A boundary-element method is applied to solve the equations describing the deformation of a two-dimensional liquid region under the influence of gradients of the curvature of its outer boundary. This research is motivated by a desire to obtain a better understanding of viscous sintering processes in which a granular compact is heated to a temperature at which the viscosity of the constituent material becomes low enough for surface tension to cause adjacent particles to deform and coalesce. The boundary-element method is capable of showing how a moderately curved initial shape transforms itself into a circle. Initial shapes showing more extreme curvature gradients, which are relevant in the initial stages of a sintering process, cannot be dealt with by the boundary-element method in its present form. The numerical solution of the continuous model shows a tendency to create oscillations in the outer boundary of the liquid region. On the other hand, an analytical small-amplitude analysis shows that rapid oscillations vanish exponentially fast.
Mathematical models are presented that describe diffusion‐controlled etching near resist edges. To understand the role of the various physical parameters, a simple maskless one‐dimensional model is studied first. The study of a purely diffusion‐controlled case suggests that mathematical models for etching problems may be solved by means of perturbation techniques that assume relatively small displacements of the etching surface. The perturbation procedure is then applied to a two‐dimensional problem that involves a mask. Assuming a stationary etchant and diffusion control, it is shown that etch rates are largest close to the resist edge. As a result, the etching profile reveals a bulging shape near the mask edge, confirming earlier observations reported in the literature. A case with convection is considered next. It is shown that the very same bulge that resulted from the analysis of the stationary case may also appear when convection plays a role. The perturbation procedure depends upon an important dimensionless parameter β. Tabulated values of this parameter for various etching systems are presented.
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