The linear stability of the two-dimensional steady flow in an infinite cavity with a right-angled triangular cross-section is investigated numerically by the finite-element method. We consider the case when one of the walls enclosing the right angle moves away from it. Neutral curves, eigenmodes and kinetic-energy production rates are computed. Five different instability modes are found, depending on the aspect ratio, i.e. the length ratio of the walls enclosing the right angle. The spatial structure of the kinetic-energy transfer between the basic flow and the critical modes indicates that three of the critical modes for very shallow cavities are due to an elliptic instability mechanism. Two other critical modes, for moderately shallow to deep cavities, arise due to a centrifugal mechanism. The instabilities found are discussed and compared with those arising in rectangular cavities.

We investigate the hydrodynamic drag force on a viscous sphere in a fluid of different viscosities at small but finite Reynolds numbers when interfacial slip is present at the surface of the sphere. The sphere is small enough for it to retain its spherical shape, as is the case with most small droplets. By using a singular perturbation method, the exterior flow field of the droplet is decomposed into an inner region, where the viscous effects dominate, and an outer region, where the inertia is important. The interior flow of the viscous sphere is also solved analytically. By applying appropriate boundary conditions to the surface of the viscous sphere and matching the conditions between the inner and outer flow fields, stream functions up to the order of Re ² log Re for both the exterior and the interior flow are obtained. Thus, an analytical expression for the drag force coefficient of the viscous droplet is derived. This general expression yields, as spe...