# Effect of Foaming Conditions on Foam Properties and Drying Behavior of Powder from Magenta (Peristropheroxburghiana) Leaves Extracts

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}), chi-square (χ

^{2}), and root mean square error (RMSE). Among the five mathematical models tested with experimental data, the Page model could be applied to describe the foam-mat drying process of magenta leaves extract. The highest value of R

^{2}(99.54%), the lowest value of χ

^{2}(0.0007), and RMSE (0.0253) were observed for a air drying temperature of 60 °C. The effect of temperature on diffusion is described by the Arrhenius equation with an activation energy of 100.21 kJ/mol. Effective moisture diffusion values ranged from 2.27 × 10

^{−10}to 6.71 × 10

^{−10}m

^{2}/s as the temperature increased. The effect of drying conditions on anthocyanin changes of magenta leaves powder was compared. The results showed that the highest quality of the sample was observed when the sample was dried at 60 °C.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Preparation of Magenta Extract

#### 2.2. Investigate the Effects of Egg Albumin, Xanthan Gum and Whipping Time on Foam Properties

#### 2.2.1. Foam Expansion Volume Determination

_{1}is initial volume (mL) and V

_{2}is final volume (mL).

#### 2.2.2. Foam Density Determination

#### 2.2.3. Anthocyanin Content Determination

#### 2.2.4. Hygroscopicity Determination

_{i}(% wb) is the free water content of the powder before exposure to the humid air environment.

#### 2.2.5. Statistical Analysis

_{o}Y is the intercept (constant), b

_{n}is the regression coefficient for the linear effect of X

_{n}on Y, b

_{nn}and b

_{nm}are the regression coefficients for the interaction and quadratic effect on Y and X

_{n}, and X

_{m}are the independent values

_{1}, X

_{2}, and X

_{3}, respectively. Based on the R

^{2}value obtained through multiple regression, the reference equation was chosen to match the data. When compared to the R

^{2}value for the other reference interaction, the selected reference equation should have a higher R

^{2}value.

#### 2.3. Drying Procedure

#### 2.3.1. Calculation of Drying Rate

_{t}

_{+dt}and M

_{t}are moisture contents (g water/g dry matter) at time (t + dt) and time t, respectively.

#### 2.3.2. Mathematical Modeling

_{t}or M

_{o}, and the error involved in the simplification is negligible. Therefore, Equation (6) was used to represent the simplest form of MR [22].

_{t}and M

_{o}are the instantaneous and initial moisture content (kg water/kg dry matter) of the product.

^{2}), chi-square (χ

^{2}), and root mean square error (RMSR) were used in the regression analysis to determine the best model for drying the magenta leaves extract at various temperatures. The best fit with experimental data and mathematical model is shown by the highest R

^{2}and the lowest χ

^{2}and RMSE [20,21].

#### 2.3.3. Calculation of the Effective Moisture Diffusivity and Activation Energy

_{eff}is the effective diffusivity (m

^{2}/s), t is drying time (s), and L is the half thickness of the slab (m).

_{a}), which expresses the dependency of the effective diffusion coefficient on the air drying temperature [27].

_{o}is the diffusion coefficient corresponding to infinite temperature (m

^{2}/s), E

_{a}is the activation energy (kJ/mol), R is the universal gas constant (8.314 J/mol.K), and T is the absolute drying temperature (K).

#### 2.3.4. Statistical Analysis

## 3. Results and Discussion

#### 3.1. Effect of Egg Albumin, Xanthan Gum, and Whipping Time on Foam Properties

#### 3.1.1. Foam Density

_{1}) and whipping time (X

_{3}) were shown to have significant impacts on foam density (p < 0.05); however, xanthan gum concentration (X

_{2}) and interactions (X

_{1}X

_{3}, X

_{2}X

_{3}) were not affected (p > 0.05). Foam density was significantly impacted by the quadratic effects of X

_{1}and X

_{3}, as well as the interaction effect of the remainder (p < 0.05). The non-essential terms have already been removed, and Equation (10) contains the significant parameters that enhanced the foam density response.

^{2}(93.47%) and adjusted R

^{2}(92.94%) for response variables were observed. The Lack-of-fit is insignificant (p = 0.476 > 0.05) and the p-value of the model also was significantly different(p = 0.001 < 0.05), suggesting that the selected model is accurate enough to explain the behavior and predict foam density.

_{1}is egg albumin (%), X

_{2}is xanthan gum (%), and X

_{3}is whipping time (min).

_{1}, X

_{2}, and X

_{3}) on foam density.

#### 3.1.2. Foam Expansion Volume

_{1}), xanthan gum (X

_{2}), and the whipping time (X

_{3}) all influenced the foam expansion volume, with the exception of the double interaction (X

_{1}X

_{3}, and X

_{2}X

_{3}), which did not affect the foam expansion volume (Table 4). The linear factors (X

_{1}, X

_{2}, and X

_{3}), double interactions (X

_{1}X

_{2}, X

_{1}X

_{3}, and X

_{2}X

_{3}) and second order interactions (X

_{1}

^{2}, X

_{2}

^{2}, and X

_{3}

^{2}) all show high reliability (p < 0.05). The significant parameters that improved the foam expansion volume response were given in Equation (11). The high coefficient of determination (R

^{2}= 98.96%) and adjusted R

^{2}(98.85%) for response variables were observed. The Lack-of-fit is insignificant (p = 0.188 > 0.05) and the p-value of model was lower than 0.05, which indicates the goodness fit of a model. The correlation between the experimental data and the predicted data from Equation (11) is found.

_{1}is egg albumin (%), X

_{2}is xanthan gum (%), and X

_{3}is whipping time (min).

#### 3.1.3. Multiple Response Optimization

#### 3.2. Drying

#### 3.2.1. Effect of Temperature on Moisture Ratio and Dehydration Rate

#### 3.2.2. Drying Kinetics

^{2}, lower chi square χ

^{2}, and RMSE values are the best criteria for selecting an appropriate drying model. Almost all the models tested had high correlations with the experimental data, and the R

^{2}values were found between 77.93 to 99.69%, RSME 0.0206 to 0.184, and χ

^{2}from 0.0005 to 0.564. The Page model, which had the highest R

^{2}value and lower χ

^{2}and RMSE, was the most successful in describing the drying behavior of magenta leaves extract. Table 6 also summarizes the constant values for all the models. The Page model may be assumed as the best-fitted model to exhibit the good drying behavior for most of the peach samples. Doymaz [41] indicated that the Page model fit the experimental drying data of persimmon slices better than other empirical models at 50, 60, and 70 °C. The drying process of butterfly pea flowers was well-described by the Page model, according to Thuy, Minh, Ha, and Tai [10]. The Page model was discovered to be suitable for drying red chiles [42]. Figure 6 shows a high correlation between experimental and calculated data, with a high R

^{2}value (99.51%).

#### 3.2.3. The Moisture Diffusivity and Activation Energy

_{eff}values showed an upward trend with increasing temperatures. The effective diffusivity values of foam-mat dried magenta leaves extract at 50 to 80 °C were in the range of 2.267 × 10

^{−10}to 6.707 × 10

^{−10}m

^{2}/s. As others reported, the resultant values are found to be greater. The estimated D

_{eff}values for the Vernonia amygdalina leaves [43] with the effective diffusivities ranged from 4.55 × 10

^{−12}to 5.48 × 10

^{−12}m

^{2}/s at 40 to 60 °C. The estimated D

_{eff}values of dried butterfly pea flowers varied in the range of 2.392 × 10

^{−12}to 7.756 × 10

^{−12}m

^{2}/s at 55 to 70 °C [10]. The values of ln(D

_{eff}) vs. 1/T (1/K) are plotted to determine the influence of temperature on effective diffusivity. Over the temperature range studied, the plot was found to be a straight line, demonstrating Arrhenius dependence. The activation energy (E

_{a}) was determined to be 100.21 kJ/mol by calculating the slope of the straight line [26]. This value obtained from our investigation is found to be different with other dried products, such as mint leaf (82.93 kJ/mol), as reported by Jin Park et al. [44], and black tea 406.028 kJ/mol [45]. Lesser activation energy corresponds to lower sensitivity to air temperature [44].

#### 3.2.4. Effect of Drying Temperature on Physicochemical Properties of Foam-Mat Dried Magenta Leaves Powder

_{w}in the range of 0.205 to 0.293 (Table 7).

## 4. Conclusions

^{2}), the smallest chi-square value (χ

^{2}), and RMSE were obtained. In addition, anthocyanins in plants that are very sensitive to high temperatures and difficult to dry could be easily dried using a foam-mat drying method (at 60 °C) with the highest anthocyanin content maintained. By using this technique, the final product can be produced in a short drying time (3.5 h) with minimal quality change.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Response surface of foam density as a function of egg albumin, xanthan gum and whipping time. (

**a**) whipping time 5 min; (

**b**) xanthan gum 0.5%; and (

**c**) egg albumin 10%.

**Figure 2.**Response surface of foam expansion volume as a function of egg albumin, xanthan gum, and whipping time. (

**a**) Egg albumin 10%; (

**b**) Xanthan gum 0.3%; and (

**c**) Whipping time 5 min.

**Figure 3.**The overlay plot of foam density and foam expansion volume of magenta leaves extract and optimum value * (different levels of input variables). (

**a**) Whipping time 5 min; (

**b**) Xanthan gum 0.3%; and (

**c**) Egg albumin 10%.

**Figure 5.**Drying rate of foamed magenta leaves extract versus drying time at different temperatures.

**Figure 6.**Correlation between the experimentally determined MR values and the MR values predicted for magenta leaves powder using Page model.

Variables | Factors Level | ||
---|---|---|---|

−1 | 0 | 1 | |

Albumin content (X_{1}, %w/w) | 5 | 10 | 15 |

Xanthan gum content (X_{2}, %w/w) | 0.1 | 0.3 | 0.5 |

Whipping time (X_{3}, min) | 2 | 5 | 8 |

Models | Equation |
---|---|

Henderson and Pabis | MR = a.exp(−kt) |

Page | MR = exp(−kt^{n}) |

Logarithmic | MR = a.exp(−kt) + c |

Two-term | MR = a.exp(−kt) + b.exp(−k_{o}t) |

Two-term exponential | MR = a.exp(−kt) + (1 − a)exp(−kat) |

_{o}, n are the model constants.

Source | Sum of Squares | Df | Mean Square | F-Ratio | p-Value |
---|---|---|---|---|---|

X_{1} | 0.0610 | 1 | 0.0610 | 433.68 | 0.0000 |

X_{2} | 0.0000 | 1 | 0.0000 | 0.04 | 0.8372 |

X_{3} | 0.0095 | 1 | 0.0095 | 67.30 | 0.0000 |

X_{1}^{2} | 0.0396 | 1 | 0.0396 | 281.56 | 0.0000 |

X_{1}X_{2} | 0.0238 | 1 | 0.0238 | 169.33 | 0.0000 |

X_{1}X_{3} | 2.78 × 10^{−8} | 1 | 2.78 × 10^{−8} | 0.00 | 0.9888 |

X_{2}^{2} | 0.0063 | 1 | 0.0063 | 44.94 | 0.0000 |

X_{2}X_{3} | 0.0001 | 1 | 0.0001 | 0.89 | 0.3506 |

X_{3}^{2} | 0.011 | 1 | 0.011 | 77.97 | 0.0000 |

Lack-of-fit | 0.0028 | 17 | 0.0002 | 1.19 | 0.3065 |

Pure error | 0.0076 | 54 | 0.00014 | ||

Total (corr.) | 0.1618 | 80 | |||

R^{2} = 93.55% | R^{2} (adjusted for d.f.) = 92.73%; Standard Error of Est. = 0.012 |

Source | Sum of Squares | Df | Mean Square | F-Ratio | p-Value |
---|---|---|---|---|---|

X_{1} | 33,531.4 | 1 | 33,531.4 | 1921.35 | 0.0000 |

X_{2} | 5218.75 | 1 | 5218.75 | 299.04 | 0.0000 |

X_{3} | 6805.38 | 1 | 6805.38 | 389.95 | 0.0000 |

X_{1}^{2} | 27,494.1 | 1 | 27,494.1 | 1575.42 | 0.0000 |

X_{1}X_{2} | 43,119.2 | 1 | 43,119.2 | 2470.74 | 0.0000 |

X_{1}X_{3} | 17.5421 | 1 | 17.5421 | 1.01 | 0.3205 |

X_{2}^{2} | 11,228.3 | 1 | 11,228.3 | 643.39 | 0.0000 |

X_{2}X_{3} | 2.0449 | 1 | 2.0449 | 0.12 | 0.7334 |

X_{3}^{2} | 5300.27 | 1 | 5300.27 | 303.71 | 0.0000 |

Lack-of-fit | 430.746 | 17 | 25.338 | 1.45 | 0.1496 |

Pure error | 942.405 | 54 | 17.4519 | ||

Total (corr.) | 134,090 | 80 | |||

R^{2}= 98.98%, R^{2} (adjusted for d.f.) = 98.85%; Standard Error of Est. = 4.18. |

Predicted Value | Actual Value | |
---|---|---|

Foam density (g/mL) | 0.252 | 0.259 * ± 0.05 ** |

Foam expansion volume (%) | 298.17 | 286.87 ± 2.79 |

**Table 6.**Regression parameters of tested mathematical models for foam-mat drying of magenta leaves extract at different temperatures.

Model | Temperature (°C) | Model Constants | RSME | R^{2} (%) | χ^{2} |
---|---|---|---|---|---|

Logarithmic (2008) | 50 | a = 2.0313; k = 0.1246; c = −0.8623 | 0.1018 | 91.70 | 0.0119 |

60 | a = 2.0270; k = 0.2114; c = −0.8778 | 0.0946 | 94.08 | 0.0112 | |

70 | a = 1.9324; k = 0.2842; c = −0.7741 | 0.1101 | 92.63 | 0.0161 | |

80 | a = 1.9396; k = 0.3457; c = −0.7940 | 0.1137 | 92.91 | 0.0184 | |

Page (2008) | 50 | k = 0.0219; n = 2.8211 | 0.0242 | 99.51 | 0.0006 |

60 | k = 0.1207; n = 2.6131 | 0.0253 | 99.54 | 0.0007 | |

70 | k = 0.1938; n = 2.7593 | 0.0206 | 99.69 | 0.0005 | |

80 | k = 0.3542; n = 2.8701 | 0.0276 | 99.52 | 0.0009 | |

Two-term exponential (2007) | 50 | a = 0.9990; k = 0.2227 | 0.1637 | 77.93 | 0.0293 |

60 | a = 2.2903; k = 0.7918 | 0.0825 | 95.12 | 0.0079 | |

70 | a = 2.3275; k = 0.9867 | 0.1101 | 95.00 | 0.0146 | |

80 | a = 2.3341; k = 1.2570 | 0.0907 | 94.85 | 0.0103 | |

Henderson and Pabis (2008) | 50 | a = 1.1967; k = 0.2807 | 0.1396 | 83.94 | 0.0215 |

60 | a = 1.1813; k = 0.4748 | 0.1378 | 86.00 | 0.0219 | |

70 | a = 1.1802; k = 0.6066 | 0.1484 | 85.22 | 0.0264 | |

80 | a = 1.1695; k = 0.7710 | 0.1594 | 84.67 | 0.0317 | |

Two-term (2007) | 50 | a = 0.5983; k = 0.2811; b = 0.5983; k_{o}=0.2800 | 0.1468 | 83.94 | 0.0261 |

60 | a = 0.5906; k = 0.4762; b = 0.5906; k_{o}=0.4730 | 0.1498 | 86.00 | 0.0306 | |

70 | a = 0.5901; k = 0.6048; b = 0.5901; k_{o}=0.6082 | 0.1660 | 85.22 | 0.0413 | |

80 | a = 0.5847; k = 0.7714; b = 0.5847; k_{o}=0.7703 | 0.1840 | 84.67 | 0.0564 |

_{o}, nare models constants.

Drying Temperature (°C) | Moisture Content (%) | Water Activity | Moisture Absorption Capacity (%) | Anthocyanin (mg/g) |
---|---|---|---|---|

50 | 3.96 ^{a} ± 0.12 | 0.293 ^{a} ± 0.011 | 19.69 ^{d} ± 0.16 | 1.60 ^{c} ± 0.04 |

60 | 3.75 ^{b} ± 0.10 | 0.259 ^{b} ± 0.005 | 21.07 ^{c} ± 0.18 | 2.04 ^{a} ± 0.08 |

70 | 3.58 ^{b} ± 0.07 | 0.288 ^{c} ± 0.002 | 22.61 ^{d} ± 0.29 | 1.90 ^{a} ± 0.06 |

80 | 3.35 ^{c} ± 0.11 | 0.205 ^{d} ± 0.008 | 24.29 ^{d} ± 0.20 | 1.76 ^{b} ± 0.05 |

Drying Temperature (°C) | L* | a* | b* |
---|---|---|---|

50 | 42.64 ^{a} ± 0.89 | 4.26 ^{a} ± 0.11 | −6.47 ^{c} ± 0.16 |

60 | 46.64 ^{c} ± 0.38 | 4.62 ^{a} ± 0.25 | −9.32 ^{a} ± 0.12 |

70 | 48.56 ^{d} ± 1.31 | 4.46 ^{a} ± 0.14 | −9.24 ^{a} ± 0.15 |

80 | 44.72 ^{b} ± 1.02 | 4.49 ^{a} ± 0.29 | −8.07 ^{b} ± 0.19 |

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## Share and Cite

**MDPI and ACS Style**

Thuy, N.M.; Tien, V.Q.; Van Tai, N.; Minh, V.Q.
Effect of Foaming Conditions on Foam Properties and Drying Behavior of Powder from Magenta (*Peristrophe**roxburghiana*) Leaves Extracts. *Horticulturae* **2022**, *8*, 546.
https://doi.org/10.3390/horticulturae8060546

**AMA Style**

Thuy NM, Tien VQ, Van Tai N, Minh VQ.
Effect of Foaming Conditions on Foam Properties and Drying Behavior of Powder from Magenta (*Peristrophe**roxburghiana*) Leaves Extracts. *Horticulturae*. 2022; 8(6):546.
https://doi.org/10.3390/horticulturae8060546

**Chicago/Turabian Style**

Thuy, Nguyen Minh, Vo Quoc Tien, Ngo Van Tai, and Vo Quang Minh.
2022. "Effect of Foaming Conditions on Foam Properties and Drying Behavior of Powder from Magenta (*Peristrophe**roxburghiana*) Leaves Extracts" *Horticulturae* 8, no. 6: 546.
https://doi.org/10.3390/horticulturae8060546