Steering a Thermocapillary Droplet Motion in Combined Couette–Poiseuille Flow Steering a thermocapillary droplet motion

• Published in: Journal of engineering mathematics Vol. 151; no. 1
• Main Authors: Basak, Arindam, Lakkaraju, Rajaram, Sekhar, G. P. Raja
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.04.2025
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Theoretical and Applied Mechanics; Couette–Poiseuille flow; Thermocapillary; Marangoni effect
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-025-10432-z

Classical studies on surfactant-laden droplets in a tubular Poiseuille flow by Pak et al. (J Fluid Mech 753:535–552, 2014) and Dandekar and Ardekani (J Fluid Mech 902:A2, 2020) have elucidated remarkable cross-stream migration phenomena as a second-order effect in low surface Péclet number P e s ( = V c a / D s ) limit, where V c is the characteristic flow velocity, a denotes the droplet radius and D s is the diffusivity of the surfactant. However, in many biomedical lab-on-a-chip devices, droplet motion occurs between two parallel plates due to combined shear and pressure-driven flow. We unravelled that such a combined flow can lead to better steering of the droplet with enhanced migration velocity. Our model incorporates heat generation by living cells via a thermal dipole within the droplet, surrounded by a non-isothermal medium. We found that the cross-stream migration velocity can be at the leading order in P e s , provided the thermocapillary effects combined with the strength of the thermal dipole are strong enough. A novel aspect of this work is the definition of flow control parameters based on a constant volumetric flow rate condition, which governs the droplet migration and flow patterns. We illustrate that a careful transition between flow profiles, specifically from Poiseuille to Couette, provides optimal control in droplet migration, and employing a rectangular geometry instead of a tubular gives better regulation on steering a droplet for accurate microfluidic investigations.