Unrolled diameter

Unrolled Diameter The mean chord length through the center of gravity of the particle... 

The carbon nanotubes do, however, demonstrate the interesting consequences of curvature upon Vs(r), which are common to all of the systems that we have studied, regardless of structure (n, m) or composition. As the curvature increases, each point on the inner surface is brought into closer proximity with more nuclei. Thus the inside surfaces are always somewhat more positive (or less negative) than the outside ones. This effect naturally becomes more pronounced as the diameter decreases, and at the caps of the closed tubes. On the other hand, if the tube is unrolled into a flat sheet (graphene), Vs(r) is the same on both sides.74... 

FIGURE 2.2 Multitude of particle diameters (a) definition of unrolled radius R (b) unrolled curve. Taken fiiton Figure 4.1 in Allen [1]. 

Considering that in most extruder screws the screw diameter is much larger than the channel depth (D/H 1, usually about 5), the change in channel width and helix angle over the depth of the channel will be rather small. If it is assumed that the channel curvature can be neglected, the screw channel can be unrolled onto a flat plane. The error that is made in this process may be acceptable considering the limited accuracy and reproducibility of most data on the coefficient of friction, as discussed in Section 6.1.2. Two simplifications resuit from this assumption. The first one is that now the channel width and helix angie are constant over the depth of the channei. The second simplification is that the extra force F can be determined directiy from a force balance in the cross-channei direction ... 

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