I n this paper numerical results are presented for the buoyancy-driven rise of a deformable bubble through an unbounded quiescent fluid. Complete solutions, including the bubble shape, are obtained for Reynolds numbers in the range 1 < R 6 200 and for Weber numbers up to 20. For Reynolds numbers R < 20 the shape of the bubble changes from nearly spherical to oblate-ellipsoidal to spherical-cap dependingon Webernumber; at higher Reynoldsnumbers 'disk-like ' and 'saucer-like ' shapes appear a t W = O( 10). The present results show clearly that flow separation may occur at a smooth free surface at intermediate Reynolds numbers; this fact suggests a qualitative explanation of the often-observed irregular (zigzag or helical) paths of rising bubbles.

We present here a brief description of a numerical technique suitable for solving axisymmetric (or two-dimensional) free-boundary problems of fluid mechanics. The technique is based on a finite-difference solution of the equations of motion on an orthogonal curvilinear coordinate system, which is also constructed numerically and always adjusted so as to fit the current boundary shape. The overall solution is achieved via a global iterative process, with the condition of balance between total normal stress and the capillary pressure at the free boundary being used to drive the boundary shape to its ultimate equilibrium position.

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Focusing on the Permian-Triassic boundary, ca. 251 Ma, I explore the possibility that mass extinction can be caused by an extremely fast, explosive release of dissolved methane (and other dissolved gases such as carbon dioxide and hydrogen sulfide) that accumulated in the oceanic water masses prone to stagnation and anoxia (e.g., in silled basins). The mechanism of the explosive release is the same as in the Lake Nyos disaster of 1986, i.e., a watercolumn eruption caused by the interplay of buoyancy forces and exsolution of dissolved gas. The eruption brings to the surface deep anoxic waters that cause extinctions in the marine realm. Terrestrial extinctions are caused by explosions and conflagrations that follow the massive release of methane (the air-methane mixture is explosive at methane concentrations between 5% and 15%) and by the eruption-triggered floods. This scenario accounts well for the available data, and may be relevant to other phenomena.

The conical-channel flow of a dilute polymer solution is investigated theoretically. The stress field due to polymer additive is calculated using a new molecular model, based on the physical picture of the polymer molecules unravelling in strong flows and Batchelor's theory for the stress in a suspension of elongated particles. Good agreement is obtained with the experimental results of James & Saringer (1980). The absence of a significant polymer effect in a two-dimensional case (the wedge-channel flow), observed by the same authors (James & Saringer 1982a), is also explained. The fundamental differences between the proposed model and the elastic-dumbbell models are discussed.