| In this thesis, we first discuss mechanical buckling instabilities of a rigid film under compression interacting repulsively with a substrate through a thin fluid layer [1]. The buckling occurs at a characteristic wavelength that increases as the 1/4th power of the bending stiffness, like a gravitational instability studied previously by Milner et al. However, the potential can affect the characteristic buckling wavelength strongly, as predicted by Huang and Suo. If the potential changes sufficiently sharply with thickness, this instability is continuous, with an amplitude varying as the square root of overpressure. We discuss three forms of interaction important for the case of Langmuir monolayers transferred to a substrate: Casimir-van der Waals interaction, screened charged double-layer interaction and the Sharma potential. We verify these predictions numerically in the Van der Waals case.;The second part of the thesis is dedicated to the creeping motion of inviscid fluid plugs in a capillary tube with longitudinal grooves filled with a carrier fluid. This extends Bretherton's research on plug motion in a circular tube for small capillary numbers Ca.;We first study the tube corrugation effect perturbatively, which reveals the slow plug shape relaxation in the weakly grooved tubes. Tube corrugation creates an unbalanced capillary pressure and leads to a carrier fluid flux in the transverse plane. This flux controls the relaxation of the plug shape to its infinite-length limit and leads to a new decay length L* in the grooved tube. For long-wavelength corrugation, we find that L*(∼Ca-1) is much longer than the corresponding decay length Linfinity(∼ Ca1/3) in a circular tube. Thus for finite plugs with sufficiently small Ca, L* can exceed the plug length so that its shape remains perturbed by the tube corrugation. Thus small modification in the tube geometry can increase the influence of the carrier fluid film on the plug motion.;After the perturbative analysis, we perform a numerical study for the plug motion in tubes with finite corrugation. Plugs move slower in tubes with deeper corrugation due to the extra dissipation of energy. Furthermore, the finite-length effect of the plug speed U is negligible unless the plug length becomes comparable to the Bretherton remobilization length Linfinity. However, the pressure drop across the plug Delta P is more sensitive to the plug length because of the slow relaxation mode L*. The numerical data also demonstrate a non-monotonic length dependence of DeltaP for sufficiently large tube corrugation. This property may be explored experimentally to effectively transport plugs in the grooved channel. |
