Melt flow of thermoplastics

Flows can be classified into streamline, when particles in the fluid follow paths (streamlines) that remain constant with time, and turbulent, when vortices cause unpredictable changes in the flow pattern with time. The changeover occurs at a critical value of the Reynolds number, which is defined as the melt velocity, divided by the viscosity times the channel diameter. The high viscosity of thermoplastic melts causes velocities to be low. Hence, the Reynolds number is very low and the flows are streamline. We will consider steady flows, and ignore the start and end of injection and blow-moulding flows, when the melt accelerates and decelerates, respectively. However, in the RIM process (Section 5.6.5), turbulent flow of the low viscosity constituents in the mixing head achieves intimate mixing. 

In a simple shear flow, the streamlines are parallel. The velocity along each streamline remains constant, with a velocity gradient at right angles to the 

Polymer melts adhere to metals, so there is no slip at the metal/polymer interface. When one metal boundary of the melt moves parallel to another at a velocity V, the drag flow causes a shear flow with a constant shear rate (Fig. 5.4). At the interfaces, the polymer and metal velocities are equal (0 at the stationary surface and Vm at the moving surface. The shear strain rate y is given by 

Pressure flow is a shear flow between fixed metal boundaries, due to a pressure gradient in the melt. The pressure p falls down the streamlines, which are perpendicular to the isobars (Fig. 5.4). Appendix B derives the relationship between the pressure gradient, the channel dimensions and the flow law of the fluid. For rectangular, circular or annular cross sections, the shear stress r varies linearly across the channel, and the velocity is maximum at the centre. The Newtonian flow law in Chapter 3 is 

Many shear flows are combinations of pressure and drag flows. 

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