【正文】 ated by the extruder flow field in the mixing of two fluids introduced as adjacent horizontal layers.Figure14. Pathline of material elements in extruder channel. From the above arguments it is apparent that no rigorous extension of the approach used to analyze mixing for the twodimensional cavity flow is possible to the threedimensional extruder flow。 however, the possibility of approximate relations will be explored.Analysis of Mixing in Single Screw ExtruderThe approach used to analyze mixing in the extruder is similar in principal to that used for the helical annular mixer。 modifications are necessary, however, as a pletely analytical approach is not possible using the velocity field given by eq 12 and is precluded for the SFT by the discontinuities in the fluid element pathlines at the flights. Figure 13 is a diagram of the mixing of two fluids in the extruder channel. Crosssectional cuts and an axial cut display the layered structure generated by the mixing action. As for the helical annular mixer, and s are used as local measures of the state of mixedness. The distribut ions of the mixing parameters andat any channel cross section correspond to the nonhomo geneity of the flow field and to distributions in the orientations and thicknesses of the striations in the feed plane. For many applications it should be sufficient to characterize these distributions by their first few moments. Axial profiles of the means and moments of the cross sectional mixing parameter distributions can be determined as follows (see Figure 14): (i) A number of differential material planes are identified in the feed plane,the location and orientation of each corresponding to the position of the interfacial area in the feed. The number of planes chosen should be large enough that the influence of this variable on the calculated distributions is negligible。 the actual number, of course, depends on the mixing achieved。 in practice, 200300 elements were found to be sufficient for a three order of magnitude decrease in the striation thickness. Note that the RTD was found to be much less sensitive than the mixing parameter distributions to the number of material elements chosen.(ii) Equations 2 are used in conjunction with a mathematical description of the flow field to calculate the stretch histories of each of these material planes. (iii) The mean and moments of the mixing parameter distributions are determined at several axial locations. This method is very general and can be applied to other mixers. The macroscopic mixing efficiency for continuous flow systems is defined by the relation (Ottino et al., 1981) (15)Before resorting to more detailed calculations, it is instructive to examine the upper mixing bound, obtained by setting eff(z) = 1 on the righthand side of eq 15. Typically, the upper mixing bound predicts values significantly higher than are achieved in most practical mixing flows (Ottino and Macosko, 1980。 Ottino, 1983), but provides an indication of the influence of model parameters on mixing. Computation of the upper mixing bound is particularly simple for the SFT. (16)The proportionality constant required for equality is a function of the feed orientations {N}, and of , and L/H (through their influence on the mean residence time). Thus from eq 16, the relevant parameters that influence mixing are {N}, and L/H. The influence of W/H arises only indirectly through the change in the vertical coordinate of the fluid elements at the flights. On the basis that when the upper bound increases, there is a possibility of improved mixing, then from eq 16, mixing may be improved by: (i) increasingat constant L/H and。 (ii)increasin g L/H at constantand。 (iii) increasingfor, decreasingfor, at constant L/H and , where (17)andand (iv) decreasing H at constant L/H and. These conclusions are in agreement with qualitative experimental observations (Maddock, 1959。 Sheridan, 1975) and will be tested using a more plete analysis in the next section.17