/0459-1879-24-011
Li Xiangwei, Hao Haohao, Tan Huanshu. Numerical study of solute gradient-induced self-propulsion of suspended droplets. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(5): 1-10. DOI: 10.6052/0459-1879-24-011
Citation: Li Xiangwei, Hao Haohao, Tan Huanshu. Numerical study of solute gradient-induced self-propulsion of suspended droplets. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(5): 1-10. DOI: 10.6052/0459-1879-24-011

溶质梯度诱导悬浮液滴自驱动的数值模拟研究

NUMERICAL STUDY OF SOLUTE GRADIENT-INDUCED SELF-PROPULSION OF SUSPENDED DROPLETS

  • 摘要: 悬浮液滴在溶质浓度梯度下会发生自发的移动. 其原因是液滴界面处的非均匀分布溶质会使得流体界面上出现界面张力梯度, 诱发界面流动. 该过程涉及自驱动液滴的界面移动、界面附近流场与溶质浓度场的演化, 以及多物理场的耦合效应. 认识和理解这一复杂动力学过程具有一定的基础科学意义. 文章通过联合守恒型Allen-Cahn方程、不可压Navier-Stokes方程和溶质的对流扩散方程, 构建了一套能够描述溶质梯度诱导液滴自驱动现象的多相-多组分流体数值模型. 通过算例对照和理论对比(静置液滴的拉普拉斯压差、浮力驱动的气泡上升和溶质浓度驱动液滴的迁移)验证了数值模型的准确性. 模拟并研究了不同Marangoni数下溶质Marangoni效应诱导的双液滴融合或分离现象. 结果表明, 液滴的尺寸越大, 移动速度越快, 且增大Marangoni数使得自驱动液滴界面传质从扩散主导转变为对流主导, 增强了液滴移动对环境溶质场的影响, 进而推迟两液滴的融合发生时刻或者减小两者的分离速度. 为后续解决多相-多组分流体系统中的物理问题提供了一套可靠的数值模型, 为多组分微液滴操控提供了参考数据.

     

    Abstract: In the presence of solute concentration gradients, suspended droplets undergo spontaneous motion. The reason is that the non-uniform distribution of solutes at the droplet interface can cause an interfacial tension gradient at the fluid interface, inducing interfacial flow. This process involves the interface movement of the self-propelled droplet, the evolution of the near-interface flow field, the solute concentration field, and the coupling effects of multiple physical fields. Understanding this complex dynamic process holds significance. This paper constructs a multiphase-multicomponent fluid numerical model to describe solute-induced droplet migration phenomena by combining the conservation-type Allen-Cahn equation, incompressible Navier-Stokes equation, and the advection-diffusion equation for solute. The accuracy of the numerical model is validated through case studies and theoretical comparisons (Laplace pressure difference of stationary droplets, buoyancy driven bubble rise, and solute concentration driven droplets migration). The simulation investigates solute Marangonii effects under different Marangonii numbers, including phenomena of coalescence and separation of two droplets in different sizes. Results indicate that larger droplets exhibit faster movement, and an increased Marangonii number shifts the self-propelled droplet interface mass transfer from diffusion-dominated to advection-dominated, enhancing the impact of droplet movement on the ambient solute field. Meanwhile, the solute gradient at the interface is reduced, which weakens the Marangonii effect, and decreases the droplet migration speed. The larger the size of the droplet, the more significant decrease in its velocity. This study provides a reliable numerical model for solving physical problems in multiphase multi-component fluid systems in the future and provides reference data for the manipulation of multi-component micro-droplets.

     

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