6.1 Introduction
6.1.1 Simplified Criteria for Assessing Quasi-Adiabatic Processing
Two criteria were used for assessing the quasi-adiabatic state of the extrusion process. They are expressed as 1st Hypothesis and 2nd Hypothesis. The 1st hypothesis is related to temperature control of the barrels and die. If heating and cooling activity in the extruder is identical during processing in comparison to the heated but empty state, then the process can be considered quasi-adiabatic (Figure 6.1).
Figure 6.1 1st Hypothesis for quasi-adiabatic processing.
The temperature of the barrels is controlled by electrical heating cartridges and by water pumped through cooling channels while the die temperature is controlled only by electrical heating cartridges. Temperature probes are also located in each barrel and the die. The heating and cooling activity is regulated by a temperature controller.
When a temperature controller detects that the temperature is less than the target temperature, the heating cartridges turn on. Likewise, when the temperature is too low, valves open to allow cooling water to enter the channels in the barrels. When turned on, the heating cartridges operate at a fixed power, the magnitude of which
can depend on the scale and vendor. For cooling power, the temperature of the water can be adjusted, as well as frequency and duration of valve opening. The primary control, however, of heating and cooling is the length of time, also called the impulse, for which the cartridges are on or the valves are open. These times are regulated by the temperature controller, typically operating under PID logic (150).
This type of signal has been used successfully to monitor the energetics of single screw extrusion (16).
Heating and cooling activity is described by the controller output, expressed either as a percentage value in the range of -100% to 100%, with positive values indicating heating and negative values indicating cooling, or as the slope of the cumulative count of heating or cooling events over time. Actually, the former is in fact derived from the latter. A value of 100% or -100% indicates that the heating cartridges are on at all times or that the water valves are open at all times, respectively. Intermediate controller output values indicate periodic turning on and off or opening and closing.
When expressed as a slope, a slope of zero indicates no activity while a steeper slope indicates many impulses of activity and for long periods of time. For the extruders used in this study, the 40 mm extruder (ZSK40) controller output was expressed as a percentage while the 18 mm extruder (ZSK18) controller output was expressed as a slope. For the ZSK18, separate signals were produced for heating and cooling. As an approximation, when both were active, the slope of cooling line was subtracted from the slope of the heating line. In summary, the process is considered quasi-adiabatic if the percentage value of the controller output or the slope of the controller output is identical between the “heated but empty” and “heated and process running” states.
A notable complicating factor is that extruders are composed of many independently temperature-controlled zones, all of which ideally should meet the 1st Hypothesis criteria. In addition, in the “heated and process running” state, heat is generated by viscous dissipation inside the screw channel, leading to an additional heat source. In reality, it is challenging to achieve a quasi-adiabatic state because of the many channels of heat flow. For example, heat can flow between the barrel segment or die and the surrounding environment, between melt and barrel segment or die, and between barrel segment-to-barrel segment and barrel segment-to-die. Considerable
differences are also present between scales: barrel outer surface areas differ, barrel inner surface area to volume ratios (SA:V) differ and shear rates can differ. Upon scaling, the combination of reduced SA:V and potentially increased viscous dissipation could result in the need for extensive cooling, so much so that the extruder may no longer be capable of controlling the temperature, resulting in constant cooling or even increasing barrel overheating over time. Because of these complications, or specifically the heat loss to the environment, it would be acceptable to define quasi-adiabatic by, instead of exactly achieving agreement between “heated but empty” and “heated and process running” controller output, the controller output at least never enters a cooling regime. A depiction of the possible thermal energy flows for both “heated but empty” and “heated and process running” is shown in Figure 6.2.
Figure 6.2 Hypothetical thermal energy flow in an extruder. (Note: not to scale, and arrows do not indicate single points of heat transfer but are instead generalized from zone to zone).
The temperature profile (Table 6.3) for the study discussed in this chapter was used as the basis for this depiction. Arrows below the extruder refer to heating or cooling supplied by the heating cartridges or cooling water. Arrows above the extruder indicate heat loss to the environment. Arrows within the extruder refer to heat transfer between barrels or between melt and barrel.
The 2nd hypothesis is related to the relationship between the temperature of the barrel segments or die and the temperature of the melt inside the barrel segments or die. If the difference in temperature, DeltaT, at all locations along the length of the extruder is zero, then the process can be considered quasi-adiabatic (Figure 6.3). In the figure, the DeltaT is indicated at the point of maximum melt temperature, but DeltaT can be located elsewhere as well, for example at the end of the screw or at the die exit. A positive DeltaT implies that the melt received enough energy from an additional source, in this case mechanical energy from the screw, to cause an increase in temperature. The DeltaT in the core of a screw channel for an unmixed portion of polymer has been reported to be as great as 60 °C, depending on the process parameters (151).
Based on these hypotheses, it follows that a low DeltaT should correspond to a controller output close to zero. In this study, minimizing the difference between the
“heated but empty” and “heated and process running” controller output as well as minimizing the DeltaT in the portion of the extruder set to 180 °C was the primary focus, but the differences were also analyzed in the earlier, cooler sections as well.
Figure 6.3 2nd Hypothesis for quasi-adiabatic processing (note: die not to scale).
An additional hypothesis was related to use of the results from the Ludovic® model.
The question posed was: could Ludovic® guide the selection of process parameters to achieve a quasi-adiabatic state? For example, the total conducted energy (TCE), a global result and measure of how much heating or cooling occurs during steady state (Figure 7.2), could directly relate to the controller output. Evidence for this idea was present in the study performed by Zecevic, et.al., in which minimal TCE corresponded with low measured DeltaT, although controller output was not monitored (22). Further, and possibly even better, the local conduction energy (LCE) as a function of extruder length could relate to the individual barrel and die controller output. In addition, the estimated difference between melt and barrel temperature can be calculated from the temperature evolution as a function of the length of the extruder, f(x), plot in Ludovic®. One uncertainty, however, is that these results are also a function of the thermal exchange coefficient (TEC), an input value in Ludovic® (Figure 7.6). Therefore, any result is always only an estimate for the real process
unless the model is tuned or validated with experimental data. Such validation is challenging if not impossible because of measurement limitations, such as temperature at all locations in the extruder.