Thermocapillary manipulation of microfluidic droplets: Theory and applications

It was recently demonstrated by our group that a focused laser beam could be used to produce a net force on a moving microfluidic drop. The aim of the paper is to establish a scaling law for this net force by a examining the closely related but simpler situation of a very thin stationary circular drop of fixed shape submitted to a thermocapillary (Marangoni) stress. This leads us to recall the depth-averaged model for a microfluidic pancake-like undeformable drop submitted to a thermocapillary forcing. Our numerical method to solve the associated equations is then introduced and validated. In the case of a localized heating and for an 'inverse' Marangoni effect (i.e. the surface tension increases with temperature) mimicking the experimental situation of a focused laser beam impinging on a surfactant laden water-oil interface, the flow field is computed and compared to experimental observations. The viscous shear stresses (normal and tangential) and the pressure force are then computed on the interface, yielding a simple expression for the total force acting on the droplet. Further numerical investigations are conducted and enable us to propose a scaling law for the net force combining all pertinent parameters.