Answer to the April 15, 2000 Question

Diagnostic Quiz in Polymer Processing Basics

Perspective Meter:

1. A Newtonian liquid is subject to drag flow between parallel plates. The upper plate moves with velocity V while the lower plate is stationary. illustrate: a) the velocity profile and b) the shear rate profile in the flow as functions of the coordinate y normal to the direction of flow.

The velocity profile varies linearlly from 0 at the stationary plate to V at the moving plate. The shear rate is constant and equal to the velocity difference divided by the height of the gap.

2. Write the continuity equation. What basic principle does this equation represent?

The continuity equation represents the principle of conservation of mass. It comes in many forms, a couple of which are given here.

3. In a stress relaxation experiment, a cylinder of material is instantaneously stretched from length Lo to length Lf and held at Lf. Sketch qualitatively the tensile stress as a function of time which is required to maintain this deformation for a) an elastic solid; b) a viscoelastic solid; and c) a Newtonian liquid.

4. Give one specific example of a chain-growth polymerization reaction.

There are many examples of chain-growth polymerization. One for polyethylene is provided here.

5. Sketch the tensile modulus as a function of temperature for a typical non-crystallizable thermoplastic polymer. Identify particular regions of interest on the curve.

6. Velocities u and v in a flow in the x-y plane are governed by the following pair of partial differential equations:
From the flow symmetry it is known that v is a function of x only. The boundary conditions are as follows:
What are the velocities v(x) and u(x,y)?

7. A long, narrow slab of hot amorphous polymer of width W at temperature Ti is quenched into a large water bath at Twater at time=0. Sketch how you would expect the temperature distribution within the slab to vary as a function of time and distance x from the centerline of the slab.

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