## 3.1 Physical properties

The typical optical image of Cassia tora seeds is given in Fig. 1a. It can be seen that it demonstrated a cuboid-like shape with oblique flanks. Length, thickness and width of the seeds were denoted as insert. Figure 1b shows that the pre-treated Cassia tora seeds with their initial moisture content have an average dimension of 4.44 mm × 2.42 mm × 2.31 mm (length× thickness × width) obtained from about 100 Cassia tora seeds.

The dimensions (length, thickness and width) of Cassia tora seeds determined with various moisture contents were exhibited, as shown in Fig. 2a. It can be seen that the dimensions of the Cassia tora seeds show a linear increase trend with the increased moisture contents. When moisture contents increase from 7–19% (w.b.), the length (L) increased from 4.52 to 5.87 mm, the thickness (T) from 2.51 to 3.51 mm and the width (W) from 2.36 to 3.02 mm, respectively. It can be linearly fitted with a regression equation of \(L{\text{=}}0.1093M{\text{+}}3.9007\) with R2 = 0.9540, \(T{\text{=}}0.0583M+2.0497\)with R2 = 0.9689, and \(W{\text{=}}0.0553M+1.9367\) with R2 = 0.9851, respectively. Similar trends have been found for maize kernels [17], millet [18], lespedeza seeds [19] and barley kernels [20]. This phenomenon is due to water imbibition of plant seeds [21].

As depicted in Fig. 2b, the bulk density and true density of Cassia tora seeds decreased from 775.83 to 654.17 kg/m3 and from 1295.21 to 1154.72 kg/m3, respectively, when moisture content varied from 7–19% (w.b.). It can also be concluded that the bulk density remains lower than the true density at identical moisture content. Figure 2b displays linear relationships between density and moisture content, thus linear regression equations of \({\rho _{\text{b}}}{\text{=11}}{\text{.801}}x{\text{+1369}}{\text{.9}}\) with R2 = 0.9621 and \({\rho _{\text{t}}}{\text{=}}10.301M{\text{+839}}{\text{.86}}\) with R2 = 0.9537 were reached for bulk density and true density, correspondingly.

Figure 2c. shows that porosity increased from 40.10–43.35% when the moisture content varied from 7–19% (w.b.). Furthermore, they were observed to have a linearly relationship with a regression equation as \(\varepsilon {\text{=}}0.2806M{\text{+38}}{\text{.37}}\) (R2 = 0.9420).

The 1000 seeds mass of Cassia tora seeds at different moisture contents is given in Fig. 2d. Mass of 1000 seeds of Cassia tora varies with moisture content and they show a positive linear relationship. The linear dependence of mass of 1000 seeds with moisture content could be represented by \({W_{1000}}{\text{=}}0.4413M{\text{+21}}{\text{.247}}\) with R2 = 0.9902.

The laboratorial angle of repose values raised from 18.6 ° to 26.8 ° when moisture content varied from 7–19% (Fig. 2e). The mathematical model for angle of repose and moisture content can be described by the formula depicted as: \(\theta {\text{=}}0.67M{\text{+13}}{\text{.49}}\) with R2 = 0.9417. This finding agrees with the reports for rapeseed [22], roasted bengal gram meal [23] and soybean grains [24]. This may be due to the fact that adhesion of seed surface increased with increasing moisture content, hence it is more difficult to slip and roll. Therefore, angle of repose increased when moisture content increased within the studied range.

The coefficient of friction (µ) against four kinds of surfaces (rubber, galvanized iron sheet, glass and plywood) were shown in Fig. 2f. Analysis shows that the static coefficient of friction increase linearly with the increased moisture content and their relationship can be fitted as follows:

\({\mu _{{\text{ru}}}}{\text{=}}0.0059M{\text{+0}}{\text{.3153}}\) (*R*2 = 0.9768) (Fit. 1)

\({\mu _{{\text{ga}}}}{\text{=}}0.003M{\text{+0}}{\text{.3256}}\) (*R*2 = 0.9138) (Fit. 2)

\({\mu _{{\text{pl}}}}{\text{=}}0.0046M{\text{+0}}{\text{.2702}}\) (*R*2 = 0.9772) (Fit. 3)

\({\mu _{{\text{gl}}}}{\text{=}}0.0029M{\text{+0}}{\text{.2659}}\) (*R*2 = 0.9764) (Fit. 4)

It is known that moisture on surface layer of biological material bound them together due to surface tension effect, and the adhesion force shows increasing tendency with the increased moisture content. Hence, it becomes relatively difficult for the seeds to roll and slide when they possess higher moisture content, resulting in the increase of static friction coefficient. These findings agreed with the report on rapeseed [22] and tamarind seeds [25] .

## 3.2 Mechanical properties

The hardness, fragmentation energy and failure deformations along thickness, width and length direction, namely y, z and x axis, respectively, were investigated at different moisture contents.

The experimental values of the hardness at different loading directions were shown in Fig. 3. The highest hardness was observed along the width direction, followed by thickness direction and length direction. The hardness also varies with the wetness of the seed. The hardness decreases with increased moisture content along three directions. The mathematical model between the hardness and moisture content followed a second-order polynomial pattern, which can be written as follows:

X direction:\(H{\text{a=}}~0.0802{M^2} - 3.6148M+45.025\) (*R*2 = 0.9931) (Fit. 5)

Y direction: *H*a= 0.3929 *M*2-14.6646 *M* + 142.822 (R2 = 0.9795) (Fit. 6)

Z direction: *H*a= 0.4087 *M*2-15.8152 *M* + 158.5286 (R2 = 0.9477) (Fit. 7)

These findings and conclusions are consistent with similar studies results obtained by wheat grain [12] and olive Fruit [16].

Figure 4 shows the fragmentation energy along different directions of Cassia tora seeds affected by moisture content. The highest fragmentation energy was observed along width direction, followed by thickness direction and length direction. The experimental values of the fragmentation energy tend to decrease when moisture content increased from 7–19% along three directions, and there existed a quadratic curve correlation for fragmentation energy and moisture content of Cassia tora seeds. For the fragmentation energy, when the moisture content varies from 7–19% (w.b.), the corresponding regression equations were established as follows:

X direction:\(Fr{\text{=}}~0.0209{M^2} - 0.8736M+12.021\) (*R*2 = 0.9918) (Fit. 8)

Y direction: *Fr* = 0.1434*M*2- 4.9925*M* + 46.971 (R2 = 0.9558) (Fit. 9)

Z direction: *Fr* = 0.1697 *M*2- 0.58027*M* + 53.406 (R2 = 0.9566) (Fit. 10)

Besides, the hardness and fragmentation energy were highly correlated. Greater energy is needed to break the Cassia tora seeds of higher hardness [16, 26, 27].

The failure deformations with different moisture contents along different loading directions were presented in Fig. 5. The maximum failure deformations were observed along length direction, followed by width direction and thickness direction. The failure deformations increased quadratic linear when moisture contents increased. The corresponding regression equations were established for failure deformations of Cassia tora seeds with moisture content as follows:

X direction: \({F_{\text{a}}}{\text{=}}~0.0008{M^2}{\text{+}}0.0176M+0.6603\) (R2 = 0.9971) (Fit. 11)

Y direction: *F*a= 0.00146*M*2 + 0.00641*M* + 0.71026 (R2 = 0.9739) (Fit. 12)

Z direction: *F*a= 0.000142*M*2 + 0.05468*M* + 0.45554 (R2 = 0.8697) (Fit. 13)

The results can be attributed to the internal structure bonding and hardness of the seeds. It is known that the tighter the internal structure bonding and the higher the hardness, the stronger the ability to endure load and resist cracking. When the moisture content increases, the internal structure of the seeds softens, so the ability to endure load and resist cracking load decreases, thus the hardness and fragmentation energy of Cassia tora seeds tends to decrease. As aforementioned, the dimensions of the seeds tended to increase with the increased moisture content, thus the failure deformations are proportional to the moisture content of Cassia tora seeds.

## 3.3 Thermal properties

Thermal properties (specifically, specific heat, thermal conductivity and thermal diffusivity) are widely used in the engineering development and corresponding calculations related to thermal treatment of the seeds. The thermal-related properties were measured using the grinded seeds, which were notably influenced by particle size of the seeds meal [23]. Figure 6 shows the distribution of particle size of Cassia tora seeds meal was determined by the fourteen-layer sieve method [28]. The average particle size of the seeds meal used for the thermal measurement is thus determined to be 556.86 µm.

Since water has relatively specific heat and thermal conductivity, temperature and moisture content exert a great influence on the thermal properties of seeds. Therefore, a slight increment of moisture content results in significant increment in specific heat value (Fig. 7). When the moisture content varied from 7–19%, the specific heat enlarged from 1.714 to 3.764 J·g− 1·K− 1, 2.568 to 4.354 J·g− 1·K− 1, 2.935 to 4.769 J·g− 1·K− 1, 3.282 to 5.122 J·g− 1·K− 1, 3.892 to 5.777 J·g− 1·K− 1 and 4.197 to 6.141 J·g− 1·K− 1 at 25°C, 45°C, 65°C, 85°C, 105°C and 125°C. Similar reports were also found in gelatin-free marshmallow [29], green bean seed [30] and lespedeza seeds [19].

\({C_P}{\text{=}}~0.{\text{98+}}6.{\text{62}} \times {\text{1}}{{\text{0}}^{{\text{-2}}}}M+{\text{2}}{\text{.32}} \times {\text{1}}{{\text{0}}^{{\text{-2}}}}T\) (*R*2 = 0.9807) (Fit. 14)

The thermal conductivity of Cassia tora seeds meal, as shown in Fig. 8, was discovered to be 0.068–0.098 W·m− 1·K− 1, 0.078–0.112 W·m− 1·K− 1, 0.089–0.125 W·m− 1·K− 1, 0.098–0.136 W·m− 1·K− 1, 0.108–0.148 W·m− 1·K− 1, 0.119–0.159 W·m− 1·K− 1, respectively, at 25°C, 45°C, 65°C, 85°C, 105°C and 125°C in moisture ranges of 7%- 19% (Fig. 8). Thermal conductivity enlarged with increased moisture content and temperature. Similar phenomena and laws of thermal conductivity have also been discovered related to pomegranate (Punica granatum) fruit [31], sesame seed gum [32], soybean grains [24], and watermelon seeds [33]. Thermal conductivity can quadratic functioned with moisture content (M) and temperature (T) using multiple regression analysis:

\(k{\text{=}}~0.{\text{046+}}0.01M+6.61 \times {\text{1}}{{\text{0}}^{{\text{-5}}}}{M^2} - {\text{2}}{\text{.14}} \times {\text{1}}{{\text{0}}^{{\text{-7}}}}{T^2}+1 \times {\text{1}}{{\text{0}}^{{\text{-5}}}}MC\) (*R*2 = 0.984) (Fit. 15)

The curves and change laws between moisture contents and thermal diffusivity of seed meal at various temperatures are shown in Fig. 9. The results show that the thermal diffusivity increased as moisture contents increased. The thermal diffusivity was found to decrease from 5.21×10− 8 to 4.53×10− 8 m2/s, from 5.75×10− 8 to 4.91×10− 8 m2/s, from 6.11×10− 8 to 5.17×10− 8 m2/s, from 6.52×10− 8 to 5.36×10− 8 m2/s, from 7.17×10− 8 to 5.77×10− 8 m2/s, from 7.36×10− 8 to 5.84×10− 8 m2/s, respectively, at 25°C, 45°C, 65°C, 85°C, 105°C and 125°C in moisture ranges of 7%- 19%. An increasing trend in thermal conductivity of the grinded Cassia tora seeds was also observed with the increase in temperature. Regression analysis in the fitting equation showed that there is also a multiple relationship for thermal diffusivity (α), moisture content (M) together with temperature (T) as follows:

\(\alpha \times {10^{{\text{-}}7}}{\text{=}}0.5 - 0.5 \times {\text{1}}{{\text{0}}^{{\text{-2}}}}M{\text{+}}4.49 \times {\text{1}}{{\text{0}}^{{\text{-5}}}}{M^2}{\text{+}}0.03 \times T - {\text{4}}{\text{.20}} \times {\text{1}}{{\text{0}}^{{\text{-7}}}}{T^2} - 7.34 \times {\text{1}}{{\text{0}}^{{\text{-5}}}}MC\) (*R*2 = 0.986) (Fit.16)

The facts that thermal diffusivity of Cassia tora seed meal showed a decreasing trend with increased moisture content and increase with increased temperature, are identical with some previous findings, such as for watermelon seeds [34], jack bean seeds [35], and green bean seed [30].