"Nonlinear Stability of Interfacial Fluids in Microchannels" Entwicklung von numerischen und asymptotischen Modellen zur Beschreibung des Stabilitätsverhaltens von Grenzflächenströmungen in Mikrokanälen unter dem Einfluss von elektrischen Feldern.
Zusammenfassung der Projektergebnisse
Recent progress in the design and utilization of micro-fluidic devices has found a large number of technical applications. Examples include life-science industries for pharmaceuticals and medicine, manufacturing of photographic films, and industrial applications of combinatorial synthesis and polymer extrusion, among many others. Typically, micro-fluidic devices are operated at Reynolds numbers of order one or even smaller. As the Reynolds number is very small, inertial effects are negligible. Consequently, the flow is often stable and governed by viscous dissipation. In addition, the dynamical behavior of multiphase flows in the micro-scale regime depends on several parameters like density, viscosity, surface tension, concentration of solute, density difference between the gas and liquid phase, liquid motion (direction), van der Waals interactions, surface roughness, and operating conditions (temperature, pressure gradients, and gravity). Since these parameters are fixed for many technical systems, practical and efficient ways to control the fluid motion are very limited. The effects of an external electric field on the interfacial dynamics in two-dimensional multiphase flows has been studied computationally and theoretically in this research project. The interfacial stability in an electric field is characterized by a balance of surface tension, hydrodynamic and electric stresses at the interface. The electric stresses cause a flat interface to distort, while surface tension tends to restore the original shape. The time-dependent dynamics of the evolving interface constitutes a non-linear problem that has to be addressed numerically. The methodology that has been applied in this work encompassed numerical simulations of the full problem and analytical work on reduced model equations. Several multiphase flow problems have been considered. The computational studies cover periodic arrays of monodisperse drops, buoyant gas bubbles, and two superposed viscous fluid layers in a Couette flow device. The primary goal of the research project was to elucidate the impact of the imposed electric field on the dynamics of the evolving fluid-fluid interfaces. Both, pairs of perfect and leaky dielectrics were considered and the electrically induced force emerges due to the difference in the polarization and the electric conductivity of the media. It was found that vertical electric fields affect the interfacial deformation to produce elongated drops and faster rising bubbles compared to systems with the same flow conditions, but in the absence of the electric field. Furthermore, the numerical simulations of interfacial instability in electrified Couette flow have revealed a rich array of dynamical behavior that arises in spite of the simple model of electrified two-layer flow. The numerical simulations confirmed the theoretical finding that a vertical electric field destabilizes the perturbed interface between a pair of perfect dielectrics, irrespective of the permittivity ratio between both fluids. Increasing the strength of the electric field enhances the stress imbalance at the interface implying faster growth rates and stronger elongated fingers. At even higher field strengths localized dimples originate on the interface, which are quickly magnified into sets of interpenetrating fingers. By contract, the same electric field can either completely stabilize a system of leaky dielectrics or even further enhance its instability depending on the particular permittivity and conductivity ratio between the fluid pair. In addition, the numerical simulations also revealed an interesting and distinct nonlinear phenomenon for the fingering instability in leaky dielectrics. For some parameter combinations the unstable interface evolves as a large amplitude nonlinear wave whose crest is driven towards the upper electrode and its trough towards the lower one. The interface eventually touches both wall electrodes almost simultaneously thus producing an alternating periodic series of plug flows as observed in the experiments of Ozen et al. The present study demonstrates the potential of utilizing electric fields in the control of two-layer fluid systems in applications where stabilization or destabilization of the fluid interface is desired. Moreover, the results can be utilized to develop effective mechanisms towards active control of the dynamics flows involving gas-liquid or liquid-liquid interfaces.
Projektbezogene Publikationen (Auswahl)
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“Dynamics of Liquid Jets and Threads Under the Action of Radial Electric Fields: Microthread Formation and Touchdown Singularities”. Physics of Fluids, 21–032109, 2009
Qiming Wang, Stefan Mählmann and Demetrios Papageorgiou
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“Numerical Study of Electric Field Effects on the Deformation of Two-dimensional Liquid Drops in Simple Shear Flow at Arbitrary Reynolds Number”. Journal of Fluid Mechanics 626 367-393,2009
Stefan Mählmann and Demetrios T. Papageorgiou
