A Heat Transfer Model and Supporting Experiments to Guide the Uniform Gelation of Molecular Oleogels During Scale-up

Abstract

The quest for novel vegetable oil structuring strategies has been progressing since the discovery of the deleterious impacts of trans fats. Although oleogelation using bioderived molecular gelators has been proven to be successful as an alternative to traditional hydrogenation methods, efforts are needed to meet the industrial requirements. A major constraint during the fabrication of oleogels is to achieve consistency in physical properties during scale-up. Experiments showed that gelation fails to occur when larger volumes were prepared based on the minimum gelation concentration (MGC) of gelators, determined using the smallest oil volume (1 mL), a general laboratory practice. This observation was consistent with all the molecular gelators used in this study; sorbitol dioctanoate, mannitol dioctanoate, and 12-hydroxystearic acid. To understand this behavior, a mathematical model was developed since gelator network propagation is governed by the cooling rate. The model indicates that maintenance of a minimal thermal gradient via uniform heat dissipation and gelation time is necessary to achieve homogeneous gel propagation across the vial. With these predictions, we hypothesized and confirmed that oleogels with constant surface area-to-volume ratio could result in identical gelation times and consistent physical properties (MGC, melting temperature, melting enthalpy, yield stress, solid phase content, and oil binding capacity) during scale-up.

Graphical Abstract

Introduction

Food industries are trying to find substitutes for solid fats, especially with the advent of the trans fat ban by the FDA in 2015 (Potera 2015). Since then, partially hydrogenated oils (source of trans fats) are no longer “Generally Regarded As Safe (GRAS)” and mandated industries to reformulate their food products. This has warranted the need to come up with foods lower in trans and saturated fats. Though different oil structuring protocols have been developed over the years for food, cosmetics, and pharmaceuticals, molecular gelation is gaining attention due to the ability to solidify oil through a purely physical means as opposed to chemical means of hydrogenation (full and partial), and interesterification methods. Structured vegetable oils obtained via gelation are known as “oleogels”. These are supramolecular soft materials formed through weak non-covalent interactions such as hydrogen bonding, Van der Waal forces, and π-π stacking (Dassanayake, Kodali, and Ueno 2011). These forces hold gelators together into 3D networks, which in turn impede the flow of oil and provide solid-like nature. Consequently, due to their ease of preparation and thermoreversibility, oleogels are prognosticated as future fat substitutes and have been used to make cakes (Patel et al. 2014), chocolates (Patel et al. 2014), cookies (Yılmaz and Öğütcü 2015), ice creams (Zulim Botega et al. 2013), frankfurters (K. Zetzl, G. Marangoni, and Barbut 2012), spreads (Patel et al. 2014), shortenings (Jang et al. 2015), margarine (Cavillot et al. 2009; Hwang et al. 2013) and, controlled release devices (Zhao, Wei, and Xue 2021; Palla et al. 2022). Though oleogels show promising results at the lab scale, their commercial usage is still in its infancy and has not been explored. Other challenges in adopting oleogels by the food industry are regulative hurdles and high costs of oleogelators (Choi et al. 2020). Despite these challenges, based on these advancements, oleogel technology has been reckoned as a green and sustainable process as the gelators used in this process are either natural (waxes, fatty acids) or bioderived molecules. With the same focus of green chemistry and sustainability, our research group is involved in developing sugar-fatty acyl derivatives as molecular gelators for food applications. Over the years, we were able to structure a variety of vegetable oils using molecular gelators derived from simple sugars (sorbitol, mannitol, xylitol, and raspberry ketone glucoside) and fatty acids.

In the process of oleogelation, we try to attain sustainability by applying green chemistry principles in three steps. Foremost is the selection of raw materials (simple sugars, fatty acids), followed by the choice of methodology (a facile, lipase-mediated transesterification reaction) to synthesize molecular gelators and then the use of gelators to prepare thermosensitive supramolecular oleogels using vegetable oils. Synthesis of biocompatible gelators from natural resources using GRAS protocols seems promising for their further use to prepare foods at the industrial level. Having knowledge and expertise in the field of molecular oleogels for more than a decade (John et al. 2006; Vemula and John 2008; Jadhav et al. 2010), we aim to scale-up the oleogels without compromising key physical properties. In the process of achieving it, we come across some hurdles like inconsistency in minimum gelation concentration (MGC) and rheological properties. To understand this unexpected behavior, where physical properties are not consistent with the increase in oleogel volume, and to predict the possibility of gelation at higher volumes, a mathematical model was developed. Based on the uncertainty associated with the scale-up of molecular oleogels, we set out to investigate their gelation behavior when the volume is raised from 1 mL to 20 mL. In this regard, efforts were made to prepare gels in larger volumes (5 mL, 10 mL, 15 mL, and 20 mL) using the MGC determined with the 1 mL gel (smallest size). However, unstable gels were formed in all the samples. Henceforth, a mathematical model is imperative to understand factors affecting the gelation mechanism and provide the basis upon which stable gels could be obtained regardless of sample volume, hence facilitating the scale-up process for industrial applications. The hypothesis and considerations made to design the mathematical model are briefly explained here.

Since the oleogels in this study are thermosensitive and prepared via simple heating, we hypothesized that gelling behavior is predominantly influenced by the cooling phase associated with the crystallization and propagation of the gelator network during the self-assembly process. Cooling of the oil (gelator and oil mixture) contained in the cylindrical vial is governed by unsteady heat conduction. Although the liquid mixture in the vial is composed of gelator and vegetable oil, the conductivity of oil alone is considered for the modeling. We assumed that the thermal properties of the oil, liquid mixture, and gel are identical because of the very low gelator concentration (< 5 wt. %). Moreover, the thermal conductivity of gelators is unknown as they are new and exclusive studies are needed to determine the thermal nature of gelators. Based on these assumptions and considerations, mathematical modeling was developed. To the best of our knowledge, this is the first of its kind to report the gelation mechanism of oleogels during scale-up using mathematical modeling along with experimental results.

Materials and methods

The sugar alcohols (sorbitol, mannitol), vinyl caprylate (fatty acid precursor), and 12-hydroxy stearic acid (12HSA) were purchased from TCI chemicals, Japan. Soybean oil was a kind gift from Grupo Bimbo^®, Mexico. The sugar fatty acyl derivatives, namely, sorbitol dioctanoate (S8) and mannitol dioctanoate (M8) were synthesized in the laboratory as explained in our previously published studies (Jadhav et al. 2010; 2013). The Preparation of oleogels at MGC was tested at least three times. Further characterization of oleogels and mathematical analyses were conducted in duplicates

Preparation of oleogels

A predetermined amount (0.5 to 5 % (w/w)) of gelators (S8, M8, and 12HSA) was added to soybean oil (1g) and heated above their melting temperature under continuous agitation to form a homogeneous solution. After the complete dissolution of gelators, the homogeneous solution was cooled to room temperature to obtain a gel. The minimum concentration at which the gel formed was designated as the MGC of the gelator. The formation of oleogel was confirmed by the vial inversion method. Then, a set of oleogels for each gelator were prepared using the determined MGC in different volumes (1mL, 5mL, 10mL, 15mL, and 20mL) of soybean oil (Table 1). In other words, the gelator concentration was kept constant at their respective MGC values in all the oleogels. The formation of oleogel at each volume was checked by the vial inversion method (Jadhav et al. 2013). All the samples (both stable and unstable oleogels) were incubated at room temperature. Characterization studies were conducted after 24 h of the sample preparation.

Table 1:

Gelation results: (I) Stable and unstable gels during scale up

Vial diameter (cm)	Oil (mL)	S8		M8		12HSA
		Sample	Result	Sample	Result	Sample	Result
1.2	1.0	S1	√	M1	√	H1	√
1.8	5.0	S2	X	M2	X	H2	X
2.6	10.0	S3	X	M3	X	H3	X
3.5	15.0	S4	X	M4	X	H4	X
5.1	20.0	S5	X	M5	X	H5	X
(II) Stable gels after several trials for each vial size
2.6	3.0	S6	√	M6	√	H6	√
3.5	5.0	S7	√	M7	√	H7	√

√: Stable gel; X: Unstable gel

Rheological studies

Rheological parameters of the gels were determined by a rheometer (ARES-G2, TA instruments, USA) using cone and plate geometry with a cone angle of 0.04 radians. Samples were placed on the stainless-steel plate having a diameter of 25 mm and a 0.5 mm gap was maintained between the cone and plate during the shear. The samples were equilibrated to 25 °C and pre-sheared (0.01 Pa for 30 s) before the analysis, to remove the strain history. An amplitude or strain sweep was performed on the samples by varying the strain from 0.01 to 100 % at a constant frequency (1 Hz).

Thermal studies

A differential scanning calorimeter (DSC) (DSC822^e, Mettler Toledo, Switzerland) was used to determine the thermal parameters of the oleogels. Before the analysis, the instrument was calibrated with pure Indium (melting point: 156.9 °C). Aliquots (20–30 mg) of the gels were taken in pure aluminum (Al) crucibles (maximum volume: 50 μl) and hermetically sealed with a pierced Al lid. The crucibles were placed in the thermal cabinet together with an empty Al crucible as the reference. The crucibles were heated from room temperature to a higher temperature (above the melting point of the gelator) and then cooled to room temperature at 5 °C/min under an inert atmosphere (the thermal cabinet was continuously purged with nitrogen gas). Before the cooling, the samples were kept at the highest heating temperature for 10 minutes to erase the crystal memory (Meng et al. 2019). The obtained data was analyzed using STAR^e software associated with the instrument.

Light microscopy

The microstructure of oleogels was deciphered by viewing under a light microscope, Leica DM 2000 LED (Leica Microsystems, Germany).

Percentage of solids in oleogels

The solid phase content (SPC) of the oleogels was determined by low-resolution time-domain nuclear magnetic resonance (NMR) spectrophotometer (Minispec mq20, Bruker, Germany). The experiment was carried out by following the direct method or AOCS official method Cd 16b-93 (AOCS 2009). 3.5 ml of the molten sample was taken in an NMR tube (diameter: 10 mm) for the SPC analysis. NMR tubes with samples were conditioned at 0 °C for one hour and 30 °C for 30 min before the analysis. On the testing day, before the measurements, the instrument was calibrated with three standards (purchased from Bruker, Germany) having solid fat contents of 0 %, 31.3%, and 73.5%.

Results and discussion

In this study, soybean oil was structured by two sugar-based gelators (sorbitol dioctanoate, S8, and mannitol dioctanoate, M8), and a fatty acid-based gelator (12-hydroxy stearic acid, 12HSA) (Tamura and Ichikawa 1997; Toro-Vazquez et al. 2013). The molecular design and gelling ability of these sugar derivatives have been well established by our group (Jadhav et al. 2010; 2013), and we are currently focussed on enhancing their food and cosmetic applications to meet industrial needs. S8 and M8 are synthesized (with yields as high as 95%) by lipase-catalyzed regioselective transesterification using the respective sugar alcohols and vinyl caprylate at 250 RPM and 50 °C for 48 h. The oleogels were then prepared by dispersing gelators in soybean oil by heating while under agitation, followed by cooling to ambient temperature. For the 1 mL sample, all the gelators formed stable gels as confirmed by the tube inversion (Fig. 1). The MGC of S8, M8, and 12HSA (for the 1 mL sample) were found to be 3.25, 1.25, and 1.0 % (w/v), respectively. For the higher volumes (5 mL, 10 mL, 15 mL, and 20 mL), all gelators failed to form stable gels at their respective MGCs (found for 1 mL oil) (Table 1, Fig. 1). The ability of the stable oleogel to withstand its mass after container inversion is associated with the crystal network that has the appropriate amount of junction zones. The crystal network balances the stress caused by the mass of the samples or unloads it directly on the container. Stable oleogels (S1, M1, and H1) have the ideal lateral surface distance of the container (diameter) compared to the mass that has to be supported. On the other hand, in unstable oleogels, the lateral surface is too small compared to the mass in unstable oleogels, leading to their flow upon vial inversion. Formation of weak crystal junction zones also might be responsible for the flow of oleogels. In such a case, strength of oleogels would be compromised. To confirm this, small-scale deformation tests, in other words, rheology studies were conducted.

Fig. 1.

Oleogels based on: (a) S8, (b) M8 and (c) 12HSA. For each, inversion indicates the 1 mL sample (extreme left) is stable (non-flowing) and others (5 mL, 10 mL, 15 mL, and 20 mL) are unstable (free flowing).

During amplitude sweep, the elastic modulus (G´) is greater than the viscous modulus (G´´) (Fig. 2a–c) which is a feature of solid-like materials or proper gels (S1, M1, and H1 are S8, M8, and 12HSA stable oleogels, respectively; Table 1). However, this feature was also seen with unstable oleogels (S5, M5, and H5 are representative S8, M8, and 12HSA unstable oleogels with maximum oil volume (20 mL), respectively; Table 1) because, though free flowing, gelator network has become more solid-like (G´>G´´) and yet not strong enough to self-support as in stable gels. Such responses can be observed with mineral oils and apolar solvents (Rogers and Kim 2011). The opposite (G´´>G´) is true if the system is too diluted or aqueous (Rogers and Kim 2011). The strength and stability of gels were also judged by evaluating the linear viscoelastic region (LVR) of G´ (G´_LVR), the length of LVR, the difference between G´_LVR and G´´_LVR, and yield stress (Y_s). All the curves have shown that G´_LVR and the length of LVR in stable gels are higher than their counterparts (Fig. 2a–c). Higher Y_s suggested that S1, M1, and H1 are stronger and stable over S5, M5, and H5, respectively (Fig. 2d). Thus, the differences observed in vial inversion and rheometry confirm the inconsistency in gelation of the oleogels when scaled up. This was further assessed using the ‘Winter-Chambon’ gel theory (Chambon and Winter 1987).

Fig. 2.

Amplitude sweeps of (a) S8, (b) M8, and (c) 12HSA oleogels and their (d) yield stress. G´ and G´´ are shown as closed and open symbols, respectively.

‘Winter-Chambon’ theory or gel theory

Consistent gelation behaviors were indeed not maintained with larger sample sizes although the respective MGC values were kept constant, the gelation behavior was further assessed using the ‘Winter-Chambon’ theory (Chambon and Winter 1987). According to this theory, gelation is a transition from viscoelastic liquid to viscoelastic solid. The gelation at the cross-over point is given by the Winter-Chambon gel equation which follows the power law (Curtis et al. 2015), G(t) = St^−α, where, G(t) denotes the stress relaxation modulus at time t, S is the gel strength parameter or stiffness and α is the stress relaxation exponent. S and α are material property parameters necessary to characterize the linear viscoelastic properties at the time of gelation. α was established by considering the phase angle (δ) between stress and strain during the gel-to-sol transition, tanδ = G″/G′ and α = 2δ/π. α values vary between 0 and 1; the lower and higher limits correspond to the solid- and liquid-like nature of the formulations, respectively.(Izuka, Winter, and Hashimoto 1997) The observed α values indicate that S5, M5, and H5 possess higher liquid component over solid component (Table S1), as a result of poor gelation. The increase in α associated with the decrease in ‘S’ and fractal dimension (D_f), D_f = (D + 2)(2α − D)/(2(α − D)), D is the Euclidian or space dimension (D=3) (Izuka, Winter, and Hashimoto 1997; Muthukumar 2002). The stiffness of S8, M8, and 12HSA stable oleogels is ~500, ~180, and ~900 pa.s^α, respectively; on the other hand, S5, M5, and H5 have ~39, ~69 and ~382 pa.s^α, respectively. The increase in D_f (Table S1) suggests the increase in the dimensionality of the crystal growth and formation of a stronger gelator network in stable gels and the growth of the network seems to be hindered when the same scaled up.

To support the veracity of the observed trend, more samples were prepared, and their gelation behavior was observed (Table S2). The results still suggested that higher volumes of oil failed to gel at MGCs. However, when a large number of gels were prepared in two vials with diameters 2.6 cm and 3.5 cm, interestingly, these vials could withstand stable gels up to a certain volume of oil (Table S2). The maximum amount of oil that was gelled using vials with 2.6 cm and 3.5 cm was 3 mL and 5 mL, respectively and the results are shown in Table 1(II). This indicates that by using MGC, oil can be gelled at higher volumes (beyond the smallest volume, 1mL) depending on the diameter of the vial. To understand this unexpected outcome, a time-dependent investigation was conducted on stable and unstable gels. After finely dispersing the gelators and setting for cooling (t=0), the gelator-oil mixture was transparent and as time progresses, turbidity started appearing at the bottom of the vials (shown in red circles) and then progressed to the top (Fig. 3). In case of stable gels, turbidity appeared uniform (relatively) throughout the vials. This indicates that uniform and non-uniform gelation might be happening in stable and unstable gels, respectively. The disparity in turbidity which is associated with gelator network formation can be directly related to heat dissipation from vials. To elucidate how diameter (of vial) and volume (of oil)—parameters associated with heat dissipation—influenced the gelation and consistency of physical properties, a mathematical model was developed.

Fig. 3.

The gelation of unstable (left) and stable (right) oleogels

Mathematical model

The model was based on the fact that heat transfer from a hot cylindrical vial takes place in all directions. The cooling process during oleogelation satisfies this condition by having two modes of heat transfer—across the radius and length of the vial. This is governed by the unsteady (assumed axisymmetric) heat conduction equation for the temperature, which is nondimensionalized using the length scale H, and the time scale H²/κ_oil where κ_oil is the thermal diffusivity of oil (Bird, Stewart, and Lightfoot 2002).

$$\frac{\partial \Theta }{\partial \tau }=\left\{\frac{{\partial }^2\Theta }{\partial z^2}+\frac{1}{r}\frac{\partial }{\partial r}\left\{r\frac{\partial \theta }{\partial r}\right\}\right\}$$

$$\Theta =\frac{T-T_a}{T_i-T_a}$$

where Θ (z, r, τ) is the nondimensionalized temperature, In the above, T is the dimensional temperature, and T_a and T_i are the dimensional ambient and initial temperatures. As shown in Scheme 1, H is the height of liquid in the vial, a is the inside radius of the vial, and r and z are the radial and axial nondimensional coordinates, scaled by the height ‘H’ of the oil in the vial and τ is the nondimensional time, scaled by H² ⍴_oil C_oil/ k_oil where _oil and C_oil are the density and heat capacity of the oil. The physical properties of the oil and gel are considered equal because of the low concentration of gelator and are given in the Supporting Information.

Scheme 1:

Vial with possible heat transfer from the hot gelator-oil mixture to the surroundings

As the oil cools to gel, heat is conducted out of the oil in in three possible ways, from the open top interface into the ambient gas phase with a heat transfer coefficient h_T and, from the bottom and sides with h_B and h_S, respectively. The resistance to heat transfer is much larger near bottom and sides against top surface as glass is at the interface and also the difference in air flow near the sides and bottom of the vial has made the system to be even more complex. Thus, three independent heat transfer coefficients are needed to account for the cooling process.

Rate of cooling near the three surfaces with respect to the axial and radial positions is given by the following nondimensional equations which account for natural convection (Chapman 1984):

$$\begin{gathered} -{\left[\frac{\partial \Theta }{\partial z}\right]}_{|z=0,r}\text{ +}\left[\frac{k_{\mathit{\text{air}}}}{k_{\mathit{\text{oil}}}}\right]\left[\frac{H}{1.8a}\right]{\text{Bi}}_B\Theta (r,z=0)=0 \\ {\left[\frac{\partial \Theta }{\partial z}\right]}_{|z=1,r}\text{ +}\left[\frac{k_{\mathit{\text{air}}}}{k_{\mathit{\text{oil}}}}\right]\left[\frac{H}{1.8a}\right]{\text{Bi}}_T\Theta (r,z=1)=0 \\ {\left[\frac{\partial \Theta }{\partial r}\right]}_{|z,r=a/H}\text{ +}\left[\frac{k_{\mathit{\text{air}}}}{k_{\mathit{\text{oil}}}}\right]{\text{Bi}}_S\Theta (r=a/H,z)=0 \end{gathered}$$

where Bi represents the Biot number for the particular surface bounding the gel and are given in the supporting information.

The general solution for the nondimensional temperature field Θ(z, r, τ) assuming an initial temperature T_i is:

$$\begin{gathered} \Theta (r,z,\tau )=\sum _{p=1}^{\infty }\sum _{i=1}^{\infty }{a}_{pi}{e}^{-\left\{{\lambda }_i^2+{\beta }_p^2\right\}\tau }{R}_p(r)Z_i(z) \\ {a}_{pi}=\frac{\underset{0}{\overset{a/H}{\int }}\underset{0}{\overset{1}{\int }}Z(r)R(r)rdrdz}{N_{Z,\text{ i}}^2{N}_{R,p}^2} \end{gathered}$$

where

1. Z_i(z) and R_p(r) are eigen functions in z and r directions respectively and given by

   $Z_i(z)=\frac{B{i}_B}{{\lambda }_i}\text{sin}{\lambda }_{i}z+\text{cos}{\lambda }_{i}z$ with eigen values λ_i that satisfy $B{i}_B+B{i}_{B}B{i}_T\frac{\text{tan}{\lambda }_i}{{\lambda }_i}+B{i}_T=0$,

   R_p(r) = J_o(β_pr) with eigen values β_p that satisfy $J_1({\beta }_p\frac{a}{H})-\frac{1}{{\beta }_p}{\text{Bi}}_S{J}_o({\beta }_p\frac{a}{H})=0$;

2. N²_z,i and N²_R,p are eigen function normalization constants and given by

   $$N_{Z,i}^2=\frac{1}{2}+\frac{1}{4}sin2{\lambda }_i+\frac{B{i}_B}{{\lambda }_i}sin2{\lambda }_i+\frac{B{i}_B}{4{\lambda }_i^2}\left\{1+cos2{\lambda }_i\right\}$$

   $$N_{R,p}^2=\frac{a^2}{H^2}\left\{1+\frac{B{i}_S^2}{{\beta }_p^2}\right\}{J}_o^2({\beta }_p\frac{a}{H})$$

The eigen values λ_i and β_p are solved first from their transcendental equations to obtain the eigen functions, and the coefficients a_pi are then obtained. Finally, for a particular value of z and r, the transition time (τ_tr) required to cool down to the transition (crystallization or melting) temperature Θ_tr = T_tr − T_a/T_i − T_a (where T_a = 25 °C; T_i = 140 °C; T_tr = transition temperature (can be either crystallization (T_c) or melting (T_m) temperature of gels, measured using DSC (Table S4)) is obtained from the general solution. In detail, the position r,z is fixed along with the time t (starting at a time just past zero), and the series is summed over a finite number of terms to get the temperature using Matlab. The number of terms is then increased until the result for the temperature does not change to a given precision (one percent), indicating the remaining terms are not needed for this precision. The time is then increased with the position fixed and the process is repeated to get a new temperature. This process is repeated in time until the transition temperature is reached, at which point the time for gelation at that spatial point is recorded. The entire process is then repeated for a different position. To construct Fig. 4, this procedure is repeated at ten radial and 5 axial positions to generate the three-dimensional plot of the transition time. The transition temperature is achieved as a function of radial and axial position as given in Fig. 4. The numerical procedure was verified in the limits in which the heat transfer coefficients are large and the surfaces are at fixed temperature which are classical problems with numerical solutions presented in the literature (Bird, Stewart, and Lightfoot 2002).

Fig. 4.

The surface plots, showing transition times (τ_tr) of stable (S1, H1, M1) and unstable (S5, M5, H5) oleogels concerning axial and radial positions. In all the plots, the upper surface represents crystallization and the bottom surface represents the melting phenomenon of gelators across the vials. The color scale in the surface plots indicate time in sec.

The calculated transition times (τ_tr) of crystallization and melting at the axial and radial locations of stable and unstable gels were plotted (Fig. 4) in dimensional form. The transition times of stable gels are confined to a small time range, unlike their unstable counterparts. The transition times of unstable gels were found to increase from the periphery towards the center of the vial in both axial and radial directions, suggesting that gelation happened quicker near the boundary compared to the center of the vial. On the other hand, stable oleogels have shown near identical transition times in all directions, suggesting uniform gelation across the vials. This indicates that, when the sample volume is raised, stability of oleogels can be achieved by maintaining uniform or identical transition times across the vial of any diameter.

These intriguing findings suggest that heat dissipation and transition times have to be uniform throughout the vial in order to achieve stable oleogels irrespective of volume. In this regard, we have hypothesized that by maintaining a constant surface area-to-volume (S/V) ratio of sample in the vials, uniform heat dissipation and identical transition times could be achieved. By considering the S/V ratio of the stable gel (e.g. S1) as the reference value (5), the volumes that need to be taken in other vials were calculated (Table S3). When tested, they formed stable gels at MGC of the smallest vial (Fig. 5). Upon careful observation, we noticed that the volumes that formed gels for the vials with diameters 2.6 cm and 3.5 cm (Table S3) coincided with the volumes of stable gels with same vial diameters in Table 1(II). This indicates that the same S/V ratio was retained to facilitate the formation of stable gels during trials. By maintaining the same S/V conditions, transition times were calculated using the developed mathematical model. Surface plots showed identical transition times (Fig. S1), suggesting uniform heat dissipation from the stable gels.

Fig. 5.

Stable (a) S8, (b) M8, and (c) 12HSA oleogels having the same S/V ratio. Diameters of the vials are given at the bottom of the respective vials.

Based on the surface plots, the cooling rate from melting to crystallization (phase transition) at different axial and radial locations in each vial was calculated. Fig. 6 suggests that the cooling rates of stable gels are faster as compared to unstable gels. These cooling rates provide crucial insight regarding the phase transition and self-assembly of molecular gelators during gelation. During self-assembly, the prevalence of thermal gradient results in a higher time gradient for nucleation in different locations of vials which in turn arrest the propagation of a continuous 3D network. When network propagation is incomplete, the self-assembled gelators aggregate and undergo sedimentation under the influence of gravity. Consequently, unstable gels have shown non-uniform cloudiness (Fig. 3) and non-uniform transition times (Fig. 4) in the vials. Fig. 6 suggests that gels are more stable with faster cooling rates, which seem to have facilitated the propagation of a self-assembled network throughout the vial, henceforth uniform cloudiness in vials. The developed model was extended to evaluate the gelation of 20 mL of soybean oil using S8 and M8. The model has suggested that to gelate 20 mL of oil at MGC, a vial with a diameter of 7.5 cm is necessary so that the heat dissipation will be uniform throughout the vial and form stable gels (Table S3, Fig. S2) with cooling rates during phase transition (Fig. 6) are similar to that of other stable gels. Based on the tests conducted, the developed mathematical model seems to have the capacity to predict the stability of the oleogels during scale-up. This was verified by conducting a series of tests to evaluate the physical properties of oleogels before and after considering the mathematical model-based scale-up.

Fig. 6.

Cooling rates of stable and unstable oleogels

Evaluation of physical properties of oleogels

DSC studies

Melting thermograms of the selected samples are shown in Fig. 7a–c. A single peak was observed in the melting endotherm of all samples, suggesting that the gelators are highly pure and completely dispersed in soybean oil. The peak temperature corresponding to the endotherm is regarded as the melting temperature (T_m) and the area under the endothermic curve is represented as the fusion enthalpy (ΔH_m) of oleogels. The melting parameters (T_m and ΔH_m) of S5sv were found to be close to S1, but a significant difference was observed between S5 and S1 (Table S4). The same trend was followed in the endotherms of M8 and 12HSA-based oleogels as well (Table S4). The presence of such melting profiles suggests that similar thermal behavior of oleogels could be achieved by maintaining a constant S/V ratio. Higher T_m and ΔH_m values of oleogels with the same S/V ratio indicate that these oleogels are thermally more stable as compared to oleogels without constant S/V ratios (S5, M5, and H5). Henceforth, uniform melting parameters were achieved in formulations irrespective of the solvent volume when their S/V ratio was kept constant.

Fig. 7.

(a), (b), (c) Melting endotherms and (d, e, f) crystallization exotherms of the oleogels. Areas under the melting and crystallization peaks were calculated as Fusion enthalpy (ΔH_m) and crystallization enthalpy (ΔH_c), respectively.

Thermal stability of oleogels can be further explained by crystallization exotherms (Fig. 7d–f). The crystallization onset temperature (T_co) and crystallization temperature (T_c) of the samples have followed a similar trend (Table S4) as that of the melting temperature of the endotherms. In general, the crystallization of LMWGs is facilitated by the heat release during non-covalent interactions between gelator molecules. The released heat during the phase change of gelators from their solubilized state to the self-assembled crystals is referred to as crystallization enthalpy (ΔH_c) and was measured by calculating the area under the exothermic crystallization curve. The crystallization enthalpies of S5, M5, and H5 were found to be lower than that of the stable oleogels (Table S4), suggesting that less amount of heat was released. During the phase change, less number of solubilized molecules might have converted to solid networks which lead to the formation of weak gels. In the case of stable oleogels, more gelator molecules might have crystallized and resulted in higher crystallization enthalpy. The released heat during crystallization is in general, countered by the entropic forces associated with the demixing of gelators during crystal nucleation. Based on the crystallization enthalpy, the change in entropy during the phase change or crystal nucleation was calculated by ΔG = ΔH_c − T_c ⋅ ΔS_c, where, ΔG is the change in Gibbs free energy and ΔS_c is the change in entropy during crystallization (Sagiri et al. 2015).

When the sample reaches crystallization temperature, Gibbs free energy tends to be zero (Lam and Rogers 2011) by considering this, entropy change during the phase change was calculated (Table S4). Interestingly, change in entropy during crystallization was found to be lower for the unstable formulations (S5, M5, and H5), and on the other hand, it is higher and consistent in stable gels, suggesting that the stable gels have followed a uniform crystallization process. Since entropy is a measure of disorderedness, lower entropy change associated with the unstable formulations suggests that the phase change of gelators from disordered liquid molecules to ordered crystals has been minimal. Thus fewer gelator molecules have undergone phase change from the liquid state to the crystals. This led to the lack of well-defined crystals for the immobilization of solvent which in turn has yielded unstable oleogels. The time-dependent transformation of gelators from solution to gel state was verified by fitting the crystallization data in the Avrami equation and the analysis is given in supporting information.

For a better understanding of the gelator crystals, light microscopy was conducted and the results are shown in Fig. S6. Irrespective of the oleogel stability, all gelators showed similar crystals in the tested oleogels. S8 formed small, irregular, and needle-like crystals. On the other hand, M8 and 12HSA formed long, fiber-like crystals. In addition to crystal size and shape, a distinct difference in crystal density was noticed between S8 and, other (M8 and 12HSA) oleogels (Fig. S6). Higher MGC of S8 (3.25 % (w/w)) against M8 (1.25 % (w/w)) and 12HSA (1.0 % (w/w)) is responsible for the observed crystal density of oleogels. Amongst the S8 oleogels, S5 showed a less dense gelator network with no significant difference in crystal size and shape. This kind of distinction was not observed between the stable and unstable oleogels of M8 and 12HSA. Figure 6 indicated that stable oleogels are having faster cooling rates compared to unstable oleogels. Literature suggests that faster cooling rates yield smaller crystals and vice versa (Giacomozzi et al. 2019). It was expected that microscopic observation would confirm this result by having distinct large crystals in stable oleogels (e.g. S1, S5sv) against their counterparts (e.g. S5). Bright-field microscopy did not reveal such a gelator crystal network orientation in the studied oleogels. This could be due to the less prominence of the crystal size differences in the studied oleogels. It seems a high cooling rate difference must be maintained to achieve significant change in crystal sizes. Giacomozzi et al. have identified the crystal size differences in monoglycerides when they were subjected to 0.1 °C/min and 10 °C/min cooling rates (Giacomozzi et al. 2019). In the present study, such a high difference in cooling rates was not observed (Figure 6). Though the variation in crystal size was not deciphered, its impact on the strength of oleogels was identified by performing rheology studies.

Rheology studies

The difference in crystallinity has in turn affected the strength of the oleogels, proved by rheological studies. Higher Storage modulus and yield stress of stable oleogels indicate their higher strength over the others (Fig. 8). Amplitude sweep data also shows that the G´ curves of stable oleogels are overlapping, suggesting that the rheological parameters (LVR, strength) of the oleogels have been conserved after maintaining the constant S/V ratio. Winter-Chambon theory has also suggested that although oil volume is increased (e.g. S5sv), stiffness and stress relaxation component remained same as that of the other stable oleogels (e.g. S1). Having the same/similar stiffness and stress relaxation for oleogels suggest the same dimensionality in the gelator network during gelation (evident from fractal dimension (D_f) data, Table S1). Avrami crystallization kinetics also suggested the increase in dimensionality during the crystal growth of stable oleogels with the same S/V ratio (supporting information). The relaxation exponent and fractal dimension of the stable oleogels not only support the higher gel strength but are also very consistent with each other. This kind of consistency was achieved due to the maintenance of a constant S/V ratio during the preparation of oleogels in different volumes. The differences associated with the relaxation exponent and fractal dimension have affected the gel strength of the oleogels. The gel strength or stiffness of stable oleogels was found to be higher against S5, M5, and H5. The stiffness of S8, M8, and 12HSA stable oleogels is in the range of ~500, ~180, and ~900 pa.s^α, respectively (Table S1). Though the sample volume was increased, the stiffness of the stable oleogels corresponding to each gelator has not varied at an alarming level.

Fig. 8.

Amplitude (at frequency 1 Hz) sweeps of (a) S8, (b) M8, and (c) 12HSA oleogels. G´ and G´´ are shown as closed and open symbols, respectively. The (d) yield stress of the oleogels was shown.

Conclusion

The present mathematical and analytical study showed that a minimal thermal gradient across the oleogels has to be maintained during scale-up. Our results have also shown that the oleogels to be scaled up should possess an S/V ratio as that of the sample used to determine the MGC (in our case, the smallest sample). We believe that having a constant S/V ratio across all the samples facilitates identical physical properties of the oleogels because it results in uniform heat dissipation as confirmed by the results from the developed mathematical model. Having minimal thermal gradient and faster cooling rates during phase transition are crucial to achieving stable oleogels and physical consistency irrespective of their volume. The consistency of physical properties such as thermal, rheological, SPC and OBC of oleogels was also evaluated in detail. This is a preliminary work of its kind. Further studies to evaluate the effect of the thermal gradient across the vials on the crystallization of gelators (as it affects the quality of structured oil (fat)) and the large-scale deformation of oleogels (for the evaluation of textural properties like firmness and spreadability) may provide additional insights into their use as future trans-fat alternative in food, cosmetic and pharmaceutical formulations.