Dynamics and stability of non-inertial coating flows over heterogeneous surfaces
The further development of numerous applications involving micro- and nano-technology requires a fundamental understanding of small-scale, free-surface flows over surfaces with heterogeneity in chemistry, topography, or temperature. Because the surface to volume ratio scales inversely with the characteristic length scale, interfacial effects such as capillary forces and gradients in surface tension dominate in these microscale systems. The combined effects of these forces leads to fascinating dynamical behavior because the liquid-gas interface is deformable, and the velocity field is coupled to this free-surface profile. These flows often are susceptible to hydrodynamic instabilities that produce regular patterns and lead to spatial variations in the free-surface shape, which is undesired in many applications.
This dissertation is focused on a theoretical investigation of the motion and stability against rupture of a thin liquid film flowing over a locally heated surface, which has applications to coating technology and heat transfer devices. The temperature gradient imposed by the heater induces a gradient in surface tension, or Marangoni stress, that opposes the bulk flow and leads to the formation of a pronounced ridge in the gas-liquid interface. This ridge has been observed in experiments to break up into an array of parallel rivulets aligned with the flow, which can lead to film rupture and dry-out. The theoretical analysis predicts two types of instabilities that can lead to film breakdown. The rivulet instability is linked to the curvature of the fluid ridge at the upstream edge of the heater. A novel, oscillatory instability due to a lateral thermocapillary flow above the heater is also found for volatile fluids with sufficiently large heat transfer from the free surface. It is shown that appropriate topographical patterning of the substrate can modify the capillary pressure gradient and stabilize the flow for a large range of parameters. The nonlinear dynamics of the flow after instability onset is computed using a disjoining-conjoining pressure model that enables the simulation of film rupture and the subsequent dynamics.
Several related problems involving coating flows on heterogeneous surfaces are also explored. A theoretical analysis of the selective dip-coating of chemically micropatterned surfaces is performed in the presence of surfactants and for non-Newtonian rheology, both of which are relevant to microfabrication and self-assembly processes. Finally, the fingering instability of thin liquid films spreading across inclined substrates due to thermocapillarity is studied. The role of a gravitational counterflow on the spreading behavior and in stabilizing the fingering instability at the advancing contact line is investigated.