Melting Zone in a Plasticating Single Screw Extruder

3 Melting Zone in a Plasticating Single Screw Extruder 

Cutting a cross-section A-A of the channel contents in Fig. 6.68, leads to a cross-sectional view that is shown Fig. 6.69. Furthermore, to help visualize and to aid in the mass balances, we can break the channel contents in the melting section down to a differential element shown in Fig. 6.70. 

The Tadmor model assumes Newtonian fluids and shallow channels. The channel cross section and that of the solid bed are assumed to be rectangular. The width of the solid bed profile is denoted by X(z), which is the the main objective that we are seeking with the model. The solid bed that develops at steady state conditions is the focal interest here. Furthermore, Tadmor assumed that melting only occurs at the barrel surface and the solid bed is homogeneous, continuous and deformable. 

From observation, it is clear that the solid bed has a local down channel velocity usz and a local velocity component into the melt film of usy. As before, we resolve the barrel surface velocity Ub into a down channel, v,bz, and a cross channel component, ubx. Using Tadmor s notation, we define the relative velocity between barrel surface and solid bed as 

The change in the solid width is obtained by a differential mass balance as follows 

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