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<p>While the thermocapillary migration of single and compound droplets has been extensively studied in unbounded media, the synchronized transport and interaction dynamics of multiple compound droplets within confined geometries remain poorly understood. This study addresses this gap by numerically investigating the thermocapillary migration of two axially aligned compound droplets inside a microchannel featuring a localized geometric constriction. Using the front-tracking method, we aim to delineate the transition between interacting and non-interacting regimes, a distinction critical for the precise control of multi-phase flows in microfluidic systems. The coupled thermal and hydrodynamic behaviors are systematically analyzed as a function of the Marangoni number (<i>Ma</i>), the axial positioning of the leading droplet, the inner-to-outer droplet size ratio (<i>R</i><sub><i>io</i></sub>), and the relative constriction depth (<i>d/R</i><sub><i>c</i></sub>). Our results reveal that inter-droplet interaction is primarily triggered when the trailing droplet catches up to the leading one near the constriction, where local velocity reaches its minimum. We identify <i>Ma</i> as a dominant control parameter; higher <i>Ma</i> values intensify thermal convection, which disrupts the local temperature field and delays the onset of interaction by reducing the trailing droplet’s velocity. Crucially, we find that geometric and internal configurations dictate the interaction mode: shallow constrictions (<i>d/R</i><sub><i>c</i></sub> &lt; 0.58) or larger inner cores (<i>R</i><sub><i>io</i></sub> ≥ 0.7) promote independent passage by enabling droplet elongation or rapid escape. In contrast, deeper constrictions and smaller inner cores reduce interfacial deformation, thereby facilitating closer proximity and significant multi-body interaction. The study culminates in the establishment of a comprehensive phase diagram based on <i>H</i><sub>0<i>L</i></sub><i>/R</i><sub><i>o</i></sub>, <i>R</i><sub><i>io</i></sub>, and <i>Ma</i>. This diagram serves as a predictive tool to define the boundaries between interacting (<i>ID</i>* = 0) and non-interacting (<i>ID</i>* &gt; 0) regimes. By providing a mechanistic understanding of how geometry and thermal forces can be leveraged to synchronize or separate double emulsions, this work offers a framework for the optimized design of microfluidic devices for targeted drug delivery and advanced material synthesis.</p>

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Thermocapillary Interaction of Two Aligned Compound Droplets in a Constricted Microchannel

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Vinh T. Nguyen,
  • Nang X. Ho,
  • Vinh D. Nguyen,
  • Kien T. Nguyen,
  • Truong V. Vu

摘要

While the thermocapillary migration of single and compound droplets has been extensively studied in unbounded media, the synchronized transport and interaction dynamics of multiple compound droplets within confined geometries remain poorly understood. This study addresses this gap by numerically investigating the thermocapillary migration of two axially aligned compound droplets inside a microchannel featuring a localized geometric constriction. Using the front-tracking method, we aim to delineate the transition between interacting and non-interacting regimes, a distinction critical for the precise control of multi-phase flows in microfluidic systems. The coupled thermal and hydrodynamic behaviors are systematically analyzed as a function of the Marangoni number (Ma), the axial positioning of the leading droplet, the inner-to-outer droplet size ratio (Rio), and the relative constriction depth (d/Rc). Our results reveal that inter-droplet interaction is primarily triggered when the trailing droplet catches up to the leading one near the constriction, where local velocity reaches its minimum. We identify Ma as a dominant control parameter; higher Ma values intensify thermal convection, which disrupts the local temperature field and delays the onset of interaction by reducing the trailing droplet’s velocity. Crucially, we find that geometric and internal configurations dictate the interaction mode: shallow constrictions (d/Rc < 0.58) or larger inner cores (Rio ≥ 0.7) promote independent passage by enabling droplet elongation or rapid escape. In contrast, deeper constrictions and smaller inner cores reduce interfacial deformation, thereby facilitating closer proximity and significant multi-body interaction. The study culminates in the establishment of a comprehensive phase diagram based on H0L/Ro, Rio, and Ma. This diagram serves as a predictive tool to define the boundaries between interacting (ID* = 0) and non-interacting (ID* > 0) regimes. By providing a mechanistic understanding of how geometry and thermal forces can be leveraged to synchronize or separate double emulsions, this work offers a framework for the optimized design of microfluidic devices for targeted drug delivery and advanced material synthesis.