The influence of boundary configurations on the dissipation and stability in fluids at low Reynolds numbers

Abstract

The physical nature of boundaries that restrict the spreading of fluids or appear as interfaces between two immiscible fluids can have a significant influence on the static and dynamic properties of a fluidmechanical system. The aim of the present work is to investigate the influence of different boundary configurations on the energy dissipation and stability of fluid systems in the case of creeping flows, as they typically occur in microfluidic devices. The motion of charged interfacial microparticles induced by an applied electric field is theoretically investigated in this work. In addition to the functional relationship, which relates the velocity of the particle with the strength of the electric field and depends, among others, on the wetting properties of the particle, the deformation of the fluid interface is also determined, which results as a consequence of the charge of the particle and the resulting electric double layer, which is different in both bulk phases. The presence of multiple interfacial particles can effectively be described by a change in the rheological properties of the fluid interface. The theoretical model developed in this work is suitable for determining the effective shear and dilatation viscosity of the interface, which can be expressed as a function of the particle concentration and the contact angle of the particles. Microfluidic systems are typically characterized by a small volume-to-surface ratio, whereby the influence of the boundary conditions on the global properties of a flow increases dramatically. A charged, weakly deformed circular obstacle subjected to a pressure-driven flow can be isolated by a locally restricted electro-osmotic flow induced on the walls of the channel such that the hydrodynamic force on the body vanishes. The exact charge distribution that encloses the solid at the walls of the channel and provides hydrodynamic isolation, is determined theoretically and validated with the help of numerical simulations. The aim of many technical applications is to create an uniform liquid film on a flat surface. However, under certain external conditions, defects or holes can form which, if they are stable, may even lead to component failure. In the course of this work, a stability criterion is determined that predicts under which conditions the defects in spatially limited liquid films will self-heal. In addition, the dynamics of the closure of single circular defects is investigated theoretically and compared with experiments on different substrates. As an extension of the investigation on single defects in liquid films, a model is developed which predicts the temporal evolution of multiple defects. The theoretical results are validated by a comparison with experiments.