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The migration characteristics of a suspended deformable droplet in a parallelplate microchannel is studied, both analytically and numerically, under thecombined influence of a constant temperature gradient in the transversedirection and an imposed pressure driven flow. Any predefined transverseposition in the micro channel can be attained by the droplet depending on theapplied temperature gradient in the cross-stream direction or how small thedroplet is with respect to the channel width. For the analytical solution, anasymptotic approach is used, where we neglect any effect of inertia or thermalconvection of the fluid in either of the phases. To obtain a numericalsolution, we use the conservative level set method. Variation of temperature inthe flow field causes a jump in the tangential component of stress at thedroplet interface. This jump in stress component, which is the thermalMarangoni stress, is an important factor that controls the trajectory of thedroplet. The direction of cross-stream migration of the droplet is decided bythe magnitude of the critical Marangoni stress, corresponding to which thedroplet remains stationary. In order to analyze practical microfluidic setup,we do numerical simulations where we consider wall effects as well as theeffect of thermal convection and finite shape deformation on the cross-streammigration of the droplet.

Cross-stream migration characteristics of a deformable droplet in a non-isothermal Poiseuille Flow through Microfluidic Channel