Effect of Rotation Speed and Powder Bed Volume on Powder Flowability Measured by a Powder Rheometer: Evaluation of the Humidity Effect on Lactose Powder Flowability

Abstract

Relative humidity during storage is known to affect powder flowability, although its effect on powder flowability remains unclear. Various techniques have been used to evaluate powder flowability, including measurement of the rotational torque of the powder bed, which is a novel method. However, studies investigating the effect of relative humidity on powder flowability using rotational torque measurements are limited. Therefore, this study aimed to examine the influence of relative humidity during storage on the flowability of lactose powder through rotational torque measurement of the powder bed using an Anton Paar powder rheometer. Rotation speed had a minimal effect, except when the powder was stored at a high relative humidity of 99%. The effect of relative humidity was more pronounced at a smaller powder volume (30 mL) than that at the other volumes tested. Of the techniques employed, including the angle of repose and bulk density measurements, the rotational torque measurement of the powder rheometer exhibited the highest sensitivity to variations in relative humidity. It was also found that the measured rotation torque hardly changed when the rotation speed was below a critical value, indicating that the optimal rotation speed exists to measure the representative rotation torque of each powder.

1. Introduction

Powder flowability is crucial for the pharmaceutical [1], food [2], and ceramic [3] industries because it influences various processes such as storage, transportation, and shape forming. For example, the feeding of several powder types into a dye from a hopper during tablet fabrication in the pharmaceutical industry requires precise control of flowability to regulate the powder amount. Especially for active pharmaceutical ingredients composed of organic compounds, the flowability of these powders are usually poor; thus, granulation is necessary to improve their flowability in advance. In continuous granulation processes, several kinds of raw materials are supplied and then mixed. In order to guarantee the quality and the homogeneity of the mixed powders, it is important to evaluate physical properties, including flowability. Improvements in productivity to reduce costs in the food industry necessitate accurate and efficient powder packing during manufacturing. When using fine food powders such as flour, rice flour, etc., powder bridging and/or powder agglomeration may occur in hoppers, feeders, conveying pipes, and mixers. It is necessary to precisely evaluate powder flowability for determining the optimal conditions of surface modification of the fine powders to prevent the above troubles in the manufacturing processes of the food industry. In the press forming of ceramics, the production of a dense and homogeneous green body is crucial for manufacturing a high-quality product. There are some desired properties for ceramic powders in press forming, such as good flowability and packing ability. Thus, the measurement of the flowability of ceramics powders is essential, similar to pharmaceutical and food powders, as mentioned above.

Powder flowability plays a crucial role in various processes; however, evaluating this parameter is challenging because it depends on complex factors. These include powder properties such as particle size distribution, shape, density, and surface properties, as well as environmental factors such as temperature, relative humidity, and stress hysteresis [4,5,6]. In regards to powder flowability, the particle size influence arises from the effect of the surface area on the powder flow. Generally, for particles <100 µm, the powder flow is governed by a cohesive effect and often has some troubles. If the particles have similar size distributions but diverse morphology, the powders show different flow behavior because the contact area among these particles is quite different. Similarly, the surface roughness of particles also affects powder flowability because the surface roughness alters the contact area of the particles, changing the magnitudes of both electrostatic and van der Waals interactions. When the particles are exposed to low-humidity air, their electric charge reduces, causing a change in their flow behavior. On the other hand, when the particles are stored in high-humidity conditions for a long time, particle surfaces change and lead to particle aggregation due to a liquid bridge, which drastically changes the particles flow behavior.

Additionally, the requirements for evaluating powder flowability vary depending on the specific process and operation, such as storage, extrusion, transportation, mixing, and packing [7,8]. Selecting an appropriate evaluation technique is essential, with options including shear tests [9], measurement of the angle of repose [10], and measurement of the rotational torque of the powder bed [11,12,13,14,15,16,17,18,19,20].

The evaluation procedures and conditions for those methods are not yet well standardized. For instance, the rotational torque measurement of powder beds is a relatively new evaluation technique, and studies reporting the effect of measuring conditions on rotational torque remain limited. While the FT4 powder rheometer is commonly used to measure rotational torque [11,20], the Anton Paar powder cell employed in this study has been less frequently utilized [13,14,16,17,19]. In studies using Anton Paar powder cells, rotational torque was typically measured under aeration below the powder bed [13,14,16,19]. Mishra reported that the torque required to rotate the impeller in an Anton Paar powder cell may characterize the defluidization of cohesive particles [14]. Lupo reported that rotational torque changed linearly with impeller depth and decreased with the aeration rate [13]. Tomasetta developed mathematical models to relate torque measurements in a fluidized bed rheometer to powder flow properties obtained from standard flow testers [19]. Salehi showed that the torque required rotating the impeller in Anton Paar flow cells depends on factors such as material properties, the applied air flow rate, impeller depth, and impeller blade height [16]. However, few studies have measured rotational torque without aeration of the powder bed [13,17]. Torque measurement of powder beds with aeration is crucial for controlling powder fluidization and achieving highly reproducible evaluations of powder flowability. Nonetheless, measuring rotational torque without aerating the powder bed is also essential, as the conditions in fluidized and non-fluidized beds differ significantly. Rotational torque measurement without aeration seems to be particularly useful for estimating the powder flow behavior in small hoppers and mixers, in which particles flow under low consolidation. Thus, rotational torque measurement without aeration is also crucial for applications using Anton Paar powder flow cells.

In pharmaceutical and food industries, humidity control during the storage of powder is important because the moisture content in the powder can alter not only powder flowability, but also powder plasticity, affecting the powder tableting performance [21], and it was shown that the effect of moisture content on the powder flowability is complicated [22]. Previous studies reported an effect of relative humidity on powder flowability [12,15,18]. Lumay et al. [12] used a rotating drum method to evaluate the effect of relative humidity on lactose powder flowability, revealing that the optimal relative humidity for flowability ranged between 30 and 50%. Salehi et al. [18] investigated the effects of temperature and humidity on mannitol powder flowability using a shear tester similar to a conventional shear cell. The results showed that the flow properties of mannitol remained stable at a relative humidity <60%, but above this threshold, adverse effects on flowability were observed. Opalinski et al. [15] employed an annual shear cell-type powder rheometer to elucidate the effect of the moisture content on food powder flowability. Their results show that at specific moisture levels, the shear stress of the powder bed reached a maximum, regardless of particle size, under certain shear rate conditions. However, studies investigating the effects of relative humidity on powder flowability through rotational torque measurements remain limited. Nakamura et al. [23] measured the rotation torque of glass beads with different moisture contents by using an originally developed rotation torque measurement device; however, the powder bed was applied a constant normal force, which means that the powder flowability was measured while restraining. In addition, the rotation torque was measured at a constant powder bed volume and a rotation speed. Therefore, this study aimed at investigating the influence of relative humidity during storage on the flowability of lactose powder through measurements of the rotational torque of the bed using an Anton Paar powder rheometer, which can allow for particles to move under no restraint. Additionally, the measured rotational torque was compared to conventional powder flowability parameters, such as the angle of repose and bulk density. It must be important to clarify the effect of measuring conditions on the measured rotation torque especially for the Anton Paar powder rheometer which is less frequently utilized; thus, we investigated the effect of rotation speed on the measured rotation torque as well. In addition, we tried to identify the minimum powder bed volume for the precise measurement of its rotation torque in order to apply this method for characterization of a limited quantity of a rare powder sample.

2. Experiment

2.1. Materials

The test powder used was lactose with a nominal particle size of 120 µm. Before evaluating powder flowability, 75 mL of the powder was evenly spread in an acrylic container (180 × 130 × 40 mm) and placed in a humidity adjustment device (AHCU-2, Kitz Micro Filter Corp., Nagano, Japan) at room temperature. The lactose powder was stored in the device for five days at relative humidity levels of 10, 30, 50, 70, 85, and 99%, respectively. Finally, we obtained six types of lactose powders, each stored under different relative humidities.

Table 1. Summary of powder weight before and after storage at different humidities.

Powder Bed Volume (mL)	Relative Humidity During Powder Storage (%)
	10			30		50		70		85		99
	Before		After	Before	After	Before	After	Before	After	Before	After	Before	After
30			18.76	18.76	18.99	18.76	19.13	18.76	19.31	18.76	19.63	18.76	20.01
40			25.02	25.02	25.31	25.02	25.50	25.02	25.75	25.02	26.17	25.02	26.69
50			31.27	31.27	31.62	31.27	31.89	31.27	32.20	31.27	32.50	31.27	33.10
75			46.91	46.91	47.43	46.91	47.84	46.91	48.30	46.91	48.76	46.91	49.65

shows the water content in powders stored at different moisture contents.

2.2. Powder Flowability Evaluation of the Powder Flow Cell

The rotational torque of the powder bed was measured using a rheometer (MCR302, Anton Paar, Graz, Austria) equipped with a powder flow cell ( Figure 1). First, the lactose powder, prepared as described in Section 2.1, was filled into a cylinder with an inner diameter of 5 cm. An impeller with a flat blade was then placed into the powder bed. The rotational torque of the impeller was recorded using a rheometer every 12 s for 20 min with varying rotational speeds from 50 to 70 rpm. The volume of the powder bed was varied from 30 to 75 mL. At a powder volume of 40 mL, the top of the powder bed reached the top of the blade, whereas, for a volume of 30 mL, the top of the powder bed reached the center of the blade (Figure 1). To keep the amounts of dry powder constant for all tests, the dry weights of the powder were set at the lowest relative humidity of 10%. These weights corresponded to the powder weight stored at relative humidity. The dry weights were 18.76, 25.02, 31.27, and 46.91 g for powder bed volumes of 30, 40, 50, and 75 mL, respectively.

In addition, the rotation torque of lactose powder stored at a humidity of 30% was measured with varying rotational speeds from 1 to 800 rpm in order to examine the broad range effect of the rotational speed on the rotation torque. The powder volume of this test was 30 and 50 mL. In order to verify the generality of the rotation speed effect on the measured rotation torque, we also examined the above torque measurement for 50 mL of zirconia powder (nominal particle size = 300 µm) and glass beads (nominal particle size = 1 mm).

2.3. Measurements of the Angle of Repose and Bulk Density

The angle of repose of the lactose powder was measured using a commercial angle of repose measurement device (ASK-01, As One Corp., Tokyo, Japan). The angular dip of the pile formed by free-falling powder from a hopper with an inner diameter of 33 mm onto a horizontal plane was measured using a protractor. The bulk density of the lactose powder was determined using a commercial bulk density measurement device (KAM-01, As One Corp., Tokyo, Japan). The powder was added to the container by free-falling from the hopper, and the extra powder above the top of the container was leveled off. Bulk density was calculated based on the container volume (100 mL) and the weight of the powder in the container. For the angle of repose and bulk density measurements, powders stored at relative humidities of 70, 85, and 99% did not fall freely. Therefore, external force was applied to discharge the powder from the hopper. We conducted measurements of the angle of repose and bulk density three times each.

3. Results and Discussion

3.1. Evaluation via the Powder Flow Cell

Figure 2 shows typical rotation torque measurements obtained using a powder flow cell. Two distinct types of time-dependent rotational torque behaviors were obtained in this study. First, similar to the result of the 30 mL powder stored at a relative humidity of 10%, the measured torque was almost constant over time, and the average torque value remained almost unchanged as the rotation speed varied (Type A). The flow behavior for these powders remained consistent regardless of changes in the rotational speed, and the powder flowed homogeneously. Figure 3a–e shows that the top surface of the powder bed underwent minimal changes during measurement, almost retaining the initial appearance before measurement. These findings suggest that the friction between particles governs the flow behavior of the powder bed at all rotation speeds for Type A powders.

In contrast, similar to the result of the 50 mL powder stored at a relative humidity of 99%, the average torque value changed with rotation speed, and the measured torque decreased over time or fluctuated (Type B). Generally, the rotational torque increases with higher rotational speeds owing to the centrifugal force, which tends to push the particles outward, leading to increased torque. Upon observing the top surface of the bed after rotational torque measurement (Figure 3f), a compacted powder layer around the cylinder walls was visible for Type B powders. This indicates that the particles migrated from the center toward the cylinder wall. The decrease in torque over time was attributed to granulation during the rotation of the powder bed. As granulation progressed, larger granules flowed more smoothly than those of smaller primary particles. Figure 3f shows several millimeters of particles after the rotational torque measurement, indicating that granulation occurred for Type B powders via the rotation of the powder. During this process, the measured rotational torque fluctuated as granulated lactose particles sometimes hit the impeller, causing variations in torque measurements.

Table 2. Summary of flow behavior for lactose powders (Type A: the rotation torque was independent of the rotation speed; Type B: the rotation torque depended on the rotation speed).

Powder volume (mL)	30
Relative humidity (%)	10	30	50	70	85	99
Rotation speed dependency	A	A	A	A	A	B
Powder volume (mL)	40
Relative humidity (%)	10	30	50	70	85	99
Rotation speed dependency	A	A	A	A	A	B
Powder volume (mL)	50
Relative humidity (%)	10	30	50	70	85	99
Rotation speed dependency	A	A	A	A	A	B
Powder volume (mL)	75
Relative humidity (%)	10	30	50	70	85	99
Rotation speed dependency	A	A	A	A	A	A

summarizes the measured torque behavior (Type A or B) under various experimental conditions, including relative humidity during storage, rotational speed, and powder bed volume. Type A behavior was most frequently observed, whereas Type B behavior occurred at a relative humidity of 99% for all powder bed volumes except for 75 mL. At 99% relative humidity, the moisture content in the powder was the highest, and water acted as a binder, resulting in granulation during the rotation of the powder bed.

For the 75 mL powder bed volume, the weight of the powder was more significant. Thus, the measured rotational torque was independent of time, classifying its flow behavior as Type A. These findings indicate the need for caution when evaluating powder flowability based solely on the measured (average) rotational torque from the powder flow cell, particularly when granulation occurs during rotation, as observed at 99% relative humidity. However, since Type A behavior was observed in most cases (Table 2), the average torque values for three varying rotational speeds were used to discuss the effect of relative humidity on powder flowability during storage.

3.2. Effect of Relative Humidity on Powder Flowability During Storage

Figure 4 shows the effect of relative humidity during powder storage on the measured average rotational torque. For all powder bed volumes, the average torque increased with higher relative humidity during storage. This indicates that powder flowability decreases as relative humidity increases, owing to the formation of liquid bridges between particles that result in a higher average rotational torque.

Figure 5 shows the ratio of the measured torque at each relative humidity to that at 10% relative humidity for all powder bed volumes used in this study. As shown in Figure 4, the measured torque increased with relative humidity; however, Figure 5 indicates that the torque difference became more pronounced as powder bed volume decreased. This suggests that the sensitivity of powder flowability evaluation improves when the powder bed volume is smaller.

To further investigate the effect of relative humidity on powder flowability during storage, the effect of liquid bridges between particles was estimated following the approach proposed by Endo and Kousaka [24]. Laplace–Young equations [25] were obtained for a liquid bridge formed between two particles of the same diameter (Figure 6):

$$P_{\mathrm{L}}=\sigma \left({\displaystyle \frac{1}{r_1^{\prime }}}-{\displaystyle \frac{1}{r_2^{\prime }}}\right)$$

(1)

$$r_1^{\prime }={\left\{1+{\left({\displaystyle \frac{dy}{dx}}\right)}^2\right\}}^{{\displaystyle \frac{2}{3}}}{\left({\displaystyle \frac{d^{2}y}{d{x}^2}}\right)}^{-1}$$

(2)

$$r_2^{\prime }=y{\left\{1+{\left({\displaystyle \frac{dy}{dx}}\right)}^2\right\}}^{{\displaystyle \frac{1}{2}}}$$

(3)

where P_L is the negative pressure inside the liquid bridge, σ represents the surface tension of the liquid, and r₁′ and r₂′ are the radii (Figure 6). Conversely, the vapor pressure directly above the liquid surface, P_d, is given by the following Kelvin equation [25]:

$${\displaystyle \frac{P_{\mathrm{d}}}{P_{\mathrm{s}0}}}=\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{M}{RT}}{\displaystyle \frac{\sigma }{{\rho }_{\mathrm{L}}}}·{\displaystyle \frac{ds}{dv}}\right)$$

(4)

where P_s0 is the saturated vapor pressure above the liquid surface, M denotes the molecular weight of the liquid, R represents the gas constant, T is the absolute temperature, ρ_L is the liquid density, s is the interface area between vapor and liquid, and v is the liquid volume. By examining Equations (1)–(3), the following approximate expression is proposed [26]:

$${\displaystyle \frac{ds}{dv}}\approx {\displaystyle \frac{1.5}{r_2}}$$

(5)

Thus, in this study, the radius of the narrowest point of the liquid bridge was estimated using the following equation, derived by substituting Equation (5) into Equation (4):

$$r_2=-{\displaystyle \frac{M}{RT}}{\displaystyle \frac{1.5\sigma }{{\rho }_{\mathrm{L}}}}\mathrm{l}\mathrm{n}{\displaystyle \frac{P_{\mathrm{d}}}{P_{\mathrm{s}0}}}$$

(6)

Figure 7 shows the relationship between relative humidity during powder storage and the radius of the narrowest point of the liquid bridge, as calculated using Equation (6). The results show that the radius of the narrowest point of the liquid bridge increased with higher relative humidity and that the estimated radius ranged from submicrons to microns, except for that at a relative humidity of 99%. Figure 8 illustrates the relationship between the radius of the narrowest point of the liquid bridge and the average rotational torque. The average rotational torque increased as the radius of the narrowest point of the liquid bridge increased, indicating that liquid bridge formation affects powder flowability. The increase in the average rotational torque was more significant for smaller powder bed volumes. This is because the effect of the powder bed weight was more dominant as the powder bed volume increased, which weakened the effect of liquid bridge formation on the average rotational torque. The difference in powder flowability was less distinguishable when the powder bed volume exceeded 40 mL (Figure 8). This corresponds to the powder bed volume that covers the entire impeller blade. This finding indicates that an optimal powder bed volume exists, and smaller volumes are more suitable for evaluating powder flowability when the relative humidity during powder storage (or moisture content) is varied.

3.3. Effect of Rotation Speed on the Measured Rotation Torque

Figure 9a,b shows the measured rotation torque for powder volumes of 30 and 50 mL when changing the rotation speed from 1 to 800 rpm. Figure 10 and Figure 11 show the appearance of a powder bed during rotation torque measurement. From Figure 9a, the measured torques reached equilibrium values in a short time except for a rotation speed of 500 rpm, the maximum rotation speed in this research. The equilibrium measured torque hardly changed when changing the rotation speed from 1 to 200 rpm, while the measured torque became larger at rotation speeds of 300 and 500 rpm for a powder volume of 30 mL. It was also found that the measured torque suddenly decreased for a rotation speed of 500 rpm. From Figure 10, we can see the motion of powders in the vicinity of the vessel wall became vigorous at a rotation speed of 300 rpm compared to other rotation speeds below 300 rpm. When the rotation speed increased to 500 rpm, this trend became more remarkable, resulting in larger measured rotation torque; however, the powder motion near the wall was too vigorous to scatter. This caused the decrease in the number of powders contacting the impeller, resulting in a sudden drop in the measured rotation torque in Figure 9a. From Figure 9b for a powder volume of 50 mL, it was shown that the rotation torque hardly changed until a rotation speed of 300 rpm, and then the rotation torque became larger at rotation speeds above 300 rpm. When the rotation speed became larger than 300 rpm, we could clearly see a cavity around the impeller, indicating that more particles moved to the vessel wall. This particle motion made the measured rotation torque larger than that measured at a rotation speed below 300 rpm.

Figure 12 shows the relationship between the equilibrium rotation torque for lactose, zirconia and glass beads measured at various rotation speeds. Here, we compared the equilibrium rotation torque because the measured rotation torques of all powders were almost independent of measuring time when the powder volume was 50 mL. It was shown that the measured rotation torques drastically increased above the critical rotation speeds, that is, 300 rpm for lactose powder and 100 rpm for zirconia powder and glass beads.

Similarly to the lactose powder mentioned above, the powder motion became vigorous at the critical rotation speed, resulting in the rapid increase in the measured rotation torque for zirconia powder and glass beads. Even though the density of zirconia is larger than that of glass beads, the nominal particle size of glass beads is larger than that of zirconia powder; thus, the effect of the powder weight on the rotation of the impeller seems to be similar for zirconia powder and glass beads used in this research.

From the above experimental results and discussion, it was suggested that there should be a critical rotation speed from which the measured rotation torque increased with the rotation speed, and the critical rotation speed should be changed by the powder properties including the particle size distribution and the particle density. Further investigation is necessary to quantitatively estimate the critical rotation speed for each powder.

3.4. Comparison of the Angle of Repose and Bulk Density

Figure 13 and Figure 14 show the measured angles of repose and bulk densities of the lactose powders stored at different relative humidities, respectively. For relatively high relative humidities of 70, 85, and 99%, neither the angle of repose nor bulk density could be measured using the standardized procedure described in Section 2.3. In these cases, the powder in the hopper was compulsorily discharged by applying an external force, thus making direct comparisons of these values difficult. For the powders that could be measured using a standardized procedure, the angle of repose increased, and bulk density decreased with an increased relative humidity during storage. For humidities above 70%, an external force was needed to discharge the powder from the hopper, indicating that powder flowability declined compared to those stored below 70% humidity. These findings suggest that the angle of repose and bulk density may not be suitable parameters for evaluating all lactose powders using the standardized procedure. In contrast, the powder flow cell (powder rheometer) effectively measured rotational torque for all lactose powders under the same conditions. Furthermore, rotational torque measurement using a powder flow cell enabled evaluation of the flowability of powders with diverse properties over a wide range.

4. Conclusions

The flowability of lactose powders stored at different relative humidities was evaluated by measuring the rotational torque using a powder flow cell. The effects of varying measurement conditions, such as rotational speed and powder bed volume, on rotational torque were measured. The influence of relative humidity on rotational torque was then compared with the effect of relative humidity during storage on the conventionally measured angle of repose and bulk density parameters. The following conclusions were drawn:

(1)

The effect of rotational speed on rotational torque was minimal for most lactose powders used in this study, except for those stored at a high relative humidity of 99%.

(2)

Differences in flowability of lactose powders stored at varying relative humidities were easily distinguished for a powder bed volume of 30 mL, which was the smallest value used in this study.

(3)

A powder flow cell, used with a rheometer, enables precise measurement of the rotational torque and evaluation of powder flowability under consistent conditions. In contrast, neither the angle of repose nor the bulk density could be measured reliably under the same standardized conditions.

(4)

It was suggested that there should be a critical rotation speed from which the measured rotation torque increased with the rotation speed, and the critical rotation speed should be changed by the powder properties including the particle size distribution and the particle density.

It is significant to find the minimum required amount of powder for the precise measurement of powder flowability because we can evaluate a limited amount of prototype powder and expensive powder. It is also meaningful to identify the rotation speed to be set within the range where the measured torque remains unchanged. In this study, rotational torque was measured across multiple powder bed volumes, whereas rotational speed was varied within an empirically determined range. However, the range of rotational speeds for which a powder flow cell with a rheometer can be employed is relatively wide. Thus, further investigation is required to clarify the influence of rotational speed on the measured rotational torque and we need to investigate the effect of other factors such as the impeller shape and initial state of the powder bed. Additionally, rotational torque measurements using a powder flow cell should be expanded to other powders in future studies to control industrial powder processes.