Effects of Surface Rheology in Free Surface Flows
Interfaces separating two fluids are incredibly complex physical structures and are common throughout science, technology, and nature. Examples from daily life include the air-water interface separating a water drop that is dripping from a leaky faucet from the surrounding air and the interface of a soap bubble (which actually consists of two interfaces) separating the interior of the bubble from its exterior. Other common examples from nature include interfaces between falling rain drops and the surrounding air, and the mist that one encounters at beaches, waterfalls, and fountains where the spray droplets are separated from the surrounding air by an interface. Interfaces and manipulating them are key to technological applications such as thin film coating flows and diverse processes involving drop-by-drop processing such as ink-jet printing, drop-wise manufacturing, spray coating, DNA microarraying, and chemical separations, e.g. extraction. Aside from the coating flows example, the aforementioned situations are all examples of free surface flows that involve abrupt and catastrophic topological changes of interfaces that include physical processes such as breakup (also called pinch-off) as in drop breakup, rupture as in liquid-film or liquid-sheet rupture, and coalescence as in drop or bubble coalescence (similar phenomena also arise in sintering and/or fusion of ceramic, metallic, and polymer particles). These topological changes entail what are referred to as finite-time hydrodynamic singularities. For example, at the location(s) where a drop breaks, the thickness of the drop locally tends to zero while fluid pressure and velocity diverge (hence the reason for the word singularity). In addition to hydrodynamic singularities, the presence of surface-active agents or surfactants at fluid interfaces in free surface flows is another reason scientists have been attracted to the study of such problems.
Adsorption onto and lowering of the surface tension of a fluid interface by surfactants are exploited in applications such as enhanced oil recovery, coating flows, lung surfactants, drop/jet breakup, and film/sheet rupture, with the latter two being among the prime motivators for this PhD thesis. However, surfactant concentration can be nonuniform at the interface because surfactant molecules can be transported along it by convection and diffusion and also due to normal dilatation and tangential stretching of the interface. Thus, aside from simply lowering surface tension, nonuniformity in surfactant concentration causes gradients in surface tension and gives rise to tangential interfacial (Marangoni) stresses. The latter brings about rich physics including tears of wine, interfacial turbulence in mass transfer, and droplet bouncing. In addition to lowering surface tension and the Marangoni effect, surfactants may also induce surface rheological or viscous effects as surfactant molecules deform against each other. The primary goal of this thesis is to advance the understanding of surface rheological effects in situations involving the breakup of surfactant-covered liquid threads (which also includes jets and drops) and liquid sheets. The fundamental understanding developed in this thesis is likely to prove indispensable in and/or assist the development of new technologies where surface rheological effects are central to the processes at hand, e.g. in controlling drop size distributions and avoiding undesirable satellite droplets and/or misting. An initially unexpected but highly rewarding outcome of the research has been the development of techniques for the measurement of surface viscosities, a task that has heretofore proven to be a formidable challenge to experimentalists.
In this thesis, surface rheological effects in free surface flows are examined through both analytical and numerical solution of the incompressible Navier-Stokes equations subjected to the traction boundary condition augmented by the Boussinesq-Scriven constitutive equation to account for surface viscous effects. Rigorous and robust numerical algorithms based on the Galerkin finite element (GFEM) method are developed for predictions of surfactant transport, surface rheological effects and hydrodynamics in response to the motion of moving boundaries. The accuracy of computational predictions is verified by demonstrating that computed results accord well with scaling theories.
- Doctor of Philosophy
- Chemical Engineering
- West Lafayette