Numerical simulation of non-Newtonian fluids flow over surfaces

Abstract: Wetting of surfaces by droplets of non-Newtonian fluids is important for various industrial and natural processes such as coating and cleaning of surfaces and inkjet printing, to name a few. Viscoelastic fluids are compounds of a very small amount of polymers and solvent. They are categorized as non-Newtonian fluids, and they exhibit both elasticity and shear dependent viscosity. Despite their relevance and abundance in our environment, dynamic wetting of viscoelastic fluids has been studied much less than that of the Newtonian fluids. Furthermore, many of the viscoelastic studies make simplifying assumptions of the contact line movement, for example, a constant value of the contact angle independent of the spreading speed of the droplet.In this thesis work, we implement a numerical framework for dynamic contact line problems of viscoelastic fluids, taking into account contact line friction or contact line hysteresis when necessary. We solve the coupled Cahn-Hilliard, Navier-Stokes and viscoelastic constitutive models to reveal detailed information about the flow physics, such as the polymeric stress distributions inside the drops. Especially interesting is the vicinity of discontinuity regions e.g. the contact-line and liquid bridge between the coalescing drops. First, we present the idea of dual-resolution grids to address the high interfacial resolution requirements for a viscoelastic two-phase flow. In particular, a dual-resolution algorithm is presented and validated for the wetting of viscoelastic fluids. Secondly, we apply our algorithm to investigate the effect of non-Newtonian properties on jumping of two merging droplets from a superhydrophobic surface, a problem which might be of interest for self-cleaning surfaces. In the last part, the physical effects of non-Newtonian properties are investigated on both the initial wetting regime on a smooth hydrophilic surface and the pinning and depinning of a droplet in the presence of the contact angle hysteresis.