# Hele-Shaw approach

Generalization of the Hele-Shaw approach to flow in thin curved layers [c.175]

The laser approach without a matrix can be employed in two main ways. Since the intensity and spot size of the laser pulse or beam can be adjusted, the energy deposited into a sample ranges from a very large amount confined to a small area of sample to much less spread over a larger area. Thus, in one mode, the laser can be used to penetrate down through a sample, each pulse making the previously ablated depression deeper and deeper. This approach is depth profiling, which is useful for examining variations in the composition of a sample with depth (Figure 2.4a). For example, gold plating on ceramic would show only gold ions for the first laser shots until a hole had been drilled right through the gold layer there would then appear ions such as sodium and silicon that are characteristic of the ceramic material, and the gold ions would mostly disappear. [c.12]

Equation (5.49) derived for isothermal Newtonian flow in thin cavities, is called the pressure potential or Hele-Shaw equation. Analogous equations in terms of pressure gradients can be obtained using other types of boundary conditions in the integration of components of the equation of motion given as Equation (5.41). The lubrication approximation approach has also been generalized to obtain solutions for non-isothernial generalized Newtonian flow in thin layers. The generalized Hele-Shaw equation for non-isotherraal generalized Newtonian fluids is used extensively to model narrow gap flow regimes in injection and compression moulding (Hieber and Shen, 1980 Lee et al, 1984). Other generalized equations, derived on the basis of the lubrication approximation, are used to model laminar flow in calendering, coating and other processes where the domain geometry allows utilization of this approach (Soh and Chang, 1986 Hannart and Hopfinger, 1989). [c.173]

See pages that mention the term

**Hele-Shaw approach**:

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Practical aspects of finite element modelling of polymer processing (2002) -- [ c.175 ]