On the combined role of gravity and rheology in thermocapillary-driven droplet spreading

Abstract

The complex rheology of biofluids and industrial fluids is a decisive factor in their deformation and spreading on a heated substrate. However, the intervening role of gravity forces remains unexplored. Here, we apply the lubrication approximation to the momentum equation and the power-law constitutive relation for inelastic non-Newtonian fluids, with the intermolecular forces being accounted for within the continuum hypothesis. The derived evolution equation for droplet height has been solved numerically using the finite element method. The Marangoni stress dominates the conjoining–disjoining pressure in the ‘Marangoni film regime’. The gravity effect causes a significant curvature of the rear edge, leading to a pancake-like droplet shape and reduced capillary ridge height near advancing fronts. Furthermore, increasing capillary ridge height with shear-thinning and faster-moving advancing fronts with either enhanced Marangoni stress or shear-thickening are both dampened by gravity. The droplet regime, previously observed in microgravity conditions, no longer exists under gravity. The drop deviates from its initial shape as dictated by its rheology but maintains the same shape afterwards, leading to a new regime named ‘transition without breakup.’ The gravity effect weakens after initial deformation, and the dominant conjoining–disjoining pressure results in a constant migration speed without further deformation. The ‘transition with breakup regime’, where droplets break apart into smaller droplets, is influenced by a critical interaction between Marangoni stress, intermolecular force, and gravity force. The onset of rupture strongly depends on the fluid rheology and the thermocapillary strength. The presented regime maps provide the critical parameters for switching regimes and highlight exclusive spreading states under gravity. These insights on the critical interaction between gravity, shear-dependent rheology, and thermocapillary actuation for partially wetting droplets could lead to more versatile microfluidic devices for handling complex biofluids.