Clarkson University Models

Several solids conveying models were developed by Campbell and his students at Clarkson University [19, 20]. These models will be referred to as either the Clarkson University models or the Campbell models. They proposed that the movement of the screw flight was pushing the polymer bed as the screw turns rather than the frictional force at the barrel moving the polymer pellets down the screw. For these models, they assumed that the solid bed behaved more like an elastic fluid rather than a solid and removed the torque balance constraint. Campbell and Dontula [20] reasoned that because the solid polymer pellets more closely resemble an elastic particulate fluid, no torque balance in the bed would be necessary. They further assumed that the force normal to the pushing flight was due to a combination of the force due to the pressure in the channel and a force proportional to the frictional force exerted at the barrel by the solid bed. The Campbell-Dontula model was first published as  

While this model rendered a more accurate prediction of the solids rate as a function of exit pressure, screw and barrel parameters, and pellet physical properties, It still contained significant deviations from experimental conveying data at 

is the lateral stress ratio, and oy are the stresses in the x and y directions, and ff, in the case of the single-screw extruder, is assumed to be the local downstream pressure P. Lateral stress ratios were discussed in Section 4.2. 

Unlike the previous models by Darnell and Mol [14] and Tadmor and Klein [1], which are based upon the assumption of isotropic stress conditions, Campbell s model [20] considered anisotropic stress conditions, as suggested by Schneider [15], but it was assumed to be 1.0 due to the lack of published experimental data on the subject. Variations on the model set forth by Campbell and Dontula [20] include a modification to incorporate the lateral stress ratio [19, 22], and other modifications discussed by Hyun et al. [21, 23]. A modified Campbell-Dontula model with a homogeneous lateral stress is as follows  

As stated in Appendix A5, if /jy is redefined in terms of an internal angle, then the following model results and is referred to as the Campbell-Spalding model in the appendix  

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