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The secondary breakup of liquid drops, accelerated by a constant body force, is examined for small density differences between the drops and the surrounding fluid. Two cases are examined in detail: a density ratio close to unity (d / o ϭ1.15, where the Boussinesq approximation is valid͒ and a density ratio of ten. A finite difference/front tracking numerical technique is used to solve the unsteady Navier-Stokes equations for both the drops and the surrounding fluid. The breakup is controlled by the Eötvös number ͑Eo͒, the Ohnesorge number ͑Oh͒, and the viscosity and density ratios. If viscous effects are small ͑small Oh͒, the Eötvös number is the main controlling parameter. In the Boussinesq limit, as Eo increases the drops break up in a backward facing bag, transient breakup, and a forward facing bag mode. At a density ratio of ten, similar breakup modes are observed, with the exception that the forward facing bag mode is replaced by a shear breakup mode. Similar breakup modes have been seen experimentally for much larger density ratios. Although a backward facing bag is seen at low Oh, where viscous effects are small, comparisons with simulations of inviscid flows show that the bag breakup is a viscous phenomenon, due to boundary layer separation and the formation of a wake. At higher Oh, where viscous effects modify the evolution, the simulations show that the main effect of increasing Oh is to move the boundary between the different breakup modes to higher Eo. The results are summarized by ''breakup maps'' where the different breakup modes are shown in the Eo-Oh plane for different values of the viscosity and the density ratios.

The secondary breakup of impulsively accelerated liquid drops is examined for small density differences between the drops and the ambient fluid. Two cases are examined in detail: a density ratio close to unity and a density ratio of 10. A finite difference/front tracking numerical technique is used to solve the unsteady axisymmetric Navier-Stokes equations for both the drops and the ambient fluid. The breakup is governed by the Weber number, the Reynolds number, the viscosity ratio, and the density ratio. The results show that Weber number effects are dominant. In the higher density ratio case, d / o ϭ10, different breakup modes-oscillatory deformation, backward-facing bag mode, and forward-facing bag mode-are seen as the Weber number increases. The forward-facing bag mode observed at high Weber numbers is an essentially inviscid phenomenon, as confirmed by comparisons with inviscid flow simulations. At the lower density ratio, d / o ϭ1.15, the backward-facing bag mode is absent. The deformation rate also becomes larger as the Weber number increases. The Reynolds number has a secondary effect, changing the critical Weber numbers for the transitions between breakup modes. The increase of the drop viscosity reduces the drop deformation. The results are summarized by ''breakup maps'' where the different breakup modes are shown in the WeRe plane for different values of the density ratios.

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The field of solid modeling has developed a variety of techniques for unambiguous representations of three-dimensional objects. Feature recognition is a sub-discipline of solid modeling that focuses on the design and implementation of algorithms for detecting manufacturing information from solid models produced by computer-aided design (CAD) systems. Examples of this manufacturing information include features such as holes, slots, pockets and other shapes that can be created on modern computer numerically controlled machining systems. Automated feature recognition has been an active research area in solid modeling for many years and is considered to be a critical component for integration of CAD and computer-aided manufacturing. This paper gives an overview of the state-of-the-art in feature recognition research. Rather than giving an exhaustive survey, we focus on the three of the major algorithmic approaches for feature recognition: graph-based algorithms, volumetric decomposition techniques, and hint-based geometric reasoning. For each approach, we present a detailed description of the algorithms being employed along with some assessments of the technology. We conclude by outlining important open research and development issues.