3.1. Mill Design
The objective was to design a continuously operating process that can achieve a high submicron particle content in a single passage of the material, with the prototype annular gap mill as the main comminution equipment. Therefore, the relevant process parameters and their ranges must be considered during the design phase. The groundwork for this was established in a previous work on the melt milling of the griseofulvin-xylitol system [
7]. Using different stress intensities and frequencies in a custom annular gap batch mill, the energy utilization was optimized for a rapid comminution towards the submicron particle size. The obtained values are summarized in
Table 1 and served as the basis for the continuous process design phase.
A mathematical model was used to gain insight into the influence of different design choices regarding hold-up volume and flow patterns on the resulting particle fineness. The cumulative PSD
obtained from continuous melt milling, for a certain particle size
and a median residence time
, can be predicted from a batch grinding kinetic
and an assumed RTD density function
according to Equation (1) [
20].
The resulting prediction of the PSD is only valid if identical stress conditions are applied for the continuous and the batch case. Therefore, the mill geometry and its key dimension had to be maintained, as changes to the rotor/stator proportions could alter the energy transfer. The annular gap design was carried over as it provides a narrow RTD [
21,
22], which is considered favorable with regard to a uniform PSD.
The first step was to conduct a batch grinding experiment using the energy-optimized process parameters (also see
Section 2.2.2 and
Table 1) to obtain
for the fastest observed comminution. A deviation towards non-optimized process parameters would have prolonged the grinding times, making continuous manufacturing impossible. Next, the time-discrete particle size data, representing the batch grinding kinetic, were fitted to the first order solution of the population balance model in Equation (2) [
23]. This smooths the results of Equation (1). It does so by enabling the numerical integration at any step size, rather than being bound to the sampling intervals of the batch grinding experiment.
The cumulative oversize function describes the fraction larger than a given particle size at a certain timepoint . The selectivity parameter and the offset were used as independent variables, while was constrained by the PSD of the raw material. A total of 101 particle size classes , based on the default output of the laser diffraction system, were fitted.
The axial dispersion model was chosen to represent the residence time distribution
, as it is applicable to annular gap mills and can be parameterized only by its mean transportation velocity (
) and the Peclet number (Pe) [
21]. Various solutions to Equation (1) were generated using variations for
. Solutions for Pe ≤ 16, which represents a back-mixed system, were calculated from the closed–closed solution in Equation (3), according to Mavros [
24].
For Pe > 16, the analytical open–open solution (Equation (4)) was used as an approximation of a system close to a plug-flow characteristic [
24].
For a single passage of the material, the mean residence time
is approximately equal to the ideal filling time
, which can be connected to the grinding chamber volume
and operating conditions, such as grinding media volume
and volume flow rate
[
21]
Based on the combination of Equations (2)–(5) with (1), the submicron content
, which acts as the key quality attribute of an SCS, can be predicted as a function of time and the material transport pattern (
Figure 3).
An increase in the mean residence times leads to a shift in the submicron content up to a value of ~94%, regardless of Pe number. At this point, an insufficient colloidal stability suppresses comminution (grinding limit), which matches the behavior of the underlying physical system. With a shift from back-mixed to plug-flow behavior (Pe↑), the required mean grinding time for a constant submicron content will decrease. The reduced short-circuit flow, associated with the plug-flow, lowers the coarse fraction in the product.
Although a mean axial transport velocity
can be assumed based on the throughput and length of the mill
, the Pe number (
) for a certain mill design cannot be determined a priori, because the axial dispersion coefficient
is unknown. A complex fluid dynamic model describing all interactions between fluid and solid phases would be required for this. However, according to
Figure 3, the influence of axial dispersion on the submicron content is only relevant for short mean residence times, but negligible after 30 min. Hence, this duration was chosen as the target mean residence time in the grinding active zone. The existence of a grinding limit in the unstabilized system does not justify longer grinding times, as it would only lead to additional grinding media wear without improving the product quality.
Figure 4 gives a cross-sectional view of the continuous mill design based on the above-mentioned findings. As the gap width had to be maintained from the batch process in order to not alter stressing conditions and break the validity of Equation (1), achieving the required filling time was only possible by scaling the axial dimension. At a length of 859 mm, corresponding to 30 min of mean residence time, processing of up to 1.27 kg/h SCS can be achieved. Such throughput was considered technically relevant. With a length-to-diameter ratio of 10 (commonly ranging from 1 to 6 [
22]), the mill needs to be horizontally started and operated, for the purpose of reducing the (start-up) power draw. Power is provided by a 7.5 kW motor with a frequency converter through a belt–pulley system. The material inside the grinding chamber is 1.4571 stainless steel for the stator and PEEK GF 30 for the rotor. The grinding chamber wall is surrounded by an outer shell to form a jacket for the heat-transfer fluid. In- and outlets for suspension (and heat-transfer fluid) are realized through the flanges, so that the full length of the mill is utilized and a narrower RTD is obtained. Circular screen meshes are integrated into the suspension in- and outlet ports to retain the grinding media. Both ends are equipped with shaft bearings and dual mechanical seals (Cartex DN25, EagleBurgmann, Wolfratshausen, Germany) to stabilize rotary motion. On the outlet-side, the rotor is fixed to the shaft, while on the inlet-side axial movement is allowed to compensate for thermal expansion.
3.2. Design Verification
The initial testing of the mill design focused on the general behavior, the experimentally achievable throughput, and if the set targets could be met. As the applied pressure gradient in continuously operated media mills can introduce grinding media compression, usually at the outlet separation device, a minimum and maximum throughput exist, which define a boundary of the process. Special internal designs can be used to delay the onset of this phenomenon, but the basic annular gap design is prone to blockage because the unobstructed flow path between inlet and outlet does not allow internal bead circulation. Since direct detection of grinding media compression by measuring the local bead distribution (e.g., by radiometric densitometry [
25]) is complex, indirect substitute-indicators (motor power and inlet pressure) were employed.
The power draw of the driving motor is given in
Figure 5A for different mass flows of water. Without grinding media (GM) and with a horizontal orientation (α = 0°) of the mill, the constant power consumption is mainly determined by the friction of the dual mechanical seals (no load power). With grinding media added, bead–bead and bead–wall interactions cause additional friction and the base load increases. After a short initial plateau, the power draw increases for throughputs greater than 0.6 kg/h, which is the typical indication for packing [
26]. This operating point is not feasible considering the lower viscosity of water, compared to the more viscous SCS (~200–500 mPas at 120 °C), and the maximum target throughput of up to 1.27 kg/h. A tilt angle α of the mill towards the outlet was applied to introduce sedimentation as a countermeasure for grinding media compression (see forces in
Figure 5B). For tilt angles α > 0°, three distinct operating regimes can be identified based on the power draw trend. In regime (a), power draw decreases as the throughput increases, regime (b) features a minimum constant power draw, and regime (c) begins when power draw increases rapidly with mass flow. This course can be explained by three distinct states of the grinding media inside the annular gap, visualized in
Figure 5B:
- (a)
Gravitational force () outweighs drag force () and buoyancy in axial direction ()—grinding media sediments to the inlet;
- (b)
Balance of all axial forces—grinding media floats and is evenly distributed;
- (c)
Drag force () and buoyancy in axial direction () outweigh gravitational force ()—grinding media is compressed at the outlet.
For larger tilt angles, onset of the desired regime (b) shifts towards higher mass flow rates, because higher drag force is necessary to counter the growing axial component of the gravitational force acting towards the inlet. A broadening of regime (b) is also observed for a larger α, supposedly due to a self-regulating effect. Beads in a downward motion lower the local porosity at the inlet, increasing the effective flow velocity and thus the drag force, pushing them upward until they are evenly distributed, and the process starts over. For an angle of 10°, the regime (b) extends so far that regime (c) is not observed in the tested throughput range. Usually, packing is strongly connected to the throughput and can only be influenced by an increase in tip speed, bead size, and density or a decrease in filling ratio and viscosity [
22]. Adaptions to these key process parameters would decrease energy utilization and come at the cost of a reduced product quality. The tilting approach decouples this relationship, so that optimal process parameters can be applied over a wide range of throughputs without severe packing.
Additionally, glycerol at 20 °C was employed as a substitute liquid, since its density and viscosity closely match that of the molten SCS at 120 °C. The objective was to create comparable forces on the grinding media and identify a stable operating angle α that could be used with the molten suspension. This time, the inlet pressure (
Figure 6, top), which is an alternative indirect packing indicator [
26], and the outlet mass flow (
Figure 6, bottom) were monitored for a set mass flow of 1 kg/h. As the tilt angle of the mill is increased, the equilibrium pressure (pressure after 30 min runtime) steadily decreases to a minimum, which indicates a transition from regime (c) to (b). Similarly, the outlet mass flow increases and matches the set throughput when regime (b) is achieved. Tilting above 12° tips the force balance and the grinding beads settle at the inlet, causing higher backpressure and lower throughput as the local porosity decreases. In comparison to the determination of the process limits using water, it is confirmed that the usable regime (b) shifts for higher viscosity fluids. The higher drag force on the grinding media requires either lower flow rates at the same angle or larger angles at the same flow. A broad plateau for regime (b) as seen in
Figure 5A was not identified in the case of glycerol, which limits the usable operating space. Deviations from the operating point also have a large impact on the system behavior. Yet, these trends still agree with the theoretical considerations of the acting forces given for water. Additionally, product quality was impacted by the specific operating regime.
Figure 6 pictures glycerol, processed within regime (c) (3°) and the desired regime (b) (12°). While the former is opaque from abrasion of the metallic grinding chamber, the glycerol processed in regime (b) remains translucent. Therefore, another advantage of the tilting strategy is that wear can be minimized without deviation from the operating parameters with the highest energy utilization.
3.3. Residence Time Distribution
In order to uncover the effect of tilting the apparatus on the flow inside the grinding chamber, residence time distributions were measured using an aqueous salt tracer solution. The volume flow was matched to the molten suspension during processing.
Figure 7 gives the mean residence time and mean Peclet number for different tilt angles of the mill (bottom), as well as observed power draw ranges (top). The ideal filling time (Equation (5)) of the grinding chamber (
) and the hydrodynamic residence time of the system (
), which additionally includes the free volume of tubes and peripherals, are given as reference. The closed–closed solution of the axial dispersion model was used to fit the experimental data (R
2 > 0.99).
For 0° and 4°, the observed mean residence time is greater than the system filling time, which suggests an increased degree of backflow as the apparent system volume is larger. This agrees with the fitted Peclet numbers for these tilt angles, which are lower in comparison to 8°. For this angle, the mean residence time drops below the system filling time. Power draw increased with the tilt angle, so compression at the inlet is likely to occur. Thus, the trend of the mean residence time in
Figure 7 can be explained by the formation of a grinding media-free zone towards the outlet, in which back-mixing is reduced and short-circuit flow is promoted.
The measured mean residence times lie within the design scope of
Figure 3 and the set target of 30 min. If comminution takes place under packing conditions, deviations in the predicted grinding results are expected, because stressing is not guaranteed over the full length of the mill. Furthermore, higher tilt angles introduced more variability in the mean residence time, which in turn affects the obtained particle size. In consequence, suitable process analytical technology will be implemented to monitor the position and distribution of the grinding media for a pharmaceutical application in future, as non-compliance results in an out-of-specification product based on the above result.
3.4. Process Results
The developed continuous melt milling process involved the extrusion of a powder mixture. In this upstream step, the material is partially melted to form a well-mixed suspension, which is then fed via an intermediary buffer vessel to the mill. During processing, the tilt angle was adapted in response to the measured process parameters. The submicron content and particle size of the final product was evaluated offline from samples taken in regular intervals and is shown in
Figure 8, along with the predictions based on the modeling presented in
Section 3.1. Only fully recrystallized product was considered to ensure the absence of remaining glycerol. The data start with the washout of glycerol (striped area), which acts as a heat-transfer fluid during startup. After approximately 40 min, the glycerol was washed out based on the samples taken at the outlet, which fully crystallized after the experiment, while previous samples did not. Note that the particle size from the upstream extrusion was constant over the process time and in good agreement with the results during the experiments conducted for the determination of the batch kinetics.
First, the achieved submicron content of 80–90% in the SCS, which was selected as the primary quality attribute, is promising, as it matches the published batch result [
7]. Second, the determined sub-micron content is in good agreement with the predictions. This highlights the suitability of the theoretical approach for the design of this mill. Deviations between experiment and prediction likely stem from the fact that stress events did not occur uniformly across the full length of the mill, due to an uneven axial distribution of grinding media (assumption for Equation (1)). More stress events will take place in zones with a high local filling ratio (here, the inlet), while the outlet region of the grinding chamber contributes less to comminution. Furthermore, the d
10 and d
50 were stable across the process time. Inter-sample variability can be explained by the inconsistent mass flow rate, again, causing fluctuations in the number of stress events.
In addition to the product properties, the process characteristics with respect to the power draw, inlet pressure, outlet mass flow (
Figure 9), and temperatures at several positions of the mill were also monitored during the tests.
Two pressure spikes were countered by tilting the mill to 4°, resulting in an increased mass flow rate. Over the runtime, further adjustments to the tilt angle were executed, based on the available process data. The continuously increasing power draw, which after 75 min had risen by 100% compared to the start of washout, required major adjustments to 8° and 10°, each time stabilizing the power draw briefly. This was interpreted as the opening of a blockage. Shortly thereafter, power consumption (and pressure) abruptly spiked above the motor’s limit and the run was terminated. Crystallization of melt in the annular gap or at the mechanical seals could have led to such an increase in the power consumption, but the monitored temperatures were constantly above the melting temperature of xylitol. Upon disassembly of the mill, the rotor was visually inspected. Adhering melt at the inlet was discolored grey, while the melt at the outlet was still white. This was previously observed under packing conditions (compare
Figure 6). The applicability of the tilting strategy during the run was confirmed to control grinding media packing.