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Dynamic absorption efficiency of paracetamol powder in microwave drying

  • Di Zhai , Fucheng Zhang , Cong Wei , Xiaobiao Shang EMAIL logo , Junruo Chen , Meihong Liu and Jinhui Peng
Published/Copyright: September 8, 2019
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High Temperature Materials and Processes
From the journal High Temperature Materials and Processes Volume 38 Issue 2019

Abstract

In microwave drying technology, research into the dynamic absorbing properties of the powder is indispensable. In this study, the reflection loss coefficient of paracetamol powder under different temperature, water content, and thickness was calculated based on the principle of electromagnetic wave transmission. The results show that the absorption performance of powder fluctuates dynamically with a series of absorption peaks, and the position of the absorption peak shifts toward the smaller thickness direction as the water content increases or the temperature rises. Because of the influence of the powder thickness on absorbing efficiency, the powder thickness should be adjusted in real time to increase drying efficiency. This study provides the thickness range for which the absorption performance of paracetamol powder under different conditions is over 99%. This study is of great significance for understanding the drying mechanism and optimizing process parameters for microwave drying of pharmaceutical powder.

Keywords: paracetamol; pharmaceutical powder; microwave drying; absorption efficiency; reflection loss

1 Introduction

Drying is a common processing technique that is currently used in the manufacture of biotherapeutic products [1]. Moisture removal offers many benefits, including ease of processing and storage, low shipping costs and high product stability. Freeze-drying is a common drying method, and is used in food manufacture, pharmaceutical processing, and bioengineering [2]. However, freeze-drying also has many disadvantages, such as long processing times, low energy efficiency, and high costs of purchasing and maintaining equipment. In addition, freeze-drying is suited to mass production, which makes it potentially difficult for use in continuous production processes. Such restrictions have motivated studies into the next generation of drying technologies that can be applied to the manufacture of biotherapeutic products. Microwave drying technology has been widely used in many applications in the pharmaceutical industry such as drying, synthesis, extraction, and sterilization because of its high efficiency, low environmental impact, and energy efficiency [3, 4].

Paracetamol is currently the most commonly used non-anti-inflammatory antipyretic analgesic and is one of the most widely applied drugs in the world [5, 6], and the drying process is an indispensable part of paracetamol production. Compared with traditional drying methods, microwave drying can be better applied to continuous and automated mass production of drugs because of its fast drying speed, high finished product quality, and high energy efficiency. In the microwave drying process, the complex permittivity of the heated medium changes dynamically with the decrease of moisture content [7], which results in changes in absorption efficiency. Given that the microwave absorption property plays a decisive role in microwave heating, any change in the microwave absorption property eventually leads to continuously changing microwave heating efficiency, which would reduce the heating efficiency in most cases [8]. Therefore, the study of the dynamic absorption efficiency of the heated media is particularly important to increase the utilization of microwave energy.

At present, studies of Microwave heating have been applied in the field of metallurgy [9, 10]. Pan ShunKang et al [11] calculated and analyzed the absorbing properties of Mn55Al45 alloy for different high-energy ball-milling times and tempering temperatures. They found that when the temperature was lower than 400∘C, the absorption peaks shifted toward lower frequency with increased grinding time; however, when the temperature was higher than 400∘C, the absorption peaks shifted toward higher frequency with increased grinding time. They also calculated the minimum reflectance values at 200, 400, and 600∘C.

Studies on the dynamic absorption efficiency of pharmaceutical powders are still relatively rare. Magee et al [12] measured the dielectric properties of commonly used pharmaceutical powders, such as paracetamol, and modeled the data. They found that the magnitudes of the dielectric constant (ϵ′), the loss factor (ϵ′′), and the microwave penetration depth (Dp) are affected by frequency, moisture content, temperature, and powder type. Notably, the dielectric properties of pharmaceutical powder containing water increase linearly with moisture content, but the relationship between temperature and dielectric properties is a quadratic form. Currently, studies of drug powders remain focused on the measurement of parameters, and the microwave absorption efficiencies of the relevant drug powders are yet to be calculated. Microwave heating efficiency is not only related to the complex permittivity of the material in the microwave drying process [13], but also to the size and shape of the heated medium, the location, the design of the microwave heating equipment, and other factors [14, 15]. As a result, some adjustments to the size of the heated medium can make it a strong absorber [16, 17]. However, the influence of the thickness of the absorbing material is usually ignored by researchers. Although high moisture content can make the heated medium a strong absorber in the initial stages of microwave drying, the wrong thickness may soon convert the material into a weak absorber of microwaves. Conversely, a suitable thickness can make a low-moisture medium in the later stages of microwave drying become a strong absorber. Therefore, studies on microwave absorption properties under different conditions (moisture content, temperature, powder thickness) are meaningful. Despite this need, there is a scarcity of reports on theoretical calculations of the absorption efficiency of paracetamol powder in microwave drying.

This study calculated the reflection loss coefficient of paracetamol powder based on the principle of electromagnetic wave transmission, with a frequency of 2450 MHz, and using the variables of temperature (20–70∘C), moisture content (0.2–1.0 kg kg−1), and powder thickness (0–0.060 m). The study analyzed the relationships between the absorption efficiency and the temperature, moisture content, and powder thickness, which may provide a reference for the selection of the best thickness interval in microwave drying.

2 Reflection Loss Theory

Microwave heating is a process in which a material absorbs incident electromagnetic wave energy and converts it into thermal energy. Two main factors should be considered in the specific evaluation of the microwave absorption property of materials. One is the impedance match of the material [18]. The electromagnetic waves must penetrate the inside of the material as much as possible for the high-efficiency absorption of electromagnetic waves. Therefore, the input impedance of the material must match the wave impedances of the free space to offset the interference by the two columns of reflected electromagnetic waves (two columns of waves reflected back into the air medium at the former and latter interfaces of the absorbing layer), as displayed in Figure 1. The second factor is the electromagnetic wave attenuation properties of the material [19, 20]. The attenuation properties refer to the ability of the material to absorb electromagnetic waves (the electromagnetic loss property of the material). The main parameters affecting these two properties are the electromagnetic parameters of the material, which are affected by the moisture content and temperature. For non-magnetic materials (paracetamol is regarded as non-magnetic), the main parameter affecting microwave heating is the relative complex permittivity of the material. Table 1 presents the relative complex permittivity of paracetamol powder at a frequency of 2450 MHz (the frequency used in this study), with the temperature

Figure 1 Schematic of a single absorber under microwave irradiation.
Figure 1

Schematic of a single absorber under microwave irradiation.

Table 1

The relative complex permittivity of paracetamol at various moisture contents and temperatures (2450 MHz).

relative complex permittivityMoisture content (X/kg kg−1)
0.20.40.60.81.0
Temperature (∘C) 20∘8.87-0.54j16.91-1.55j22.47-1.98j24.86-2.24j26.58-2.83j
30∘12.22-1.01j22.91-2.66j25.02-2.99j26.91-3.27j27.77-3.36j
40∘13.42-1.14j25.12-2.79j26.21-3.17j29.09-3.54j32.70-4.09j
50∘19.28-2.18j26.48-3.61j32.26-3.96j34.73-4.33j36.34-4.52j
60∘24.01-3.23j30.74-3.86j33.54-4.03j39.40-4.82j44.73-5.61j
70∘27.08-3.38j34.45-4.29j39.13-4.80j44.73-5.54j48.31-5.94j

of 20–70∘C, and the moisture content of 0.2–1.0 kg kg−1 [12].

Figure 1 is a schematic view showing the transmission of electromagnetic waves through an absorber with a metal plate having strong reflection characteristics as the substrate. According to transmission line theory [21],when a fixed-frequency uniform-plane electromagnetic wave is perpendicularly incident on the surface of a single-layer absorbing material, the power reflection of the material on the electromagnetic wave can be calculated with the reflection loss coefficient RL (dB) [22, 23]:

(1)RL=20lg |Zin−1Zin+1|
(2)Zin=μr/εr⋅tanh[j(2πfd/c)μr⋅εr]

where Zin is the input impedance of the absorber; μr is the relative complex permeability of the material (μr = μ′−jμ′′; μ′ = 1 and μ′′ = 0 for non-magnetic material); εr is the relative complex permittivity of the material (εr = ε′ − jε′′); c is the velocity of light; f is the frequency of the electromagnetic wave; and d is the thickness of the absorbing material. Based on Eqs. (1) and (2), the absorption efficiency is mainly subject to the frequency of the electromagnetic wave, the thickness of the absorption layer, and the relative complex permittivity of the material under the corresponding conditions. Therefore, an expression for the reflection loss coefficient that changes with the thickness of the absorbing material can be calculated with data from Table 1. When the particle size of the powder is much smaller than the wavelength of the electromagnetic wave, the interaction between the particles is negligible [24]. The particle size of the pharmaceutical powder used in this study was much smaller than the wavelength of the electromagnetic wave, so it was considered to be a single uniform medium.

Different from the traditional heating method, the microwave heating process requires electromagnetic waves to penetrate into the material to be lost and converted into heat energy, thereby achieving the purpose of heating. Because of the electromagnetic wave attenuation properties of the material, microwave heating also has the problem of uniformity. In most cases, Dp is the microwave penetration depth, which measures the uniformity of microwave heating. The penetration depth equation for microwaves in non-magnetic materials is [25]:

(3)Dp=λ02π(2εr')1/2{[1+(εr''εr')2]1/2−1}−1/2

where Dp is the penetration depth of the microwave in the medium, which is defined as the distance at which the dissipated power is attenuated to 1/e (e ≈ 2.718, 1/e ≈ 36.8%); and λ0 is the microwave wavelength in free space (λ0 = c/f). The microwave penetration depth of paracetamol powder can be calculated at 2450 MHz, under different temperature and moisture conditions, with the parameters in Table 1. As shown in Figure 2 and Table 2, except for the case where the penetration depth of the paracetamol powder with a moisture content of 0.2 kg kg−1 is in the range

Figure 2 Microwave penetration depth in paracetamol at temperatures between 20 and 70∘C and in the moisture contents range of 0.2–1 kg kg−1 (2450 MHz).
Figure 2

Microwave penetration depth in paracetamol at temperatures between 20 and 70∘C and in the moisture contents range of 0.2–1 kg kg−1 (2450 MHz).

Table 2

The microwave penetration depth in paracetamol at temperatures between 20 and 70∘C and in the moisture contents range of 0.2–1 kg kg−1 (2450 MHz).

Dp/mMoisture content (X/kg kg−1)
0.20.40.60.81.0
Temperature (∘C)20∘0.10750.05180.04670.04340.0356
30∘0.06750.03510.03270.03100.0306
40∘0.06270.03510.03150.02970.0273
50∘0.03930.02780.02800.02660.0260
60∘0.02960.02800.02810.02540.0233
70∘0.03010.02670.02540.02360.0228

of 0–0.10 m, the penetration depths under the other conditions were below 0.06 m in this study. From these data, the thickness range of paracetamol powder under uniform heating conditions can be calculated, which then allows further studies on the microwave absorption property of the material with different thicknesses.

3 Results and discussion

3.1 Impact of temperature on absorption efficiency of paracetamol powder

Figure 3 presents the patterns of the reflection loss coefficient of the paracetamol powder, which changes with thickness at different temperatures (20, 30, 40, 50, 60, 70∘C) with a certain fixed moisture content (0.2, 0.4, 0.6, 0.8, 1.0 kg kg−1). Figure 3 shows that the reflection loss of the paracetamol powder fluctuates at different temperatures and there are several troughs (absorption peak) in the RL curves. (Although RL is a negative value, the larger the absolute value of RL, the smaller the energy of the electromagnetic wave reflected by the material surface, indicating more energy taken by the material and better absorption efficiency of the material.) The fluctuation can be explained by the 1/4 wavelength theory [26, 27]: the matching thickness of the corresponding material is very close to 1/4 of the wavelength of the microwave in the material and multiplied by an odd number, at which an interference phenomenon occurs, thereby forming an absorption peak.

When the moisture content is fixed, the number of absorption peaks of the paracetamol powder at different temperatures in the same thickness range is different. For example, when the water content is 0.2 kg kg−1 and the thickness range is 0–0.10 m, there are five absorption peaks at 20∘C, but when the temperature rises to 70∘C, there are eight absorption peaks. This is because the increase in temperature results in an increase in the dielectric constant of paracetamol powder, which makes the microwave wave-length in the powder shorter. The wavelength variation law and the wavelength values under various conditions are shown in Figure 4 and Table 3. The wavelength in the medium is given by [28]:

Table 3

The microwave length in paracetamol at temperatures between 20 and 70∘C and in the moisture contents range of 0.2–1 kg kg−1 (2450 MHz).

λd/mMoisture content (X/kg kg−1)
0.20.40.60.81.0
Temperature (∘C)20∘0.04110.02970.02580.02450.0237
30∘0.03500.02550.02440.02360.0232
40∘0.03340.02440.02390.02270.0214
50∘0.02780.02370.02150.02070.0203
60∘0.02490.0220.02110.01950.0183
70∘0.02350.02080.01950.01830.0176
(4)λd=2λ{ε′μ′′−ε′′μ′′        +[(ε′μ′)2+(ε′′μ′′)2+(ε′μ′′)2+(ε′′μ′)2]1/2}−1/2

where λd is the propagation wavelength of the electromagnetic wave in the medium. According to the 1/4 wavelength theory, the wavelength in the drug powder medium becomes shorter, which leads to an increase in the number

Figure 3 Temperature dependence (20, 30, 40, 50, 60, 70∘C) of reflection loss of paracetamol as thickness varies from 0 to 0.1 m for moisture contents: (a) 0.2 kg kg−1, (b) 0.4 kg kg−1, (c) 0.6 kg kg−1, (d) 0.8 kg kg−1, (e) 1.0 kg kg−1.
Figure 3

Temperature dependence (20, 30, 40, 50, 60, 70∘C) of reflection loss of paracetamol as thickness varies from 0 to 0.1 m for moisture contents: (a) 0.2 kg kg−1, (b) 0.4 kg kg−1, (c) 0.6 kg kg−1, (d) 0.8 kg kg−1, (e) 1.0 kg kg−1.

Figure 4 Microwave length in paracetamol at temperatures between 20 and 70∘C and in the moisture contents range of 0.2–1 kg kg−1 (2450 MHz).
Figure 4

Microwave length in paracetamol at temperatures between 20 and 70∘C and in the moisture contents range of 0.2–1 kg kg−1 (2450 MHz).

of absorption peaks in the same thickness interval, and the positions of the absorption peaks also shift toward the smaller thickness direction. The shorter wavelength makes the microwave phase constant increase, because the dielectric constant varies widely, so the values of the position shift of the absorption peaks are larger as the temperature increases. As the thickness increases, the subsequent position shift accumulates an extra wavelength deviation. Thus, more absorption peaks appear later, which is the more obvious sign of this shift phenomenon. For example, when the moisture content was fixed at 0.2 kg kg−1, the first absorption peak at 20∘C was located at a thickness of 0.01078 m, while at 70∘C, the first absorption peak was at 0.00596 m; the fifth absorption peak at 20∘C was located at a thickness of 0.09257 m, and at 70∘C it was at 0.05288 m. Table 4 lists the distribution of absorption peaks of paracetamol powders at different temperatures and moisture contents (values at which RLs tend to be flat are not listed).

There is a thickness for the maximum absorption efficiency in each reflection loss curve of paracetamol powder under different conditions. For example, when the moisture content was0.2 kg kg−1 and the temperature was 70∘C, the absorption peak amplitude first increased with the powder thickness, and the maximum value (RL = −32.39 dB) was obtained when the powder thickness was 0.01765 m. Above this thickness, the absorption peak amplitude began to decrease, and at higher temperatures, this reduction was more pronounced. This is because the penetration depth of the microwave in the pharmaceutical powder decreases with the increase in temperature (the pattern of Dp is shown in Figure 2). For example, the penetration depth of the microwave was 0.1075 m when the moisture content of the paracetamol powder was 0.2 kg kg−1 and the temperature was 70∘C, but it was only 0.0301 m when the temperature increased to 70∘C. Therefore, there is still an absorption peak (RL = 47.11 dB) at 20∘C when the powder thickness is 0.09257 m, but the RL values around the peaks are slightly over -10 dB when the temperature rises to 70∘C.

According to the variation law of the absorption peaks in Figure 3, it can be found that under the premise of ensuring uniform heating (the powder thickness is smaller than the microwave penetration depth), the thickness values for the second absorption peak should be selected as the preferred thickness. This is because the position shifts of the absorption peaks around the second absorption peaks are smaller, and with higher absorption efficiency, and it applies under various temperature conditions. The complex dielectric constants of the pharmaceutical powders change dynamically under different temperature conditions. Therefore, under the condition of fixing the thickness of the powder layer, it is difficult to ensure the best heating efficiency for microwave drying under different temperature conditions. The best powder thickness should be based on the absorption peak positions and RL values that create the best absorbing efficiency under conditions that match the powder thickness. Table 5 lists the thickness ranges corresponding to the reflection loss coefficients of paracetamol powder less than −20 dB. The reflection loss coefficient that is less than −20 dB (99% of the microwave energy can be absorbed) is usually taken as an indicator of absorption efficiency [29, 30]. Therefore, in microwave drying of paracetamol powder, the thickness of the powder should be preferentially selected in the thickness range listed in Table 5.

3.2 Impact of moisture content on absorption efficiency of paracetamol powder

Figure 5 shows the variation of the reflection loss coefficients of paracetamol powder with different moisture contents and increasing thickness under fixed temperature conditions. Figure 5 shows that the impact on the reflection loss of the paracetamol powder caused by moisture content is similar to that caused by temperature: the curve of the reflection loss coefficients with powder thickness also fluctuates with different moisture contents and at the same temperature. This is because the impact on the electromagnetic parameters of the pharmaceutical powder caused by moisture content is similar to that caused by temperature. As the moisture content increases, the real and imaginary parts of the relative complex permittivity of the paracetamol powder increase. Thus, the fluctuation caused by moisture content is the same as that caused by temperature.

Figure 5 Moisture dependence (0.2, 0.4, 0.6, 0.8, 1.0 kg kg−1) of reflection loss of paracetamol as the thickness varies from 0 to 1.0 m for temperatures: (a) 20∘C, (b) 30∘C, (c) 40∘C, (d) 50 ∘C, (e) 60∘C, (f) 70∘C.
Figure 5

Moisture dependence (0.2, 0.4, 0.6, 0.8, 1.0 kg kg−1) of reflection loss of paracetamol as the thickness varies from 0 to 1.0 m for temperatures: (a) 20∘C, (b) 30∘C, (c) 40∘C, (d) 50 ∘C, (e) 60∘C, (f) 70∘C.

Table 4

Absorption peaks in the RL patterns of paracetamol (2450 MHz; thickness range: 0–0.1 m).

Absorption peakTemperature (°C)
20°C30°C40°C50°C60°C70°C
thk(m)RL (dB)thk (m)RL (dB)thk (m)RL (dB)thk (m)RL (dB)thk (m)RL (dB)thk (m)RL (dB)
Moisture0.210.01078-6.020.00906–9.570.00862–10.300.00711–16.850.00634–23.380.00596–22.90
content20.03101–18.250.02637–32.840.02515–36.890.02094–53.520.01875–31.870.01765–32.39
(X/kgkg–1)30.0515–34.740.04384–61.050.04182–49.730.03485–24.420.03121–17.910.02939–17.99
40.07203–79.310.06133–32.500.05851–29.340.04877–17.480.04367–13.410.04113–13.34
50.09257–47.110.07883–24.350.07521–22.350.0627–14.260.05614–11.270.05288–11.10
60.09191–18.680.07662–12.470.06862–10.090.06463–9.85
70.09055–11.380.08109–9.400.07638–9.10
0.410.00762–12.520.0065–19.080.0062–19.090.00603–25.240.00559–24.930.00527–26.51
20.02238–54.680.0192–41.770.01834–41.510.01785–29.190.01657–29.320.01565–27.42
30.03724–34.920.03197–21.340.03053–21.170.02971–16.730.02758–16.650.02605–15.75
40.05211-23.150.04474–15.510.04273–15.330.04158–12.590.03861–12.400.03647–11.75
50.06699-18.180.05751–12.750.05493–12.530.05346–10.620.04963–10.350.04688–9.80
60.0573–8.71
0.610.00657-13.890.00621–20.750.00607–21.620.00545–24.960.00534–24.880.00494–28.24
20.01941-85.780.01837–36.800.01795–34.780.01617–29.220.01586–29.260.01468–25.70
30.0323-29.830.03058–19.660.02988–18.910.02693–16.560.02641–16.550.02445–14.90
40.0452-20.310.0428–14.430.04182–13.930.03769–12.310.03696–12.270.03422–11.12
50.05811-16.040.05502–11.920.05376–11.540.04845–10.240.04752–10.180.04399–9.27
60.05921–9.080.05808–9.000.05376–8.22
0.810.00624-15.010.00598–22.080.00575–23.170.00525–26.690.00492–28.270.00461–31.41
20.01844–75.730.01771–33.840.01703–31.840.01558–27.230.01463–25.670.01373–23.34
30.0307–27.050.02949–18.540.02836–17.710.02595–15.660.02436–14.880.02286–13.73
40.04297–18.730.04127–13.680.03969–13.100.03632–11.690.0341–11.110.032–10.29
50.05524–14.880.05305–11.340.05102–10.870.04669–9.750.04384–9.250.04114–8.59
60.05706–8.670.05358–8.210.05028–7.64
1.010.00602–18.760.00589–22.380.00541–25.790.00513–27.400.00461–31.990.00444–32.86
20.01783–42.510.01743–33.240.01606–28.250.01523–26.510.01373–22.990.01321–22.45
30.02968–21.410.02903–18.280.02674–16.140.02537–15.310.02286–13.570.022–13.26
40.04154–15.420.04062–13.500.03743–12.040.03551–11.440.032–10.190.03079–9.94
50.0534–12.550.05222–11.190.04812–10.040.04565–9.540.04114–8.520.03959–8.30
60.05881–8.930.05579–8.480.05028–7.590.04839–7.37
Table 5

Thickness ranges of paracetamol with RL values less than –20dB at 2450 MHz.

Thickness (m)Temperature (°C)
20°C30°C40°C50°C60°C70°C
Moisture0.210.05120-0.052970.02545-0.027360.02424-0.026140.02009-0.021880.00609-0.006620.00575-0.00619
content20.07015-0.074020.04243-0.045340.04052-0.043210.03411-0.035630.01806-0.019490.01705-0.01831
(X/kg kg-1)30.09044-0.094820.05983-0.062910.05720-0.05989
40.07754-0.08019
50.09598-0.09668
0.410.02153-0.023310.01847-0.020000.01767-0.019060.00575-0.006340.00535-0.005840.00504-0.00553
20.03620-0.038340.03157-0.032370.03019-0.030880.01725-0.018490.01605-0.017110.01521-0.01611
30.05132-0.05292
0.610.01873-0.020140.00610-0.006340.00590-0.006240.00523-0.005690.00513-0.005570.00471-0.00519
20.03156-0.033070.01770-0.019090.01731-0.018630.01568-0.016690.01539-0.016360.01432-0.01506
30.04499-0.04541
0.810.01181-0.019130.00580-0.006180.00555-0.005970.00502-0.005500.00470-0.005170.00439-0.00486
20.03008-0.031360.01710-0.018370.01647-0.017630.01515-0.016040.01427-0.015010.01346-0.01401
1.010.01720-0.018500.00570-0.006090.00518-0.005670.00490-0.005380.00439-0.004860.000422-0.00467
20.02934-0.030030.01684-0.018070.01559-0.016560.01483-0.015660.01347-0.014000.01299-0.01344

In the reflection loss curve related to the moisture content of the paracetamol powder, there is also a matching thickness corresponding to the maximum absorption efficiency. After exceeding this thickness, the fluctuation of the RL curve decreased until the RL gradually approached a constant value after reaching a certain thickness. This is because water is a strong absorbing material. Therefore, the electromagnetic wave absorption of paracetamol powder increases with moisture content, and when the moisture content reaches a certain level, the powder–water mixture consumes almost all of the microwave energy. In this case, the microwave energy reflected back from the latter interface is very rare, and the superposition effect of the wave caused by the impedance mismatch of the front interface reflected wave is not obvious. Therefore, the RL curves gradually become stable. As the moisture content increases, the relative complex permittivity changes, which causes the microwave penetration depth and the wavelength in the powder medium to decrease. This decreasing trend was most pronounced when the moisture content increased from 0.2 kg kg−1 to 0.4 kg kg−1. Thus, most changes in the RL curves in Figure 5 can be explained with the above analysis and the 1/4 wavelength theory. For example, the thickness position corresponding to the absorption peak of the RL curve is at an odd multiple of 1/4 wavelength under the corresponding condition; as the moisture content increases, the number of absorption peaks increases; the position of the absorption peak shifts toward a smaller thickness direction; and as the thickness increases, the position shift increases.

The above analysis found that the second absorption peaks should be selected as the preferred thickness. In different microwave drying conditions, the best thickness of paracetamol powder for microwave drying should be based on positions of relevant absorption peaks and the thickness ranges within which the RL values are less than −20 dB, as shown in Tables 4 and 5.

3.3 Impact of thickness on absorption efficiency of paracetamol powder

As displayed in Figures 3 and 5, there is a similar rule for the variations of RL curves with thickness. When the thickness exceeds the matching thickness of the maximum absorbing efficiency, and continues to increase, the fluctuation amplitudes of the absorption peaks decrease continuously and the RL gradually tends to a constant value. These phenomena were particularly evident under conditions of relatively high temperature and high moisture content. For example, there are six absorption peaks of the RL curve of paracetamol powder within the thickness range of 0–0.06 m, at 70∘C and with a moisture content of 1.0 kg kg−1. The first absorption peak is located at the thickness of 0.00444 m, with an RL value of −32.86 dB. The RL values of the third, fourth, fifth, and sixth absorption peaks are −13.26, −9.94, −8.30, and −7.73 dB, respectively, for which the thickness range is 0.022–0.04839 m. After the third absorption peak, the smoothing of the RL curve becomes more obvious. This is because the microwave penetration depth under this condition is small (Dp = 0.0288 m). When the powder is thicker than the penetration depth of the microwave under the corresponding conditions, the microwave reflected at the latter interface has been attenuated to a small extent, and has little effect on the overall power reflection. At this time, not only is the uniform heating condition not satisfied, but the drying efficiency is also low.

The impedance matching characteristics of the material are also largely influenced by its thickness parameters. The electromagnetic parameters of the material are basically fixed when the temperature, moisture content, and frequency are fixed. In this case, the electromagnetic wave attenuation properties of the material would have little effect on the RL value. The RL value would be mainly subject to whether the impedance matching characteristics of the material are appropriate, based on the equation [26, 27]:

(5)d=(2n−1)λd/4    (n=1,2,3, … …)

where the thickness (d) of the absorbing material is an odd multiple of the λd/4 thickness of the medium, and the phase difference between the wave reflected by the former interface and the wave reflected by the latter interface is π. Therefore, when the thickness of the drug powder is larger than λd/4, the RL curve exhibits a fluctuation distribution, and, as the thickness increases, the absorption peak appears in sequence.

The above analysis found that the powder thickness should be smaller than the microwave penetration depth (Dp) as much as possible in the microwave drying of paracetamol powder. In addition, under the premise of uniform heating, the absorption efficiency of the powder can be improved by using the right powder thickness (Tables 4 and 5), thereby improving the drying efficiency.

4 Conclusions

The theory of reflection loss was applied to microwave drying, and the moisture characteristics and temperature characteristics of the paracetamol powder reflection loss were calculated and analyzed.

The absorption efficiency of paracetamol powder fluctuates with different temperatures and moisture contents as the powder thickness increases, and the best absorption efficiency occurred within in the thickness range studied. Therefore, the microwave drying efficiency of paracetamol powder can be improved by adjusting the powder thickness.

The powder thickness in microwave drying should be adjusted based on specific conditions. The powder thickness range is subject to specific drying temperatures and drying stages: the initial drying stage with high moisture content, the medium drying stage with moderate moisture content, the final drying stage with low moisture content, and dielectrically assisted drying in the final drying stage.

The findings in this study can provide a reference for the selection of thickness ranges of paracetamol powder in microwave drying, and contribute to better design of microwave drying equipment and optimized process parameters in microwave drying.

Acknowledgement

This work was supported by the Scientific Research Fund of Kunming University of Science and Technology [grant number KKSY201601045]; Yunnan Science and Technology Major Project [grant number 2018ZE008 and grant number 2018ZE027].

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Received: 2019-01-08
Accepted: 2019-02-15
Published Online: 2019-09-08
Published in Print: 2019-02-25

© 2019 D. Zhai et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Articles in the same Issue

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  2. Review Article
  3. Research on the Influence of Furnace Structure on Copper Cooling Stave Life
  4. Influence of High Temperature Oxidation on Hydrogen Absorption and Degradation of Zircaloy-2 and Zr 700 Alloys
  5. Correlation between Travel Speed, Microstructure, Mechanical Properties and Wear Characteristics of Ni-Based Hardfaced Deposits over 316LN Austenitic Stainless Steel
  6. Factors Influencing Gas Generation Behaviours of Lump Coal Used in COREX Gasifier
  7. Experiment Research on Pulverized Coal Combustion in the Tuyere of Oxygen Blast Furnace
  8. Phosphate Capacities of CaO–FeO–SiO2–Al2O3/Na2O/TiO2 Slags
  9. Microstructure and Interface Bonding Strength of WC-10Ni/NiCrBSi Composite Coating by Vacuum Brazing
  10. Refill Friction Stir Spot Welding of Dissimilar 6061/7075 Aluminum Alloy
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  12. On the Capability of Logarithmic-Power Model for Prediction of Hot Deformation Behavior of Alloy 800H at High Strain Rates
  13. 3D Heat Conductivity Model of Mold Based on Node Temperature Inheritance
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  16. The Interaction between Erosion Particle and Gas Stream in High Temperature Gas Burner Rig for Thermal Barrier Coatings
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  18. Study on Carbothermal Reduction of Titania in Molten Iron
  19. The Sequence of the Phase Growth during Diffusion in Ti-Based Systems
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  21. High-Temperature Flow Behaviour and Constitutive Equations for a TC17 Titanium Alloy
  22. Research on Three-Roll Screw Rolling Process for Ti6Al4V Titanium Alloy Bar
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  25. Casting Defects in Transition Layer of Cu/Al Composite Castings Prepared Using Pouring Aluminum Method and Their Formation Mechanism
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  31. Elastic Moduli and Elastic Constants of Alloy AuCuSi With FCC Structure Under Pressure
  32. Effect of Cl on Softening and Melting Behaviors of BF Burden
  33. Effect of MgO Injection on Smelting in a Blast Furnace
  34. Structural Characteristics and Hydration Kinetics of Oxidized Steel Slag in a CaO-FeO-SiO2-MgO System
  35. Optimization of Microwave-Assisted Oxidation Roasting of Oxide–Sulphide Zinc Ore with Addition of Manganese Dioxide Using Response Surface Methodology
  36. Hydraulic Study of Bubble Migration in Liquid Titanium Alloy Melt during Vertical Centrifugal Casting Process
  37. Investigation on Double Wire Metal Inert Gas Welding of A7N01-T4 Aluminum Alloy in High-Speed Welding
  38. Oxidation Behaviour of Welded ASTM-SA210 GrA1 Boiler Tube Steels under Cyclic Conditions at 900°C in Air
  39. Study on the Evolution of Damage Degradation at Different Temperatures and Strain Rates for Ti-6Al-4V Alloy
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  41. Evolution of Interfacial Features of MnO-SiO2 Type Inclusions/Steel Matrix during Isothermal Heating at Low Temperatures
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  43. The Microstructure and Property of the Heat Affected zone in C-Mn Steel Treated by Rare Earth
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  56. A Multi Scale Strategy for Simulation of Microstructural Evolutions in Friction Stir Welding of Duplex Titanium Alloy
  57. Partition Behavior of Alloying Elements in Nickel-Based Alloys and Their Activity Interaction Parameters and Infinite Dilution Activity Coefficients
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  60. Microstructure and Mechanical Properties of Thick Plate Friction Stir Welds for 6082-T6 Aluminum Alloy
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  77. Research Article
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  87. Effect of PWHT Conditions on Toughness and Creep Rupture Strength in Modified 9Cr-1Mo Steel Welds
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https://doi.org/10.1515/htmp-2019-0015
Keywords for this article
paracetamol; pharmaceutical powder; microwave drying; absorption efficiency; reflection loss
Creative Commons
BY 4.0

Articles in the same Issue

  1. Frontmatter
  2. Review Article
  3. Research on the Influence of Furnace Structure on Copper Cooling Stave Life
  4. Influence of High Temperature Oxidation on Hydrogen Absorption and Degradation of Zircaloy-2 and Zr 700 Alloys
  5. Correlation between Travel Speed, Microstructure, Mechanical Properties and Wear Characteristics of Ni-Based Hardfaced Deposits over 316LN Austenitic Stainless Steel
  6. Factors Influencing Gas Generation Behaviours of Lump Coal Used in COREX Gasifier
  7. Experiment Research on Pulverized Coal Combustion in the Tuyere of Oxygen Blast Furnace
  8. Phosphate Capacities of CaO–FeO–SiO2–Al2O3/Na2O/TiO2 Slags
  9. Microstructure and Interface Bonding Strength of WC-10Ni/NiCrBSi Composite Coating by Vacuum Brazing
  10. Refill Friction Stir Spot Welding of Dissimilar 6061/7075 Aluminum Alloy
  11. Solvothermal Synthesis and Magnetic Properties of Monodisperse Ni0.5Zn0.5Fe2O4 Hollow Nanospheres
  12. On the Capability of Logarithmic-Power Model for Prediction of Hot Deformation Behavior of Alloy 800H at High Strain Rates
  13. 3D Heat Conductivity Model of Mold Based on Node Temperature Inheritance
  14. 3D Microstructure and Micromechanical Properties of Minerals in Vanadium-Titanium Sinter
  15. Effect of Martensite Structure and Carbide Precipitates on Mechanical Properties of Cr-Mo Alloy Steel with Different Cooling Rate
  16. The Interaction between Erosion Particle and Gas Stream in High Temperature Gas Burner Rig for Thermal Barrier Coatings
  17. Permittivity Study of a CuCl Residue at 13–450 °C and Elucidation of the Microwave Intensification Mechanism for Its Dechlorination
  18. Study on Carbothermal Reduction of Titania in Molten Iron
  19. The Sequence of the Phase Growth during Diffusion in Ti-Based Systems
  20. Growth Kinetics of CoB–Co2B Layers Using the Powder-Pack Boriding Process Assisted by a Direct Current Field
  21. High-Temperature Flow Behaviour and Constitutive Equations for a TC17 Titanium Alloy
  22. Research on Three-Roll Screw Rolling Process for Ti6Al4V Titanium Alloy Bar
  23. Continuous Cooling Transformation of Undeformed and Deformed High Strength Crack-Arrest Steel Plates for Large Container Ships
  24. Formation Mechanism and Influence Factors of the Sticker between Solidified Shell and Mold in Continuous Casting of Steel
  25. Casting Defects in Transition Layer of Cu/Al Composite Castings Prepared Using Pouring Aluminum Method and Their Formation Mechanism
  26. Effect of Current on Segregation and Inclusions Characteristics of Dual Alloy Ingot Processed by Electroslag Remelting
  27. Investigation of Growth Kinetics of Fe2B Layers on AISI 1518 Steel by the Integral Method
  28. Microstructural Evolution and Phase Transformation on the X-Y Surface of Inconel 718 Ni-Based Alloys Fabricated by Selective Laser Melting under Different Heat Treatment
  29. Characterization of Mn-Doped Co3O4 Thin Films Prepared by Sol Gel-Based Dip-Coating Process
  30. Deposition Characteristics of Multitrack Overlayby Plasma Transferred Arc Welding on SS316Lwith Co-Cr Based Alloy – Influence ofProcess Parameters
  31. Elastic Moduli and Elastic Constants of Alloy AuCuSi With FCC Structure Under Pressure
  32. Effect of Cl on Softening and Melting Behaviors of BF Burden
  33. Effect of MgO Injection on Smelting in a Blast Furnace
  34. Structural Characteristics and Hydration Kinetics of Oxidized Steel Slag in a CaO-FeO-SiO2-MgO System
  35. Optimization of Microwave-Assisted Oxidation Roasting of Oxide–Sulphide Zinc Ore with Addition of Manganese Dioxide Using Response Surface Methodology
  36. Hydraulic Study of Bubble Migration in Liquid Titanium Alloy Melt during Vertical Centrifugal Casting Process
  37. Investigation on Double Wire Metal Inert Gas Welding of A7N01-T4 Aluminum Alloy in High-Speed Welding
  38. Oxidation Behaviour of Welded ASTM-SA210 GrA1 Boiler Tube Steels under Cyclic Conditions at 900°C in Air
  39. Study on the Evolution of Damage Degradation at Different Temperatures and Strain Rates for Ti-6Al-4V Alloy
  40. Pack-Boriding of Pure Iron with Powder Mixtures Containing ZrB2
  41. Evolution of Interfacial Features of MnO-SiO2 Type Inclusions/Steel Matrix during Isothermal Heating at Low Temperatures
  42. Effect of MgO/Al2O3 Ratio on Viscosity of Blast Furnace Primary Slag
  43. The Microstructure and Property of the Heat Affected zone in C-Mn Steel Treated by Rare Earth
  44. Microwave-Assisted Molten-Salt Facile Synthesis of Chromium Carbide (Cr3C2) Coatings on the Diamond Particles
  45. Effects of B on the Hot Ductility of Fe-36Ni Invar Alloy
  46. Impurity Distribution after Solidification of Hypereutectic Al-Si Melts and Eutectic Al-Si Melt
  47. Induced Electro-Deposition of High Melting-Point Phases on MgO–C Refractory in CaO–Al2O3–SiO2 – (MgO) Slag at 1773 K
  48. Microstructure and Mechanical Properties of 14Cr-ODS Steels with Zr Addition
  49. A Review of Boron-Rich Silicon Borides Basedon Thermodynamic Stability and Transport Properties of High-Temperature Thermoelectric Materials
  50. Siliceous Manganese Ore from Eastern India:A Potential Resource for Ferrosilicon-Manganese Production
  51. A Strain-Compensated Constitutive Model for Describing the Hot Compressive Deformation Behaviors of an Aged Inconel 718 Superalloy
  52. Surface Alloys of 0.45 C Carbon Steel Produced by High Current Pulsed Electron Beam
  53. Deformation Behavior and Processing Map during Isothermal Hot Compression of 49MnVS3 Non-Quenched and Tempered Steel
  54. A Constitutive Equation for Predicting Elevated Temperature Flow Behavior of BFe10-1-2 Cupronickel Alloy through Double Multiple Nonlinear Regression
  55. Oxidation Behavior of Ferritic Steel T22 Exposed to Supercritical Water
  56. A Multi Scale Strategy for Simulation of Microstructural Evolutions in Friction Stir Welding of Duplex Titanium Alloy
  57. Partition Behavior of Alloying Elements in Nickel-Based Alloys and Their Activity Interaction Parameters and Infinite Dilution Activity Coefficients
  58. Influence of Heating on Tensile Physical-Mechanical Properties of Granite
  59. Comparison of Al-Zn-Mg Alloy P-MIG Welded Joints Filled with Different Wires
  60. Microstructure and Mechanical Properties of Thick Plate Friction Stir Welds for 6082-T6 Aluminum Alloy
  61. Research Article
  62. Kinetics of oxide scale growth on a (Ti, Mo)5Si3 based oxidation resistant Mo-Ti-Si alloy at 900-1300∘C
  63. Calorimetric study on Bi-Cu-Sn alloys
  64. Mineralogical Phase of Slag and Its Effect on Dephosphorization during Converter Steelmaking Using Slag-Remaining Technology
  65. Controllability of joint integrity and mechanical properties of friction stir welded 6061-T6 aluminum and AZ31B magnesium alloys based on stationary shoulder
  66. Cellular Automaton Modeling of Phase Transformation of U-Nb Alloys during Solidification and Consequent Cooling Process
  67. The effect of MgTiO3Adding on Inclusion Characteristics
  68. Cutting performance of a functionally graded cemented carbide tool prepared by microwave heating and nitriding sintering
  69. Creep behaviour and life assessment of a cast nickel – base superalloy MAR – M247
  70. Failure mechanism and acoustic emission signal characteristics of coatings under the condition of impact indentation
  71. Reducing Surface Cracks and Improving Cleanliness of H-Beam Blanks in Continuous Casting — Improving continuous casting of H-beam blanks
  72. Rhodium influence on the microstructure and oxidation behaviour of aluminide coatings deposited on pure nickel and nickel based superalloy
  73. The effect of Nb content on precipitates, microstructure and texture of grain oriented silicon steel
  74. Effect of Arc Power on the Wear and High-temperature Oxidation Resistances of Plasma-Sprayed Fe-based Amorphous Coatings
  75. Short Communication
  76. Novel Combined Feeding Approach to Produce Quality Al6061 Composites for Heat Sinks
  77. Research Article
  78. Micromorphology change and microstructure of Cu-P based amorphous filler during heating process
  79. Controlling residual stress and distortion of friction stir welding joint by external stationary shoulder
  80. Research on the ingot shrinkage in the electroslag remelting withdrawal process for 9Cr3Mo roller
  81. Production of Mo2NiB2 Based Hard Alloys by Self-Propagating High-Temperature Synthesis
  82. The Morphology Analysis of Plasma-Sprayed Cast Iron Splats at Different Substrate Temperatures via Fractal Dimension and Circularity Methods
  83. A Comparative Study on Johnson–Cook, Modified Johnson–Cook, Modified Zerilli–Armstrong and Arrhenius-Type Constitutive Models to Predict Hot Deformation Behavior of TA2
  84. Dynamic absorption efficiency of paracetamol powder in microwave drying
  85. Preparation and Properties of Blast Furnace Slag Glass Ceramics Containing Cr2O3
  86. Influence of unburned pulverized coal on gasification reaction of coke in blast furnace
  87. Effect of PWHT Conditions on Toughness and Creep Rupture Strength in Modified 9Cr-1Mo Steel Welds
  88. Role of B2O3 on structure and shear-thinning property in CaO–SiO2–Na2O-based mold fluxes
  89. Effect of Acid Slag Treatment on the Inclusions in GCr15 Bearing Steel
  90. Recovery of Iron and Zinc from Blast Furnace Dust Using Iron-Bath Reduction
  91. Phase Analysis and Microstructural Investigations of Ce2Zr2O7 for High-Temperature Coatings on Ni-Base Superalloy Substrates
  92. Combustion Characteristics and Kinetics Study of Pulverized Coal and Semi-Coke
  93. Mechanical and Electrochemical Characterization of Supersolidus Sintered Austenitic Stainless Steel (316 L)
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  95. Ladle Nozzle Clogging during casting of Silicon-Steel
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