# Acquisition of Sorption and Drying Data with Embedded Devices: Improving Standard Models for High Oleic Sunflower Seeds by Continuous Measurements in Dynamic Systems

^{*}

## Abstract

**:**

_{w}= 0.10–0.95) and for drying (T = 30–90 °C, humidity of the drying air x = 0.010–0.020 kg·kg

^{−1}) was recorded for freshly harvested material. A generalized single-layer drying model was developed and validated (R

^{2}= 0.99, MAPE = 8.3%). An analytical solution for predicting effective diffusion coefficients was also generated (R

^{2}= 0.976, MAPE of 6.33%). The water vapor pressure deficit-based approach allows for an easy integration of meaningful parameters recorded during drying while maintaining low complexity of the underlying equations in order for embedded microcontrollers with limited processing power to be integrated in current agro-industrial applications.

## 1. Introduction

_{w}holds information on the availability of water for the growth of microorganisms and thus allows inference on threshold levels, above which spoilage is unlikely to occur [5]. It is defined as the partial vapor pressure of water in the measured food, divided by the partial vapor pressure of pure water [6]. This is equal to the equilibrium relative humidity, at which the measured food is in equilibrium with the surrounding atmosphere and does not adsorb nor desorb water. Sorption isotherms describe the relationship between the equilibrium moisture content (MC

_{e}), formed at a given temperature and at the relative humidity, if the food is in equilibrium with the atmospheric surroundings. In general, water activity increases at higher moisture content and, consequently, microorganisms, such as molds, yeasts, and bacteria increasingly grow at a

_{w}> 0.70, while enzymatic activity is also promoted by high values of a

_{w}[5]. The commonly applied threshold value for safe farm level storage of agricultural products is found at water activities between 0.6 ≤ a

_{w}≤ 0.7 [3,4,7].

^{−1}[19,20,21]. Sunflower seeds are comparable to multi-domain composite foods, consisting of a fibrous outer shell, and an oily kernel. Both hulls and kernels show significantly different sorption behavior [2]. In addition, whole seeds and kernels are significantly different in most physical properties, such as volume and equivalent diameter [19,22]. Sunflower kernels show significantly slower moisture diffusivity compared to hulls and, thus, are the limiting factor in drying [3,19].

## 2. Materials and Methods

#### 2.1. Plant Material

^{−1}), 10 samples of 3 g each were used.

#### 2.2. Moisture Content Determination

^{−1}). All analyses were performed in triplicates, which is commonly applied in other studies [18,22].

#### 2.3. Determination of Dynamic Vapor Sorption Isotherms

^{−1}and manually cleaned from impurities. The seeds were ground to a particle size of approximately 5 mm. To obtain hulls, seeds were manually hulled. About 12 g of dried seeds or hulls were used per sorption experiment. The samples were loaded into the sample holder and the adsorption isotherms were measured at 25 °C and 50 °C, which increased the relative humidity gradually from 10% to 85% with increments of 10% and a final step of 5%. Mass, temperature, and humidity data were recorded in 20 min intervals. The equilibrium was considered to have been reached when observing a change in weight of less than 5% of the initial sample weight during 10 consecutive measurements. Three repetitions per temperature and material were performed, which resulted in a total of 160 individually determined equilibrium moisture content data points.

#### 2.4. Sorption Isotherm Models

_{e}(kg∙kg

^{−1}), water activity a

_{w}(p

_{vs}∙p

_{sat}

^{−1}), and a, b, c as model constants. The applied model equations and their ranges of validity are shown in Table 1.

#### 2.5. Thin-Layer Drying Experiments

^{−1}. The initial seed moisture during all drying experiments was 0.317 ± 0.008 kg∙kg

^{−1}. An initial mass of 0.400 ± 0.001 kg was evenly spread on a perforated drying tray, which resulted in a layer depth of 15 mm. The tray was supported on PC6 load cells (Flintec GmbH, Meckesheim, Germany). The weight was measured every 10 min. Meanwhile, a bypass valve was opened to prevent floating of the tray. The seeds were dried until a constant weight was achieved, once the total weight change for three consecutive measurements was below 0.5 g. The drying experiments were repeated at least three times for each drying condition. The moisture content of seeds before and after drying was determined as described above Section 2.2. In total, 63 experiments with 1291 single measurements were conducted.

#### 2.6. Empirical Drying Model

_{t}the moisture content at time t, MC

_{e}the equilibrium moisture content, and MC

_{0}the initial moisture content (kg∙kg

^{−1}). The moisture ratio over time can be well depicted by the semi-empirical page equation (Equation (2)). This approach offers a compromise between inclusion of the physical theory and ease of use, which results in a semi-empirical model [6]. Fickian moisture migration, constant moisture diffusion coefficients isothermal conditions, and negligible shrinkage are the basics of this approach [26]. Two coefficients have to be fitted including k as the rate constant (min

^{−1}) and n as the dimensionless coefficient to improve the fit [19].

^{−1}) (Equation (3)) and water vapor pressure deficit ΔP (Pa) (Equation (4)), both described by an Arrhenius-type equation, were followed [27]. ΔP (Pa) was computed as the vapor pressure deficit between the drying air and saturated air under the same temperature conditions with P

_{sat}(Pa) derived from the Magnus-equation, T (°C), and rh as the relative humidity (%) (Equation (1)).

_{T}

_{1}< k

_{T}

_{2}, n

_{T}

_{1}> n

_{T}

_{2}for T

_{1}< T

_{2}and x

_{1}= x

_{2}, k

_{x}

_{1}> k

_{x}

_{2}, n

_{x}

_{1}< n

_{x}

_{2}for T

_{1}= T

_{2}and x

_{1}< x

_{2}

#### 2.7. Analytical Estimation of Diffusion Coefficients

_{v}is the kernel’s surface specific area in m

^{2}∙m

^{−3}.

_{t}= MC

_{0}for t = 0, MC

_{t}= MC

_{e}for t → ∞

_{s}can be determined with Equation (5). The limits of validity for spherical bodies, where D

_{s}is no longer essentially constant, are found at MR = 0.2 [28]. The same approximation was also adapted by Giner and Mascheroni [31] for wheat as well as by Santalla and Mascheroni [19] for sunflower seeds.

#### 2.8. Statistical Analysis

^{2}and the mean absolute percentage error MAPE with MC

_{e,exp}and MR

_{exp}as the observed and MC

_{e,pre}and MR

_{pre}as the predicted equilibrium moisture content and moisture ratio were taken as the main criteria for the goodness of fit.

## 3. Results and Discussion

#### 3.1. Analysis of Moisture Sorption Models

_{w}= 1. In general, at constant water activity, the equilibrium moisture content decreased with increasing temperature. Remarkably, for hulls, this trend was only observed for a

_{w}≤ 0.82 and for seeds for a

_{w}≤ 0.72. Above these threshold values, the equilibrium moisture content increased with increasing temperature, which is a phenomenon that usually can be observed in high sugar foods [34,35].

_{w}> 0.82 for hulls and a

_{w}> 0.72 for seeds were excluded from the non-linear fitting procedure. A random 60% of the remaining dataset was used for fitting while the entire remaining dataset was used for model performance evaluation in terms of R

^{2}and MAPE value. The fitted curves are shown as solid lines and continued as dashed lines when the above-mentioned limits of a

_{w}are exceeded, which shows what the corresponding models would predict. Figure 2b provides the predicted versus observed plots for employed sorption equations.

^{2}> 0.99 and MAPE < 10%. However, the residual plots (Figure 2c) reveal a patterned shape for all but the Mod. Henderson equation. For hulls, only the modified Oswin and modified G.A.B. equation showed R

^{2}> 0.99. However, only the modified G.A.B. equation showed random distribution of residuals.

_{w}value. Sunflower seeds are very much comparable to complex multi-domain foods, with the hulls being a fibrous matrix, allowing two to four times faster diffusivity of moisture than the kernel [19]. In addition, it is clear that the oil content in kernels highly affects the equilibrium moisture content. Similar observations have been reported by other studies [2,40]. At a constant temperature, hulls usually reach a higher MC

_{e}than seeds, which again show a higher MC

_{e}than kernels [2,18,19]. The Mod. Henderson was the only model showing both satisfying fit and random residuals for seeds. Opposed to this, hulls alone were best modeled by the Mod. G.A.B. equation. Given the fact that safe moisture levels for oilseeds are found in the region of a

_{w}= 0.64–0.70, the limits of model validity and the observed anomaly at high values of a

_{w}were considered non-critical for the development of a drying model [1,3]. Based on these insights, the fitted Mod. Henderson equation and the coefficients found for seeds were integrated in Equation (2) in order to describe the drying process.

#### 3.2. Modelling of Thin-Layer Drying Behavior

^{−1}were described well by the Page equation with high R

^{2}(>0.99) and low MAPE (<5%) values. The equilibrium moisture content MC

_{e}(kg∙kg

^{−1}) for seeds was calculated with the Mod. Henderson equation with a = 0.102, b = 207.939, and c = 1.145 (Table 2). The kinetic parameter k increased with increasing T at constant x, while n decreased. With increasing absolute humidity at constant T, k decreased and n increased. Equation (10) and Equation (10a) best described model parameters k and n as a function of T and x. The resulting course is shown in Figure 3a. Inclusion in Equation (2a) resulted in a temperature and absolute humidity-based generalized model describing the experimental data with an R

^{2}value of 0.982 and MAPE of 9.4%.

^{2}value of 0.988 and MAPE of 8.3%. This is slightly better than the model based on T and x.

_{S}with increasing temperature T. With increasing absolute humidity x, D

_{S}showed a decreasing trend for temperatures up to 70 °C, from where no obvious trend was derivable. For T below 50 °C, the threshold of MR < 0.2 usually was not undershot. The shape dependent factor f″(0) found to be 0.428 with a standard error of 1.3%. By inclusion in Equation (6), the diffusion coefficients for short times (0.2 < MR < 1) can be calculated (Table 3).

_{S}= f(T,x), which is well described by Equation (12).

^{2}of 0.966 and MAPE = 7.37%. The description of D

_{S}= f(ΔP) was described well with a similar function:

^{2}of 0.976 and MAPE = 6.33%. This is slightly better than the approach based on temperature and absolute humidity. The fit to the experimental data of both Equations (12) and (13) is given in Figure 3c,d.

## 4. Conclusions

_{w}, the equilibrium moisture content increased with increasing temperature. An anomaly, which is usually found in high sugar foods, was not yet reported for sunflower seeds. It is remarkable that most of the commonly applied equations to describe sorption isotherms showed patterned residuals, which restricted their applicability and validity. This study found the Page equation to satisfactorily describe the drying process of high oleic sunflower seeds for a wide range of drying air temperatures and humidity. It also proposes the application of water vapor pressure deficit ΔP to calculate the parameters of the Page equation including both the effect of temperature and the humidity of the drying air. This approach was found to be superior to a prediction based on temperature. Values of diffusivity ascertained with the Becker equation and a correction of the shape dependent factor are comparable to those reported in other studies, which corroborates the applicability and accuracy in thin layer drying of high oleic sunflower seeds.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

a_{w} | water activity |

MC | moisture content |

MC_{e} | equilibrium moisture content |

MC_{t} | moisture content at time t |

DVS | dynamic vapour sorption apparatus |

kg | kilogram |

g | gram |

mg | milligram |

m | meter |

mm | millimeter |

rh | relative humidity, % |

min | minutes |

P_{vs} | water vapor partial pressure, Pa |

P_{sat} | saturation vapor pressure, Pa |

T | temperature, °C |

a, b, c, d, e, f, g | model constants |

G.A.B. | Guggenheim, Anderson, DeBoer |

x | absolute humidity, kg water per kg of dry air |

s | second |

MR | moisture ratio |

t | time |

k | rate constant, min^{−1} |

n | dimensionless coefficient of page equation |

P | pressure, Pa |

D | moisture diffusivity, m^{2}∙s^{−1} |

a_{v} | kernel’s surface specific area in m^{2}∙m^{−3} |

ANOVA | analysis of variance |

MAPE | mean absolute perecentage error |

R^{2} | coefficient of determination |

p | probability level at which significance is assumed |

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**Figure 2.**(

**a**) Sorption isotherm for high oleic sunflower seeds (circles) and hulls (triangles) at 25 °C (hollow) and 50 °C (solid) predicted with different models as specified in the plot. Slashed lines are an extrapolation beyond the dataset used for fitting. (

**b**) observed equilibrium moisture content vs. predicted equilibrium moisture content and (

**c**) standardized residuals vs. predicted equilibrium moisture content.

**Figure 3.**Parameters k, n, and the fitted models from (

**a**) Equations (10) and (10a) for k, n = f(T,x) in °C and kg∙kg

^{−1}and (

**b**) modeled with Equation (11) and (11a) for k, n = f(ΔP) in Pa. (

**c**) D

_{S}= f(T,x) for temperature from 30 °C to 90 °C and absolute humidity of the drying air of 0.010, 0.015, and 0.020 kg∙kg

^{−1}modeled with Equation (12) and (

**d**) D

_{S}= f(ΔP) for the same temperature and humidity range, modeled with Equation (13).

**Figure 4.**Model performance for MR expressed as a function of ΔP calculated with Equation (2b), (

**a**) predicted MR versus observed MR values are concentrated closely to the perfect fit line of x = y, and (

**b**) the residuals are equally distributed and do not show any trend.

**Table 1.**Models for sorption isotherms. MCe = equilibrium moisture content. T = temperature in °C. a

_{w}= water activity. a, b, c = model constants [7].

Model | Original Plant Material | Validity (a_{W}) |
---|---|---|

Modified Chung-Pfost | ||

$M{C}_{e}=\frac{-1}{a}\mathrm{ln}\left(-\frac{\left(T+b\right)}{c}\mathrm{ln}\left({a}_{W}\right)\right)$ | Maize and maize components | 0.1–0.9 |

Modified Oswin | ||

$M{C}_{e}=\left(a+b\times T\right){\left(\frac{{a}_{W}}{1-{a}_{W}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$c$}\right.}$ | Various | 0.3–0.5 |

Modified Halsey | ||

$M{C}_{e}={\left(\frac{-exp\left(a+b\times T\right)}{\mathrm{ln}\left({a}_{W}\right)}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$c$}\right.}$ | Maize, wheat flour, laurel, nutmeg | 0.1–0.8 |

Modified Henderson | ||

$M{C}_{e}={\left(-\frac{\mathrm{ln}\left(1-{a}_{W}\right)}{a\left(T+b\right)}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$c$}\right.}$ | Maize | - |

Modified G.A.B. | ||

$M{C}_{e}=\frac{ab\left(\frac{c}{T}\right){a}_{W}}{\left(a-b{a}_{W}\right)\left(1-b{a}_{W}+\left(\frac{c}{T}\right)b{a}_{W}\right)}$ | Various | <0.94 |

**Table 2.**Coefficients a, b, and c, coefficient of determination R

^{2}and MAPE for the (i) Mod. Chung-Pfost, (ii) Mod. Oswin, (iii) Mod. Halsey, (iv) Mod. Henderson, and (v) Mod. G.A.B. equation fitted for high oleic sunflower seeds in the range of 10–70% equilibrium relative humidity at 31 degrees of freedom and hulls in the range of 10–80% equilibrium relative humidity and 34 degrees of freedom.

Equation | a | b | c | R^{2} | MAPE, % | ||||
---|---|---|---|---|---|---|---|---|---|

(i) Mod. Chung-Pfost | Seeds | 28.181 | *** | 208.987 | *** | 611.811 | *** | 0.988 | 7.900 |

(ii) Mod. Oswin | 0.048 | *** | −1.58 · 10^{−4} | *** | 1.607 | *** | 0.992 | 8.131 | |

(iii) Mod. Halsey | −3.895 | *** | −4.60 · 10^{−3} | *** | 1.159 | *** | 0.978 | 13.884 | |

(iv) Mod. Henderson | 0.102 | *** | 207.939 | *** | 1.145 | *** | 0.995 | 5.408 | |

(v) Mod. G.A.B. | 2.88 · 10^{−2} | *** | 0.919 | *** | 167.831 | *** | 0.994 | 5.923 | |

(i) Mod. Chung-Pfost | Hulls | 17.761 | *** | 47.204 | *** | 240.673 | *** | 0.985 | 9.173 |

(ii) Mod. Oswin | 9.94 · 10^{−2} | *** | −0.001 | *** | 1.776 | *** | 0.992 | 6.618 | |

(iii) Mod. Halsey | −3.255 | *** | −9.87 · 10^{−3} | *** | 1.245 | *** | 0.982 | 9.964 | |

(iv) Mod. Henderson | 0.208 | *** | 54.690 | *** | 1.299 | *** | 0.991 | 6.112 | |

(v) Mod. G.A.B. | 0.070 | *** | 0.775 | *** | 122.616 | *** | 0.997 | 3.207 |

**Table 3.**Moisture diffusion coefficients D for short times (MR ≥ 0.2), calculated with Equation (5) for different absolute humidity x and temperature T of the drying air, coefficient of determination R

^{2}and MAPE.

x | T, °C | D (m^{2}∙s^{−1})∙10^{−10} | R^{2} | MAPE, % | |
---|---|---|---|---|---|

0.010 kg·kg^{−1} | 30 | 0.643 | *** | 0.979 | 4.088 |

40 | 1.317 | *** | 0.985 | 6.935 | |

50 | 2.620 | *** | 0.991 | 6.217 | |

60 | 3.467 | *** | 0.970 | 10.903 | |

70 | 6.277 | *** | 0.989 | 7.547 | |

80 | 10.190 | *** | 0.996 | 5.059 | |

90 | 14.800 | *** | 0.995 | 7.399 | |

0.015 kg·kg^{−1} | 30 | 0.593 | *** | 0.984 | 4.303 |

40 | 1.231 | *** | 0.987 | 5.591 | |

50 | 2.258 | *** | 0.974 | 11.780 | |

60 | 3.222 | *** | 0.979 | 11.238 | |

70 | 4.627 | *** | 0.969 | 11.187 | |

80 | 7.796 | *** | 0.990 | 7.829 | |

90 | 14.310 | ** | 0.997 | 5.611 | |

0.020 kg·kg^{−1} | 30 | 0.342 | *** | 0.979 | 3.556 |

40 | 0.978 | *** | 0.980 | 5.790 | |

50 | 1.529 | *** | 0.954 | 10.944 | |

60 | 2.634 | *** | 0.988 | 5.715 | |

70 | 5.696 | *** | 0.982 | 9.844 | |

80 | 8.559 | *** | 0.993 | 5.203 | |

90 | 14.490 | ** | 0.999 | 2.152 |

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**MDPI and ACS Style**

Munder, S.; Argyropoulos, D.; Müller, J.
Acquisition of Sorption and Drying Data with Embedded Devices: Improving Standard Models for High Oleic Sunflower Seeds by Continuous Measurements in Dynamic Systems. *Agriculture* **2019**, *9*, 1.
https://doi.org/10.3390/agriculture9010001

**AMA Style**

Munder S, Argyropoulos D, Müller J.
Acquisition of Sorption and Drying Data with Embedded Devices: Improving Standard Models for High Oleic Sunflower Seeds by Continuous Measurements in Dynamic Systems. *Agriculture*. 2019; 9(1):1.
https://doi.org/10.3390/agriculture9010001

**Chicago/Turabian Style**

Munder, Simon, Dimitrios Argyropoulos, and Joachim Müller.
2019. "Acquisition of Sorption and Drying Data with Embedded Devices: Improving Standard Models for High Oleic Sunflower Seeds by Continuous Measurements in Dynamic Systems" *Agriculture* 9, no. 1: 1.
https://doi.org/10.3390/agriculture9010001