On a Generalized Approach to Linear Stability of Spatially Dependent Thin Film Flows: Sandra M. Troian, Princeton University

Recent interest in microscale flows, which can sustain exceedingly large surface to volume ratios, has focused attention on the use of normal or shear force actuation to effect liquid migration along a solid surface. For instance, a thin liquid film supported on a differentially heated substrate will spontaneously flow toward the cooler end in a process known as thermocapillary forcing. In another example, a film contacted by a non-uniform distribution of surface active material will rapidly flow toward the uncontaminated end under the action of Marangoni stresses. Such spreading films typically undergo fingering instabilities at the advancing front which resemble either a series of parallel liquid rivulets or highly ramified dendritic structures. During the past several years, we have used a combination of experiment and theoretical modeling in an effort to provide a unified framework describing the stability characteristics of these and related thin film flows. The presence of capillary, thermocapillary, Marangoni or van der Waals stresses in free surface films creates spatially (and temporally) dependent interface shapes. The linearized operators governing disturbances in film thickness or concentration are therefore typically non self-adjoint. A consequence of this feature is that conventional modal analysis can only describe the asymptotic behavior of these

systems. A rigorous description of the early and intermediate behavior requires a transient growth study. This type of analysis not only identifies the growth rate of optimal disturbances but reveals their initial and evolved waveform shape at all times. Strongly non-normal operators can introduce the possibility of severe disturbance amplification and subsequent non-linear coupling.

In this presentation, we outline the transient growth behavior and amplification of optimal disturbances for thermocapillary driven flows. Time permitting, we review Marangoni driven systems as well. We examine the pseudospectral behavior of the associated disturbance operators and illustrate why transient growth studies offer a more suitable probe of the stability of free surface thin film flows.