Campbell-Dontula model

F/= force due to pressure and centered on pushing surface. Fg= force due to pressure and centered on trailing surface. 

Campbell and Dontula [1] revisited the original solids conveying problem. They proposed that the flights of the screw cause the movement of the solids down the screw, and that the polymer pellets behaved more like an elastic fluid than a solid polymer plug. Therefore, a torque balance would not be applicable. The following is a list of the additional assumptions they made  

The previously unresolved force, F (F in previous models) is assumed to be proportional to the frictional force between the polymer bed and the barrel. 

The modified Campbell-Dontula solids conveying model was based on screw rotation and a normal force at the pushing flight that was directly proportional to the frictional force between the solid bed and the barrel wall. The force balance on the slab is provided in Fig. A5.4 

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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 ... 

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 ... 

Hyun et al. [21] evaluated both the original model by Darnell and Mol [14] and the model by Campbell and Dontula [19] for accuracy against experimental data, and determined that the Darnell-Mol model was less accurate than that of the Campbell-Dontula model. The incorporation of the lateral stress ratio in the calculations supported their conclusions even more. At the time of the work by Hyun et al, however, the physics for screw rotation was not well appreciated, and the evaluations for the Campbell models [23] were performed with coefficient of friction... 

Comparison of the Modified Campbell-Dontula Model with Experimental Data... 

The modified Campbell-Dontula model was developed using the LDPE resin friction data as applied to an empirical model. The empirical model is shown by Eq. 5.31 for the temperature range of 25 to 110 °C. The coefficients of dynamic friction using Eq. 5.31 is shown in Eig. 5.31. 

Figure 5.32 Solids conveying rate data calculate using the modified Campbell-Dontula model for the Dow solids conveying process using the shallow screw, 75 °C barrel and screw temperatures, and a screw speed of 50 rpm. The solids conveying rates measured from the experimental device are provided...

For the modified Campbell-Dontula model, Eq. 5.13, cp is calculated as follows for... 

The modified Campbell-Dontula model provides an acceptable prediction of the rate at the section exit pressure. For many cases, the coefficients of friction are adjusted until an acceptable performance is obtained. This model and the other models should always be used with caution. As previously discussed, these models use a static force balance to approximate a dynamic process. 

Figure A5.4 Force diagram for modified Campbell-Dontula model...

The modified Campbell-Dontula model used a lateral stress ratio [5, 6] that is defined below ... 

Campbell et al. and Yamamuro et al. assume a form for (or F ) and then determine the solids conveying angle (p. Hyun and Spalding calculated q> using a force balance and two torque balances. Campbell and Dontula and Yamamuro et al. did not use a torque balance in their analysis. The following is a list of assumptions from all the models discussed. Additional assumptions will be added as needed. Assumptions that do not have keys were used by all authors ... 

Yamamuro, Penumadu, and Campbell [5] developed another model with a force R of the same magnitude as A but acting at a skew angle a, which is an adjustable parameter. The form of the analysis is similar to that by Tadmor and Klein [7] and Campbell and Dontula [1] in nature. Fig. A5.6 illustrates forces for the model and the changes made to Fig. A5.3. The following is an extended list of assumptions they made ... 

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