Dielectric Properties of Beans at Different Temperatures and Moisture Content in the Microwave Range

Figures & data

FIGURE 1 The three varieties of Mexican beans (from left to right): “Flor de mayo,” “Bayo,” and “Negro.”

FIGURE 2 A: The designed broad band monopole antenna and B: its reflection coefficient.

FIGURE 3 Scheme of the dielectric properties measurement system.

TABLE 1 Bulk density of three varieties of beans at different moisture contents

Variety	Moisture content (%w.b.)	Density (kg/m^3)
“Flor de mayo”	8.8 ± 0.1^d	739.5 ± 3.4^b
	10.1 ± 0.3^c	753.0 ± 0.9^a
“Bayo”	10.3 ± 0.1^c	724.9 ± 5.3^c
	11.8 ± 0.1^b	705.2 ± 0.5^d
“Negro”	9.2 ± 0.1^cd	757.6 ± 1.6^a
	12.3 ± 0.8^a	730.6 ± 8.2^bc

Means with the same letter are not significantly different (p > 0.05) respect to the column.

FIGURE 4 Frequency-dependence of dielectric constant (ε’) for three bean varieties at different temperatures: A: “Flor de mayo” (8.8% of moisture content); B: “Bayo” (10.3% of moisture content); and C: “Negro” (9.2% of moisture content).

TABLE 2 Loss factor and electrical conductivity of Mexican beans for three varieties with different moisture contents (percentage in wet basis) at different temperatures in the allocated frequencies of 915 and 2450 MHz

	Loss factor (ε”)				Electrical conductivity (σ, S/m)
Variety/Temperature (°C)	915 MHz	2450 MHz	915 MHz	2450 MHz	915 MHz	2450 MHz	915 MHz	2450 MHz
“Flor de mayo”	MC = 8.8%		MC = 10.1%		MC = 8.8%		MC = 10.1%
20	0.86 ± 0.006^d	0.70 ± 0.003^c	0.98 ± 0.002^d	0.97 ± 0.006^a	0.044 ± 0.0000^d	0.095 ± 0.0000^d	0.049 ± 0.0001^d	0.132 ± 0.0008^a
30	0.94 ± 0.002^c	0.69 ± 0.001^c	0.98 ± 0.001^d	0.72 ± 0.002^b	0.047 ± 0.0001^c	0.094 ± 0.0000^d	0.049 ± 0.0000^d	0.098 ± 0.0003^b
40	0.99 ± 0.001^b	0.85 ± 0.004^b	1.08 ± 0.001^c	0.75 ± 0.012^b	0.050 ± 0.0000^b	0.116 ± 0.0000^c	0.055 ± 0.0001^c	0.102 ± 0.0016^b
50	0.98 ± 0.001^b	1.05 ± 0.003^a	1.27 ± 0.009^b	0.79 ± 0.120^b	0.050 ± 0.0000^b	0.161 ± 0.0000^a	0.065 ± 0.0004^b	0.108 ± 0.0164^b
60	1.18 ± 0.013^a	1.05 ± 0.009^a	2.56 ± 0.004^a	0.78 ± 0.006^b	0.053 ± 0.0001^a	0.143 ± 0.0000^b	0.130 ± 0.0002^a	0.106 ± 0.0008^b
“Bayo”	MC = 10.3%		MC = 11.8%		MC = 10.3%		MC = 11.8%
20	0.96 ± 0.002^b	0.77 ± 0.004^d	0.98 ± 0.001^e	0.62 ± 0.002^c	0.048 ± 0.0001^c	0.106 ± 0.0006^c	0.050 ± 0.0000^e	0.085 ± 0.0003^c
30	0.97 ± 0.001^b	0.83 ± 0.007^c	1.05 ± 0.000^d	0.77 ± 0.126^bc	0.049 ± 0.0000^c	0.113 ± 0.0009^c	0.053 ± 0.0000^d	0.106 ± 0.0172^b
40	1.06 ± 0.003^a	0.90 ± 0.020^b	1.10 ± 0.001^c	1.35 ± 0.030^a	0054 ± 0.0002^b	0.123 ± 0.0027^b	0.055 ± 0.0001^c	0.184 ± 0.0041^a
50	1.11 ± 0.002^a	1.18 ± 0.040^a	1.20 ± 0.003^b	1.38 ± 0.042^a	0.056 ± 0.0001^a	0.161 ± 0.0054^a	0.061 ± 0.0001^b	0.188 ± 0.0058^a
60	1.07 ± 0.021^a	1.15 ± 0.027^a	2.97 ± 0.002^a	0.74 ± 0.003^b	0.055 ± 0.0010^b	0.157 ± 0.0037^a	0.151 ± 0.0001^a	0.100 ± 0.0004^bc
“Negro”	MC = 9.2%		MC = 12.3%		MC = 9.2%		MC = 12.3%
20	0.88 ± 0.001^d	0.75 ± 0.005^d	1.13 ± 0.003^c	0.76 ± 0.003^c	0.044 ± 0.0010^c	0.103 ± 0.0007^c	0.057 ± 0.0001^b	0.104 ± 0.0004^cd
30	0.90 ± 0.000^c	0.84 ± 0.018^c	1.11 ± 0.001^d	0.90 ± 0.006^a	0.046 ± 0.0001^c	0.114 ± 0.0025^b	0.056 ± 0.0001^b	0.135 ± 0.0009^a
40	0.95 ± 0.001^b	0.86 ± 0.008^c	1.18 ± 0.002^d	0.72 ± 0.002^d	0.048 ± 0.0010^b	0.117 ± 0.0010^b	0.060 ± 0.0001^a	0.091 ± 0.0170^d
50	0.95 ± 0.001^b	1.01 ± 0.013^a	1.22 ± 0.001^a	0.87 ± 0.002^b	0.048 ± 0.0001^b	0.138 ± 0.0018^a	0.062 ± 0.0001^a	0.118 ± 0.0004^bc
60	2.31 ± 0.003^1	0.95 ± 0.003^b	1.22 ± 0.002^a	0.90 ± 0.008^a	0.117 ± 0.0002^a	0.102 ± 0.0005^c	0.062 ± 0.0001^a	0.123 ± 0.0011^ab

Means with the same letter are not significantly different (p > 0.05) respect to temperature for fixed frequency and moisture content.

FIGURE 5 Temperature-dependence of dielectric constant (ε’) for three bean varieties at different moisture contents: A: “Flor de mayo;” B: “Bayo;” and C: “Negro.”

FIGURE 6 Temperature-dependence of loss factor (ε”) for three bean varieties at different moisture contents: A: “Flor de mayo;” B: “Bayo;” and C: “Negro.”

FIGURE 7 The Argand diagram for dielectric properties of three varieties of beans at the allocated frequencies for microwaves.

TABLE 3 Average microwave penetration depth (cm) in beans at allocated frequencies, 915 and 2450 MHz, at different temperatures and moisture contents (percentage in wet basis)

Variety/Frequency	Penetration depth (cm)
	20ºC	30ºC	40ºC	50ºC	60ºC	20ºC	30ºC	40ºC	50ºC	60ºC
“Flor de mayo”	MC = 8.8%					MC = 10.1%
915 MHz	12.73	12.08	11.80	12.12	11.43	11.76	12.35	11.37	9.82	9.99
2450 MHz	5.55	5.68	4.62	3.46	3.85	4.11	5.24	5.51	5.80	5.46
“Bayo”	MC = 10.3%					MC = 11.8%
915 MHz	11.84	11.92	11.28	11.07	11.50	11.46	11.12	11.04	10.08	10.05
2450 MHz	4.77	4.64	4.37	3.50	3.54	6.21	5.52	3.09	3.01	4.31
“Negro”	MC = 9.2%					MC = 12.3%
915 MHz	12.61	12.25	12.39	12.62	12.61	10.24	10.72	10.34	10.12	10.22
2450 MHz	4.87	4.47	4.36	3.93	5.34	5.06	4.09	5.70	4.71	4.58