Hele-Shaw model

Today, the most widely used model simplification in polymer processing simulation is the Hele-Shaw model [5], It applies to flows in "narrow" gaps such as injection mold filling, compression molding, some extrusion dies, extruders, bearings, etc. The major assumptions for the lubrication approximation are that the gap is small, such that h < . L, and that the gaps vary slowly such that... 

A schematic diagram of a typical flow described by the Hele-Shaw model is presented in Fig. 5.18. 

There are various special forms and simplifications of the above equation and they are given below. In subsequent chapters of this book we will illustrate how the various forms of the Hele-Shaw model are implemented to solve realistic mold filling problems. 

Newtonian-isothermal Hele-Shaw model. A special form of the Hele-Shaw type flow governing equations is the isothermal Newtonian case where r/(z) = //,. This simplification leads to flow a conductance given by... 

Generalized Newtonian Hele-Shaw model using a power law viscosity. For a... 

Hele-Shaw model for compression molding of a Newtonian fluid. A special case, where the z-velocity component plays a significant role and must be included, is the compression molding process. The process is schematically depicted in Fig. 5.21. 

Using the Hele-Shaw model, analyze a compression molding problem where the melt is allowed to move only in the x-direction. Use a dimension in the x-direction of 2L, and in the y-direction of W. The gapwise thickness is h. The two flow fronts are located at x = L. 

The Hele-Shaw model was used to describe the flow in the FAN formulation. For a Newtonian case, the flow is described by... 

Write a two-dimensional finite element program, using constant strain triangles and ID tube elements, to predict the flow and pressure distribution in a variable thickness die. Use the Hele-Shaw model. Compare the FEM results with the analytical solution for an end-fed sheeting die. 

The material flow in a thin cavity can be modeled by the Hele-Shaw model. Also a lubrication approximation can be used with assumptions such as a negligible inertial force, dominant shear stress, a thin cavity (compared with the planar dimensions), incompressible fluid, a small capillary number and a generalized Newtonian fluid (Hieber and Shen, 1980 Ilicker and Folgar,1983). 

Lee, K.S. and Claridge, E.L. 1968. Areal Sweep Efficiency of Pseudoplastic Fluids in a Five-Spot Hele-Shaw Model. SPEJ. 8 (1) 52-62. SPE-1849-PA. DPI 10.2118/1849-PA. 

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