3.1. Foam Physical Properties
Table 2 shows the average density values of the foams of the 3 formulations, in the 6 mixing times evaluated (5, 10, 15, 20, 25 and 30 min). It is observed that the E2 foam (6% albumin and 1% guar gum) presented the lowest densities at all times evaluated, when compared to the other foams (
p < 0.05). In addition, significant increases in density occurred when the duration of the mixing times was increased. In the other foams, an inverse behavior was verified, where the longer the times, the lower the values obtained (
p < 0.05). This proved that the characteristics of the different materials added (such as stabilizers) cause different behaviors in the sample, mainly affecting the beating time.
To optimize the drying process, the choice of ideal mixing times must be carried out aiming at the lowest densities because these results demonstrate greater incorporation of air and the foams become more stable throughout the process, according to Dabestani and Yeganehzad [
19]. Consequently, there is better water removal due to the larger surface area [
29]. All foams evaluated showed densities lower than 0.2 g/cm
3 in at least 1 processing time, with the formulations composed with gum arabic (E1) and gelatin (E3) presenting the better performance with 30 min of mixing, with no significant difference between the values of both, while in E2, the time of 5 min showed better values.
Foam density results similar to the foams of formulations E1 and E3 were identified in melon pulp (
Cucumis melo) with different concentrations of gum arabic (0 to 15%), presenting values from 0.42 to 0.77 g/cm
3 with the mixing time of 10 min [
30]. Susanti et al. [
31], studying red sorghum extract (
Sorghum vulgare Pers var. Suritan 3) foamed with xanthan gum, gum arabic and milk protein isolate, reported density values from 0.2 to 0.8 g/cm
3, also decreasing with the mixing time (5, 10 and 15 min). Cól et al. [
13], evaluating bacaba pulp (
Oenocarpus bacaba Mart.) with different albumin concentrations and Emustab
® and adopting a fixed mixing time of 20 min, found densities ranging from 0.57 to 0.99 g/cm
3.
The volumetric expansion data (overrun), dependent on the mixing time, are shown in
Table 3. The volumetric expansions of the formulations varied from 44.00 to 765.66%, and in samples E1 and E3, there was an increase as the mixing time increased (
p < 0.05). The opposite occurs with the E2 formulation, which presented values about 200% higher than the others. The advantage of testing several stabilizers is that each one of them has its own properties, which, when adhering to the sample, cause different particularities. So, it is possible to optimize the drying process by using the most efficient additive, which has a shorter mixing time and greater stability.
It is observed for E2 that there is a direct relationship between the highest values of volumetric expansion and the lowest density in the times of 5 to 20 min, a fact also verified by Karim and Wai [
27]. Statistical differences (
p < 0.05) were also identified between the formulations in the different mixing periods evaluated, except for 5 and 30 min, in which the samples with gum arabic and gelatin did not differ from each other, and in the time of 25 min, in which E2 and E3 were statistically equal. Values lower than those of the present work for volumetric expansion were observed by Khodifad and Kumar [
32], in pinecone pulp (
Annona squamosa) foamed with albumin and carboxymethylcellulose, and by Watharkar et al. [
33], in ripe banana pulp (
Musa balbisiana) added with skimmed milk powder as a foaming agent, whose values ranged between 29.03 and 122.58% and between 9.09 and 51.78%, respectively.
Closer expansions were obtained in raspberry pulp foam (
Rubus idaeus) with potato protein, maltodextrin and pectin (79.19 to 447.48%) in 10 min of mixing [
34] and in white pulp pitayas (
Hylocereus undatus) and red pulp pitayas (
Hylocereus costaricensis) (436.18 and 582.43%, respectively), in which the overrun was proportional to the increase in the concentration of Emustab
® (1 to 5%), with mixing times between 5 and 30 min [
35]. The analysis of values presented here and in literature shows that the volumetric expansion is a function of the raw material chemical composition, of the additive combination and concentration and of the mixing time. The expansion of the foam is due to the presence of proteins, such as albumin. These proteins undergo denaturation at the interface and interact with each other to form a stable interfacial film [
36] that presents affinity with water, providing a very high viscosity in aqueous systems, even at low doses and in a short time, [
37] during the mixing process.
Figure 1 shows the foam drainage ratio as a function of mixing time. Foam stability is inversely proportional to the drainage ratio, indicating that the foaming/stabilizing agents used were effective granting 100% stability from the mixing time of 25 min, with emphasis on the formulation with guar gum (E2), which provided maximum stability (absence of drainage) at all times evaluated. A foam with a stable structure results in faster drying and easier removal of dry material from trays [
38].
Poonnakasem [
39], evaluating the effect of albumin concentration (2, 4 and 6%) in pepper sauce with 1% carboxymethylcellulose after 4 min of mixing, found stabilities varying between 98 and 100%, with the best concentrations of 4 and 6% albumin. Using the foaming and stabilizing agents albumin (2%) and methylcellulose (1.5%), after 3 min of mixing, Dehghannya et al. [
15] observed foam stability of 92.589% in lemon juice. Ng and Sulaiman [
14] found a stability range of 82.5 to 97.5% for beet foam (
Beta vulgaris) added with albumin and fish gelatin as the foaming and stabilizing agents, respectively, presenting these values after 180 min of evaluation of the foam at 25 °C. The same was verified in cocoa foam enriched with lavender extract (
Lavandula hybrida L.), foamed with albumin and gelatin, reaching 99.99% stability after 120 min [
40].
Table 4 presents the results obtained for the foam formulations’ porosity. Significant differences (
p < 0.05) were observed in the porosities between the six times used in the three foams. When the comparison is made among the formulations, there is a higher porosity of the foam with guar gum (E2) up to 20 min of mixing. As in the density and overrun, the porosity of the E2 sample has the opposite behavior to that of the E1 and E3 samples, decreasing with the mixing time. Cól et al. [
13] stated that a high porosity is responsible for the drying velocity of the foam layer compared to traditional drying, as it facilitates the movement of water from the interior to the surface through the free spaces (air bubbles) between the liquids.
Despite this, the choices of mixing times must be made based on the data set, where low density, high stability, high volumetric expansion and high porosity are preferable [
15]. Consequently, the mixing periods determined as the best were 5 min for E2 and 30 min for E1 and E3.
3.2. Foam Layer Drying
Table 5 presents the data obtained for the drying process time, yield and water content of the three foam formulations, which were prepared and submitted to drying at temperatures from 50 to 80 °C. There is a reduction of 47, 69 and 65% in the drying times with increasing temperature, between temperatures of 50 and 80 °C, in samples E1, E2 and E3, respectively. Evaluations of drying time reductions with increasing temperature were also carried out by El-Salam et al. [
11], studying papaya pulps (
Carica papaya) added with albumin and xanthan gum at temperatures of 60 and 80 °C. Ayetigbo et al. [
41] tested white and yellow cassava pulp (
Manihot esculenta) foamed with glycerol monostearate and sodium carboxymethylcellulose, subjected to drying at temperatures of 50, 65 and 80 °C. Silva et al. [
42] evaluated 3 formulations of mixed prickly pear and acerola pulp with albumin, xanthan gum, guar gum and carboxymethylcellulose, with temperature ranging from 50 to 70 °C, in which maximum and minimum drying times of 460 and 160 min were observed, with water contents (w.b.) between 5.17 and 12.05, close to those found in the present study (5.02 and 8.54).
When evaluating the yields, it is observed that there were small changes, which stayed in the range of 15.13 to 17.88%. However, there was a significant difference (
p < 0.05) among the powders obtained at the four temperatures adopted. Overall, the highest productivity was achieved by foam made with gum arabic (E1), followed by guar gum (E2) and gelatin (E3), respectively.
Table 6 shows the parameters of the 7 mathematical models adjusted to the experimental data of the drying kinetics of formulations E1, E2 and E3 at temperatures of 50, 60, 70 and 80 °C, with the respective coefficients of determination (R
2), mean squared deviations (MSDs) and chi-square (χ
2).
It is verified that all the models tested were satisfactorily adjusted to the experimental data of the drying kinetics, with R2 ≥ 0.98, MSD ≤ 0.07 and χ2 ≤ 0.005, and can be used in the prediction of drying kinetics curves. However, among all the models tested, Page resulted in the best results, with higher R2 values and lower MSD and χ2, making it the most suitable model to describe the foam layer drying process of the pulp blend formulations.
Other authors also found that Page’s model provided the best fit for foam layer drying kinetics, such as Li et al. [
30] for melon pulp with different concentrations of gum arabic; Brar et al. [
9] in peach pulp, using carboxymethylcellulose, isolated soy and pea protein as additives; Cavalcante et al. [
43], working with cagaita pulp (
Eugenia dysenterica) and using albumin as a foaming agent; and Gonzaga et al. [
44], using pineapple juice with mint, Neutral League and Emustab
® to obtain the foams.
The Page model was also reported in the literature as suitable for estimating the drying of fruits in general, using different techniques, such as tomato slices dried in a vacuum oven [
45]; mango submitted to drying in an indirect forced-convection solar dryer [
46]; and drying of bacaba pulp (
Oenocarpus bacaba Mart.), in which the Page, Midilli and Logarithmic models presented equally good fits, with values of R
2 > 0.99 [
47].
Figure 2 shows the drying kinetic curves of the 3 formulations, E1, E2 and E3, at temperatures of 50, 60, 70 and 80 °C, adjusted by the Page model. The three formulations behaved differently during drying, with E3 (albumin + gelatin) generating regularly distinct curves as an effect of the differences between temperatures, while in E1 (albumin + gum arabic) and E2 (albumin + guar gum), there are approximate representations for drying at 60 and 70 °C and for drying at 70 and 80 °C, respectively.
3.3. Effective Diffusivity
Table 7 shows the effective diffusivities for the three foam formulations evaluated. The increase in temperature results in an increase in the velocity of water extraction from the product, with a consequent tendency of diffusivity increase, with formulation E3 achieving the highest results, followed by E2. Thus, the influence of the combination of additives in the formulations on the effective diffusivity is evident, as verified by Dehghannya et al. [
15], which showed a decreasing in D
ef with the albumin concentration increasing.
D
ef values in a similar range are reported by several authors in products obtained by drying in a foam layer, such as mixed prickly pear and acerola pulp with diffusivity between 1.28 × 10
−9 and 3.19 × 10
−9 m
2/s [
48] and green banana (
Musa sapientum) with values from 2.045 × 10
−9 to 4.710 × 10
−9 m
2/s [
49], both at temperatures of 50, 60 and 70 °C.
The influence of temperature on the effective diffusivity was evaluated by an Arrhenius-type equation, with the values of the equation parameters, pre-exponential factor (D
0), activation energy (E
a) and determination coefficients (R
2) presented in
Table 8. The three samples showed E
a in the range of values for foamed food products which is 15 to 40 kJ/mol [
50]. Sample E2 presented the lowest E
a among the formulations and E1 the highest value, indicating that formulation E2 requires a lower amount of energy for the diffusion of water from the sample during the drying process. This is directly related to the lowest density and greater overrun, stability and porosity of this formulation, conditions favored by the guar gum addition.
A higher E
a value of 29.99 kJ/mol was determined by Khodifad and Kumar [
32], evaluating the pulp of sugar apple (
Annona squamosa L.) foamed with albumin (15%) and methylcellulose (0.37%), subjected to drying at temperatures of 60, 65, 70 and 75 °C. In other dried foods, also through the foam layer, E
a values higher than those of the present work were verified, as in whey formulated with 8% Emustab
®, under drying at temperatures from 40 to 80 °C and an E
a of 29.61 kJ/mol [
37], and also in cashew pulp added with 5% Emustab
® at temperatures from 50 to 80 °C, obtaining an E
a of 54.983 kJ/mol [
45]. It can be noticed that less energy was required by the samples of the present work.
3.4. Thermodynamic Properties
Table 9 shows the average values of thermodynamic properties, with the enthalpy (ΔH), entropy (ΔS) and Gibbs free energy (ΔG) results evaluated at the four drying temperatures for the three foam formulations. With the increase in temperature, there was a decrease in enthalpy (ΔH), proving that the higher the temperature, the lower the thermal energy required to carry out the drying process [
51]. It can also be seen that formulation E1 presented the highest values of ΔH and E2 the lowest, indicating that they need higher and lower energies, respectively, for drying and demonstrating the influence of additives in the process. Thus, it is generally observed for formulation E1 that the combination of albumin with gum arabic caused greater difficulty in removing water during the drying process due to the need of greater energy (ΔH and E
a) and having a lower effective diffusivity (D
ef), resulting in longer drying times. Formulation E2 showed an easier drying tendency, as it presented less energy (ΔH and E
a) for the drying and intermediate values of D
ef, ΔH and drying times. Formulation E3 showed a higher D
ef and intermediate ΔH, with shorter drying times. Positive enthalpy values characterize the process as endergonic, requiring energy absorption for the mass transfer [
52].
As with enthalpy, the entropy value (ΔS), which is a state function, decreased with increasing temperature, demonstrating that the lower the entropy, the greater the degree of order between the water molecules and the product [
53]. Negative values of ΔS show that the diffusion went from an initial state of disorder, with several sorption sites available, to an ordered state with reduced sorption sites. Low values of ΔS mean that the material undergoes physical and chemical changes, taking it close to its thermodynamic equilibrium [
52,
54].
Gibbs free energy (ΔG) is an extensive function that expresses the equilibrium condition and spontaneity of the process under a constant temperature and pressure conditions [
55]. It is observed that ΔG showed an inverse behavior to the other thermodynamic properties in the three foam formulations, which characterizes the drying as endergonic, not spontaneous and requiring thermal energy from the medium so that drying happens [
56]. In the same way as for enthalpy, formulation E1 presented the highest values of ΔG, indicating the greater presence of bound water in the samples. The Gibbs free energy measures the total energy of a thermodynamic system, and its positive value is explained by the energy absorbed during the liquid–vapor phase change [
52].
These behaviors verified in the thermodynamic properties are common in fruits and their residues, as determined by Silva et al. [
53] using prickly pear and acerola mixed pulp foam, at temperatures from 50 to 70 °C, where the formulation with albumin and xanthan gum presented enthalpy ranging from 24.42 to 24.26 kJ/mol, entropy from −0.3227 to −0.3232 kJ/mol K and Gibbs free energy from 131.69 to 138.15 kJ/mol, and by Morais et al. [
47] using bacaba pulp (
Oenocarpus bacaba Mart.) subjected to drying at temperatures of 40, 50 and 60 °C, with enthalpy ranging from 34.4054 to 34.2391 kJ/mol, entropy from −0.3039 to −0.3044 kJ/mol K and Gibbs free energy from 129.56 to 135.65 kJ/mol.
Other studies also demonstrated identical behavior, such as in bark and seeds of Trapiá dried at temperatures from 50 to 80 °C, which presented ΔH ranging from 15.50 to 15.25 and 21.52 to 21.57, ΔS from 0.3668 to 0.3676 and 0.3447 to 0.3454 and ΔG ranging from 134.06 to 145.07 and 132.91 to 143.26 [
56].