Developing melt temperatures

The equations derived in this section allow a realistic calculation of developing melt temperatures along an extruder screw. Many authors have studied developing melt temperatures [327-329] however, closed-form analytical solutions as presented in this section have not been published before. Most realistic calculations of developing melt temperatures in screw extruders require numerical analysis. For instance. 

This section describes the derivation of analytical equations of developing melt temperatures in screw extruders. The analytical equations for temperature as a function of axial distance are useful in predicting axial melt temperature profiles. The advantage of analytical equations is that the factors influencing temperature development can be easily identified and their effect determined in a quantitative fashion. Both the temperature and shear rate dependence of the viscosity strongly affect the developing temperatures in the extruder. 

In this section we will describe a method to predict the fully developed melt temperature in screw extruders based on simple analytical expressions. The method is easy to use and leads to quantitative results with a minimum of time expenditure. 

The fully developed melt temperature is reached when the viscous heat generation is balanced by the heat flux away from the polymer melt. The viscous dissipation in the extruder will cause an increase in melt temperature resulting in reduced viscosity, which will result in a reduction in viscous dissipation. The melt temperature will reach a steady state value when the viscous dissipation has reduced to the point that it equals the heat flux from the polymer melt. 

The melt temperature will rise initially and then level off as the viscous dissipation reduces with increasing melt temperature. When a steady state is achieved, the melt temperature no longer changes along the length of the extruder. This is called the fully developed melt temperature or equilibrium melt temperature. This temperature Te can be determined from a simple energy balance equating the viscous dissipation to the conductive heat loss ... 

This equation leads to the following expression for the fully developed melt temperature ... 

This analysis provides a simple and fast method to estimate the fully developed melt temperature in screw extruders. The effect of material properties, processing conditions, and machine design parameters can be determined quantitatively. As a result, the analysis can be used to predict how melt temperature will change when another... 

It should be noted that there are several simplifying assumptions in the analysis. We have assumed that the melt temperatures are uniform across the depth of the channel. In reality this is not the case in fact, large melt temperature changes can occur across the depth of the channel. We can assume that the melt temperature calculated with this analysis corresponds to a bulk average melt temperature. We have also assumed that the fully developed melt temperature is reached before the end of the extruder. This is a reasonable assumption for small diameter extruders however, this may not be a good assumption for large diameter extruders as discussed in the previous section. 

C. Rauwendaal, Estimating Fully Developed Melt Temperature in Extrusion, Conference Proceedings, 581 SPE ANTEC, Orlando, FL, 307-311 (2000)... 

In order to apply the freezeout model to developing melt temperatures, a calculation of the bulk melt temperature as a function of extruder length [1] could be used in lieu of temperature data. The freezeout layer model would then provide information where freezeout may be occurring all along the metering section of the screw. 

One key consideration in developing radiation curable adhesive systems is the thermal stability and volatility of any photoinitiators used. These chemicals are designed for liquid systems where these issues do not arise. Few of the commercial photoinitiators have adequate thermal stability at the highest hot melt temperatures (180-200°C) and many are too volatile. Reduced application temperatures and special antioxidant packages are often required. 

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