Kinetics of foam-mat drying in Formosa papaya pulp (Part I)¹

Cinética de secagem em Leito de espuma da polpa de mamão Formosa (Parte I)

ABSTRACT

Formosa papaya is valued for its distinctive aroma, flavor, and texture, as well as its rich content of vitamin C, minerals, papain, carotenoids, lycopene, and lutein. However, its highly perishable nature and rapid aging result in significant post-harvest losses. Processing and preservation techniques, such as foam-mat drying, can enhance shelf life, availability, and market potential. This study aimed to identify the optimal additive formulation and evaluate the drying kinetics of Formosa papaya foam prepared through the foam mat drying method. The foam was generated by mechanical stirring with two additives, Emustab™ and maltodextrin, at concentrations of 0.5, 1.0, 1.5, and 2.0% (w/w). Following preliminary evaluations, the foam was dried at temperatures of 40, 50, 60, 70, and 80 ˚C. Results showed that Emustab™ produced foam with superior physical properties, including enhanced stability, greater expansion, and reduced specific mass. The modified Midilli model best described the drying behavior under all experimental conditions, with higher drying temperatures accelerating the water reduction rate.

Key words:
Carica papaya L.; diffusion coefficient; food additives; mathematical modeling

HIGHLIGHTS:

The food additive Emustab™ ensured stable foam formation and enhanced physical properties.

The modified Midilli model accurately described the drying process across all experimental conditions.

Diffusion coefficients increased with higher drying temperatures.

RESUMO

O mamão Formosa é uma fruta apreciada pelo seu aroma, sabor e textura, além de ser fonte de vitamina C, minerais, papaína, carotenoides, licopeno e luteína. Todavia, por ser uma fruta perecível e de rápida senescência grandes quantidades da fruta são desperdiçadas. Assim, seu processamento pós-colheita e a aplicação de técnicas de conservação, como a secagem em camada de espuma, são ferramentas que auxiliam na manutenção e aumento da vida útil do produto, aumentando sua disponibilidade e potencial de comercialização. O objetivo deste estudo foi determinar a formulação mais eficiente de aditivo e analisar a cinética de secagem da espuma de mamão Formosa, produzida pelo método de secagem em camada de espuma. A espuma submetida à secagem foi obtida mediante agitação mecânica utilizando dois tipos de aditivos: Emustab^™ e Maltodextrina, nas seguintes concentrações 0,5; 1,0; 1,5 e 2,0% em massa. Após as avaliações preliminares, a espuma foi submetida à secagem em diferentes temperaturas (40, 50, 60, 70 e 80 ˚C). Com base nos resultados, conclui-se que: o aditivo Emustab™ forneceu as melhores características físicas para a espuma, apresentando melhor estabilidade, maior expansão e menor massa específica; o modelo matemático que melhor se ajustou a todas as condições experimentais de secagem foi o modelo de Midilli modificado e observou-se que o aumento da temperatura de secagem ocasionou aumento da taxa de redução de água.

Palavras-chave:
Carica papaya L.; coeficiente de difusão; aditivos alimentares; modelagem matemática

Introduction

Formosa papaya (Carica papaya L.) is a tropical fruit highly valued for its nutritional richness and sensory appeal. It provides various functional and health benefits, offering calcium, carotenoids, sugars, fiber, retinol, vitamin A, ascorbic acid, and other essential micro and macronutrients (Terra et al., 2020). These compounds are unevenly distributed throughout the fruit but can be fully utilized-pulp, peel, and seeds-maximizing economic value. For instance, peels and seeds produce juices, jellies, sweets, flour, and cosmetic and beauty products (Zhang et al., 2017).

In 2022, Brazil ranked as the third-largest papaya producer globally, following India and the Dominican Republic, with a production of 1.107 million tons, representing approximately 7.64% of the world’s production (FAOSTAT, 2024). Brazil also stands out as a significant exporter of papaya. However, despite high productivity and substantial economic potential, not all production reaches consumers (Serafini et al., 2021).

The FAO reports that 40% of fruits and vegetables produced worldwide are wasted or discarded before reaching consumers (Almeida et al., 2020). Of this total, 30% is lost due to post-harvest physical and chemical changes, such as alterations in texture, aroma, flavor, and color. To mitigate these losses, the development of fruit by-products, such as fruit powders, is encouraged. This industry benefits from technologies like freeze-drying, spray drying, and foam mat drying, with foam mat drying being particularly cost-effective due to its simpler equipment and methodologies (Cavalcante et al., 2018; Freitas, 2022).

Foam mat drying involves converting pulps or liquid foods into stable foams using foaming agents and mechanical agitation, followed by dehydration (Silva et al., 2021). Commonly studied additives include Emustab™, Superliga Neutra™, and maltodextrin, which serve as emulsifiers, stabilizers, or thickeners, respectively.

Several studies have examined the efficiency of these additives in forming stable foams for drying. For instance, Baptestini et al. (2021) analyzed whey drying with Emustab™; Cavalcante et al. (2020a) evaluated cagaita drying using Emustab™ and Superliga Neutra™; Pinto et al. (2018) applied Emustab™ for Pequi drying; Islam (2024) used maltodextrin to produce jackfruit powder with various drying methods; and Sousa et al. (2020) investigated passion fruit drying with Emustab™, Superliga Neutra™, and maltodextrin in different concentrations.

This technology has diverse applications in industries such as food, cosmetics, and pharmaceuticals, where dehydrated products are used in soups, ice creams, juices, and other formulations. Developing optimized formulations and drying conditions is critical, as each product has unique physical, chemical, and nutritional properties requiring tailored processes.

Many fruits remain underutilized in the production chain, leading to significant waste. Others, like Formosa papaya, face consumption limitations, necessitating alternative uses. Few studies have explored the drying kinetics of Formosa papaya pulp using the foam mat method. This research aimed to identify the optimal additive formulation and evaluate the drying kinetics of Formosa papaya pulp using the foam mat drying method under various experimental conditions.

Material and Methods

The experiments were conducted at the Laboratory of Pre-processing and Storage of Agricultural Products (LAPREP), College of Agricultural Sciences (FCA), Federal University of Grande Dourados (UFGD), located in Dourados, Mato Grosso do Sul state, Brazil. Formosa papaya fruits were sourced from farmers at the Itamarati Rural Settlement (latitude 22° 32ʼ S, longitude 55° 43ʼ W, altitude 655 m at sea level) in Ponta Porã, Mato Grosso do Sul.

The fruits were sanitized in chlorinated water at a concentration of 150 ppm and stored at room temperature (25 °C) until they reached ripening stage 4, characterized by approximately 75% yellow peel. Before drying, the optimal foam formulation was determined. Emustab™ (a compound containing distilled monoglycerides, sorbitan monostearate, and polysorbate) and maltodextrin were used as foaming agents.

Foaming agent concentrations of 0.5, 1.0, 1.5, and 2.0% (w/w) were considered to evaluate foam physical quality. Foam was generated by mechanical stirring in a domestic mixer, with additives added at the specified concentrations, and stirred for 20 min at a speed of 180 rpm (speed setting 3). Foam stability and specific mass were assessed using the method proposed by Brooker et al. (1992) and calculated according to Eq. 1:

$$\rho =\frac{m}{v}$$ (1)

where:

ρ - specific mass, kg m^-3;

m - sample mass, kg; and,

v - sample volume measured in a beaker, m³.

Foam expansion (Exp[%]) was determine using the following Eq. 2:

$$Exp\left(\%\right)=\frac{{\displaystyle \frac{1}{{\rho }_{pulp}}}-{\displaystyle \frac{1}{{\rho }_{foam}}}}{\frac{1}{{\rho }_{foam}}}\times 100$$ (2)

where:

ρ_pulp - pulp specific mass, kg m^-3;

ρ_foam - foam specific mass, kg m^-3; and,

Exp (%) - foam expansion, %.

To evaluate the effects of additives (Emustab™ and maltodextrin) at different concentrations (0.5, 1.0, 1.5, and 2.0%) on the specific mass, expansion, and stability of foams, the experiment was designed as a 2 × 4 factorial scheme. This design combined two types of emulsifiers at four concentrations in a completely randomized design (CRD) with five replicates. The data were subjected to analysis of variance (ANOVA) and regression analysis at p ≤ 0.01 by F test. For the qualitative factor (emulsifier), means were compared using Tukey’s test at p ≤ 0.01.

For producing Formosa papaya powder, 60 g of foam, prepared with a thickness of 7 mm, was dried in a convection oven with air circulation at five temperatures: 40, 50, 60, 70, and 80 °C. The drying process was conducted on a stainless-steel circular tray measuring 17 cm in diameter and 8 mm in height.

Moisture content was determined gravimetrically using an analytical scale with a resolution of 0.01 g. Drying was terminated once hygroscopic equilibrium was achieved.

The moisture ratio was calculated using the following Eq. 3:

$$MR=\frac{M-Me}{Mi-Me}$$ (3)

where:

MR - moisture ratio of the product, dimensionless;

M - moisture at dry basis, decimal (db);

Me - moisture at equilibrium, decimal (db); and,

Mi - initial moisture content, decimal (db).

The water reduction rate was determined using the following Eq. 4:

$$WRR=\frac{WM{a}_0-WM{a}_i}{DM\left(t_i-t_0\right)}$$ (4)

where:

WRR - water reduction rate, kg kg^-1 h^-1;

WMa0 - previous total water mass, kg;

Mai - current total water mass, kg;

DM - dry mass weight, kg;

t0 - previous total drying time, hours; and,

ti - current total drying time, hours.

Based on liquid diffusion theory, the effective diffusion coefficient (MR) for a flat plate system was calculated using Eq. 5:

$$MR=\frac{M-Me}{Mi-Me}=\frac{8}{{\pi }^2}\sum _{n=0}^{\infty }\frac{1}{{\left(2n+1\right)}^2}exp\left[-{\left(2n+1\right)}^2{\pi }^2{D}_i\frac{t}{4L^2}\right]$$ (5)

where:

Di - effective diffusion coefficient, m² s^-1;

L - product thickness;

t - drying time (s); and,

n - is the model term number.

The experiment followed a completely randomized design (CRD) with five drying temperatures: 40, 50, 60, 70, and 80 °C. Each temperature condition was replicated four times, resulting in a total of 20 experimental units.

Drying processes were conducted under controlled conditions, and data were collected to analyze drying kinetics for each experimental condition. Analysis of variance (ANOVA) was performed, revealing significance at p ≤ 0.05 based on the F test. Nonlinear regression analysis was then applied to identify the most suitable mathematical model for describing the relationships between variables.

The analyses were performed using STATISTICA 8.0 software, ensuring precise model fitting to the experimental data. Table 1 presents the mathematical models used to simulate the foam mat drying process.

Table 1
Mathematical models used to determine theoretical drying curves

Model name (Author)	Equation
Page (Corrêa et al., 1995)	$$MR=exp\left(-k{t}^n\right)$$	(6)
Two-terms (Henderson, 1974)	$$MR=a exp\left(-k_{0}t\right)+b exp\left(-k_{1}t\right)$$	(7)
Logarithmic (Corrêa et al., 1995)	$$MR=a exp\left(-kt\right)+c$$	(8)
Midilli (Midilli et al., 2002)	$$MR=a exp\left(-kt\right)+b$$	(9)
Modified Midilli (Ghazanfari et al., 2006)	$$MR=exp\left(-kt\right)+b$$	(10)
Copace (Corrêa et al., 1995)	$$MR=\frac{a+bt}{1+ct+d{t}^2}$$	(11)

• MR - Moisture ratio of the product, dimensionless; t -Drying time (hour); k, k₀, and k₁ - Drying constants; a, b, c, d, and n - Model coefficients

The models were selected based on their high coefficient of determination (R²), low mean relative error (P), and low standard error of the estimate (SE), as defined by Eqs. 12 and 13:

$$P=\frac{100}{n}\sum _{i=1}^n\left(\frac{\left|Y-Y\text{'}\right|}{Y}\right)$$ (12)

$$SE=\sqrt{\frac{{\displaystyle \sum _{i=1}^n}{\left(Y-Y\text{'}\right)}^2}{DoF}}$$ (13)

where:

n - number of experimental observations;

Y - experimentally observed value;

Y´ - model-estimated value; and,

DoF - degrees of freedom of the model.

Results and Discussion

The foam formulation selected for drying was determined based on its physical properties, as summarized in Table 2.

Table 2
Liquid content released during the stability test

Formulation	Mean volume released (mL) ± standard deviation
E1	0.170 ± 0.057
E2	0.000 ± 0.000
E3	0.000 ± 0.000
E4	0.000 ± 0.000
M1	6.800 ± 0.000
M2	6.500 ± 0.500
M3	9.000 ± 0.289
M4	9.200 ± 0.252

• E1- Emustab^™ concentration of 0.5%; E2- Emustab^™ concentration of 1.0%; E3- Emustab^™ concentration of 1.5%; E4- Emustab^™ concentration of 2.0%; M1- Maltodextrin concentration of 0.5%; M2- Maltodextrin concentration of 1.0 %; M3- Maltodextrin concentration of 1.5 %, and M4- Maltodextrin concentration of 2.0%

Most Emustab™ formulations showed no liquid drainage in the funnel system, except for those with a 0.5% concentration, which drained approximately 0.17 mL of liquid. In contrast, all maltodextrin samples exceeded the 1 mL drainage limit established by Karin & Wai (1999).

The efficiency of maltodextrin decreased with increasing additive concentrations, resulting in higher liquid drainage and reduced foam stability. This reduced efficiency in foam formation, which primarily increases the compound’s viscosity, can be attributed to maltodextrin’s composition derived from starch hydrolysis. Conversely, Emustab™, composed predominantly of fatty acid monoglycerides, effectively bonds with the pulp, enhancing foam formation and stability. This stability is crucial for the drying process, as the foam’s porosity increases the surface area, facilitating better contact with heated air.

Table 3 presents a summary of the analysis of variance for the specific mass and expansion of Formosa papaya foam, incorporating Emustab™ and maltodextrin at varying concentrations.

Table 3
Summary of analysis of variance (mean square values) for the specific mass and expansion of Formosa papaya foam prepared with Emustab™ and maltodextrin at concentrations of 0.5, 1.0, 1.5, and 2.0% (w/w)

Sources of variation	DF	Mean square
		(Specific mass)	(Foam expansion)
Additives (A)	1	1954573.327**	15666.048**
Formulations (F)	3	47098.361**	10140.998**
A × F	3	51306.788**	10348.096**
Residue	16	103.727	48.515
Total	23
CV (%)		1.42	8.36

• ** Significant at p ≤ 0.01 by F test; CV - Coefficient of variation

Figure 1 illustrates that the linear model provided the best fit for both specific mass and foam expansion when using maltodextrin as the additive. In contrast, the polynomial model demonstrated the best fit for both parameters-specific mass and foam expansion-when using Emustab™.

Figure 1
Average specific mass and foam expansion of Formosa papaya foam. Graphs A and C represent the results for the foam prepared with Emustab™, while graphs B and D show the results for the foam prepared with maltodextrin, at concentrations of 0.5, 1.0, 1.5, and 2.0% (w/w)

Both additives caused significant differences in physical characteristics (p ≤ 0.01), regardless of concentration. According to Van Arsdel & Copley (1964) and Cavalcante et al. (2020b), an effective additive should maintain a specific mass between 100 and 600 kg m⁻³. However, maltodextrin produced a specific mass ranging from 996.570 to 1007.595 kg m⁻³ across concentrations from 0.5 to 2.0%, rendering it unsuitable for Formosa papaya foam formation. Similarly, Emustab™ at a 0.5% concentration exceeded 600 kg m⁻³, thus proving unsuitable.

In terms of foam expansion, only Emustab™ formulations yielded favorable results. As noted by Coelho et al. (2019), an expansion above 100% is ideal for the drying process. All Emustab™ formulations, except at 0.5% concentration, met this criterion. Specific mass for Emustab™ decreased until a concentration of 1.5%, with maximum expansion observed at this level. Beyond 1.5%, further increases were attributed to unstable air bubbles caused by inadequate liquid/gas interfacial film thickness (Karim & Wai, 1999).

Apparent specific mass is critical in defining foam formulations, as it directly affects moisture migration during drying and the final product’s quality. Foaming agents and concentrations that may significantly reduce apparent specific mass should be prioritized, as this reduction results from air incorporation during agitation, promoting foam formation (Coelho et al., 2019). The 1.5% concentration was the most effective, achieving lower specific mass, higher expansion, and no liquid drainage in the funnel stability test.

Similar findings were reported by Pinheiro et al. (2020) in yeast-based foam layer drying and Cardoso & Lobo (2021) in beet powder production, where reduced specific mass and increased expansion were critical for optimizing formulations.

Table 4 summarizes the fitting of drying data for Formosa papaya foam to mathematical models. Determination coefficients (R²) exceeded 95.7% for all experimental conditions, and the estimated standard error (SE) values were low, indicating close alignment between observed and predicted data.

Table 4
Coefficient of determination (R²), relative mean error (P), and estimated standard error (SE) for the models representing experimental data

Model	Parameter
	SE	P	R2
	40 ᵒC
Page	0.027	15.830	0.991
Two-terms	0.044	30.895	0.957
Logarithmic	0.010	6.261	0.999
Midilli	0.043	28.434	0.996
Modified Midilli	0.011	6.393	0.998
Copace	0.011	7.553	0.995
	50 ᵒC
Page	0.034	19.201	0.986
Two-terms	0.044	30.895	0.957
Logarithmic	0.013	6.5749	0.999
Midilli	0.008	6.8992	0.999
Modified Midilli	0.008	3.020	0.999
Copace	0.010	6.810	0.999
	60 ᵒC
Page	0.019	11.290	0.996
Two-terms	0.017	11.701	0.997
Logarithmic	0.013	6.575	0.999
Midilli	0.021	14.250	0.999
Modified Midilli	0.011	6.698	0.999
Copace	0.012	6.845	0.998
	70 ᵒC
Page	0.028	25.004	0.992
Two-terms	0.013	12.264	0.997
Logarithmic	0.013	12.264	0.998
Midilli	0.008	6.829	0.999
Modified Midilli	0.007	5.617	0.999
Copace	0.014	12.147	0.999
	80 ᵒC
Page	0.024	22.507	0.994
Two-terms	0.068	64.741	0.959
Logarithmic	0.014	11.207	0.997
Midilli	0.008	7.013	0.999
Modified Midilli	0.009	8.326	0.999
Copace	0.013	12.285	0.996

Although these positive outcomes were observed, the coefficients alone are insufficient for selecting nonlinear mathematical models. The mean relative error (P) must also be considered as a criterion for model selection.

As noted by Dorneles et al. (2019) and Mohapatra & Rao (2005), models with mean relative error values exceeding 10% are unsuitable for representing drying processes. Among the evaluated mathematical models, the Midilli, Copace, and Logarithmic models showed P values below 10% in some instances but only under specific conditions. Conversely, the Modified Midilli model consistently demonstrated P values below 10% across all experimental drying conditions.

A mathematical model is considered satisfactory when it maintains P values within this threshold. The Modified Midilli model was the most accurate for describing the drying behavior of Formosa papaya foam under temperatures of 40, 50, 60, 70, and 80 °C.

Fitting the experimental data to the models enabled the calculation of the ‘k’ coefficient for the Modified Midilli model, as shown in Table 5. This coefficient increased with the drying air temperature. However, no consistent trend was observed for the parameter ‘b’. The ‘k’ parameter reflects the influence of temperature and is associated with effective diffusivity during the drying process, particularly in the phase dominated by liquid diffusion. Higher ‘k’ values indicate greater effective diffusivity during drying.

Table 5
Coefficients of the Modified Midilli model for Formosa papaya foam drying

Temperature (°C)	k	b
40	0.132	-0.012
50	0.235	-0.052
60	0.322	-0.026
70	0.385	-0.065
80	0.701	-0.068

Hygroscopic equilibrium in the papaya foams was achieved at drying times of 16.6, 8.0, 4.9, 3.25, and 2.15 hours for temperatures of 40, 50, 60, 70, and 80 °C, respectively (Figure 2).

Figure 2
Experimental and estimated moisture ratios for drying Formosa papaya foam, as calculated using the Modified Midilli model

Analysis of the drying time curves reveals a significant discrepancy, particularly between 40 and 50 °C, where the drying time at the lower temperature is 8.6 hours longer. Santos et al. (2019) reported a similar trend in the drying kinetics of Patauá foam, with drying times of 9, 6, and 4.5 hours at 40, 50, and 60 °C, respectively.

This discrepancy is mostly influenced by temperature. Initially, water removal occurs rapidly as surface moisture evaporates (Figure 3). Subsequently, water migration from the deeper foam layers dominates, with the drying process becoming governed by liquid diffusion, which is strongly temperature-dependent.

Figure 3
Water reduction rate of Formosa papaya foam at different drying temperatures

Diffusion coefficient values increased with higher drying temperatures, as shown in Table 6. Elevated temperatures enhance water molecule vibration, reducing viscosity-a measure of the product’s resistance to flow. These viscosity changes facilitate water diffusion and capillarity in agricultural products, accelerating the diffusion process through more intense molecular vibrations. Thuwapanichayanan et al. (2012) observed that water transport within foam occurs via capillarity and vapor diffusion.

Table 6
Effective diffusion coefficients (D_eff) of papaya foams prepared with Emustab™ at different drying temperatures

Temperature (°C)	Deff × 10-11 (m2 s-1)	R2	SE
40	55.5556	0.952	0.086
50	111.1111	0.929	0.107
60	194.4444	0.950	0.091
70	277.7778	0.928	0.115
80	416.6667	0.923	0.123

• Where: R²-coefficient of determination and SE-standard error of the estimate

During this drying phase, the process is governed solely by external conditions, including temperature, air velocity, and relative air humidity. As water moves from the interior to the surface of the papaya foam, surface moisture is no longer maintained, initiating a phase where the drying rate decreases due to the diffusion mechanism. At this stage, heat transfer outpaces mass transfer as internal resistance to moisture transport becomes greater than external resistance. Consequently, the temperature of the product rises, eventually reaching equilibrium with the drying air temperature (Brooker et al., 1992).

For Formosa papaya pulp, diffusion coefficients ranged from 55.55 × 10⁻¹¹ to 416.67 × 10⁻¹¹ m² s⁻¹ at drying temperatures of 40 and 80 °C, respectively. These values align with the effective diffusion coefficients reported for drying agricultural products, typically between 10⁻⁹ and 10⁻¹¹ m² s⁻¹ (Santos et al., 2019).

Matos et al. (2022) observed comparable diffusion coefficients in their study on the drying kinetics of mixed jambolão and acerola pulp foam, reporting values of 25.8 × 10⁻¹¹, 38.43 × 10⁻¹¹, 46.44 × 10⁻¹¹, and 51.10×10⁻¹¹ m² s⁻¹ for drying temperatures of 50, 60, 70, and 80 °C, respectively. Similar trends were noted by Araújo et al. (2021) for foam-mat drying of noni and umbu, by Silva et al. (2021) for persimmon pulp, and by Santos et al. (2019) for patauá pulp drying kinetics.

The activation energy for water diffusion during Formosa papaya foam drying was 45.66 kJ mol⁻¹, which falls within the range of 12.70 to 110.00 kJ mol⁻¹ commonly reported for agricultural products (Santos et al., 2019). These results confirm consistency with established parameters.

Conclusions

1. The characterization of Formosa papaya foams identified Emustab™ as the most effective additive, delivering optimal stability, expansion, and specific mass under all experimental conditions.

2. A 1.5% concentration of Emustab™ yielded foam with superior physical properties, outperforming other concentrations and proving more effective than maltodextrin in foam formation.

3. The Modified Midilli model was the most accurate for simulating the drying process across all experimental conditions.

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• ¹ Research developed at Universidade Federal da Grande Dourados, Laboratório de Pré-Processamento e Armazenamento de Produtos Agrícolas, Dourados, MS, Brazil

Supplementary documents

• There are no supplementary documents.

Financing statement

• The current study was funded by the National Council for Scientific and Technological Development - CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, in Portuguese) under process n° 129668/2017-8.

Edited by

• Editors: Antônio Gustavo de Luna Souto & Carlos Alberto Vieira de Azevedo

Data availability

There are no supplementary documents.

Publication Dates

• Publication in this collection
  28 Apr 2025
• Date of issue
  Aug 2025

History

• Received
  18 July 2024
• Accepted
  10 Mar 2025
• Published
  01 Apr 2025