Droplet migration in a wavy microchannel under transverse temperature gradient

The migration dynamics of droplets in confined microchannels are pivotal in advancing the design and functionality of next-generation microfluidic systems, with wide-reaching implications for biological assays, chemical synthesis, drug delivery, and thermal regulation. This study presents a comprehensive numerical investigation of droplet behavior in a wavy microchannel subjected to a transverse temperature gradient, focusing on the complex interplay between thermocapillary forces and geometric confinement. The unique non-uniform channel topology induces spatial variations in hydrodynamic resistance and pressure distribution, which, when coupled with thermally induced Marangoni stresses, generate intricate cross-stream migration patterns. Unlike in straight channels, where migration could be explained by a simple linear superposition of flow-induced and thermocapillary effects, the oscillatory nature of the wavy walls leads to highly non-linear and coupled interactions, making the migration behavior far more complex. Our parametric analyses reveal that increasing the temperature gradient intensifies the droplet's migration toward the heated wall, while amplified oscillations are due to the periodic channel geometry. Moreover, key parameters such as wave-pitch, wave-height, initial droplet position, and the thermal conductivity ratio significantly influence both the transient migration dynamics and the final steady-state positioning of the droplet. These findings reveal a rich and nuanced control mechanism for droplet manipulation, where the geometrical modulation of the microchannel synergistically interacts with thermal gradients, facilitating precise droplet steering and positioning. The results provide key insights for designing microfluidic platforms that use temperature gradients in lab-on-chip devices, thermal droplet sorters, targeted drug delivery, and advanced diagnostics, where precise droplet control is crucial.