Dynamics of Changes in Viscoelastic Properties of a Tofu During Frying

Abstract

The viscoelastic properties of a tofu were characterized using the stress relaxation test after deep-fat frying at 147–172°C for 0 to 5 minutes. The results were expressed with a model with two Maxwell elements and a residual spring in parallel. Each elastic modulus and relaxation time followed zero order reaction kinetics. The Arrhenius temperature dependency was applied for the modeling of reaction rate constant, k. The activation energies for the viscoelastic properties were 1.00 × 10⁵ − 1.49 × 10⁵ J/mol. There was a good agreement between the measured and computed data (R² = 0.976 − 0.988).

Keywords:

• Stress relaxation
• Maxwell element
• Elastic modulus
• Activation energy
• Reaction rate constant

INTRODUCTION

The tofu (soybean curd) is one of the popular Eastern origin health foods. Tofu has functional properties (anti-cancer and brain activity elevation) and high nutritional value (65% of net protein utilization).[1] Tofu is cooked in various modes, such as baking, boiling, microwave heating, pan frying and deep-fat frying.[2] The deep fat frying is the most popular mode for commercial products. A proper level of frying results in better texture and a more desirable appearance of the product compared to those of raw tofu.

In order to predict and control the product quality during deep fat frying, kinetic studies on quality parameters, such as color and viscoelastic properties are important. Predictive models for the surface color changes of a tofu during deep fat frying were developed using first order reaction kinetics and a temperature dependent reaction rate constant.[3] The models were solved using the Runge-Kutta method of fourth order, along with variable surface temperatures of product. The studies on the rheological behavior of tofu have been limited to fresh and modified tofu by chemical and physical methods. Cai and Chang[4] observed the coagulant (CaSO₄) concentration impact on the texture profiles of the tofu made from Proto soybean. For the unit operation, a blade size of 4 cm × 7 cm (thickness not shown), and a stirring time of 10 minutes were applied. As the coagulant concentration increased from 16.5 mM to 21.9 mM, the hardness of the middle part of the tofu increased from 635 to 2346 g, while the elasticity index increased from 19.7% to 62.9%. Other researchers[5,6] observed the effects of carageenan and high pressure freezing treatment on the tofu texture.

The viscoelastic properties of other food materials were presented by several investigators. Lima and Singh observed the viscoelastic behavior of fried potato crust using a dynamic mechanical analyzer.[7] Stress relaxation properties were described by a two-element Maxwell model with a parallel spring. Correia and Mittal[8] studied the kinetics of stress relaxation of meat batters during smokehouse cooking. Using zero order reaction kinetics and Eyring’s absolute reaction rate theory, kinetic models were developed to predict viscoelastic parameters of meat batters as a function of product temperatures and cooking times.

During the frying of tofu, its components undergo physicochemical changes, which affect its texture. Pant et al.[9] compared tofu textures before and after frying at 185°C for 4 minutes. The hardness of tofu increased from 3.4 to 13.2 N after frying. No detailed kinetics of viscoelastic properties of tofu during thermal treatment or cooking was investigated. Thus, in this study, kinetics of viscoelastic properties of tofu was studied during deep fat frying at various oil temperatures. This will enable us to predict texture changes during the process and achieve improvement of product quality through optimization of processing conditions.

MATERIALS AND METHODS

Tofu

Commercial tofu (extra firm variety, 350 g packets, Toronto based manufacturer) was obtained. For uniform quality, the outer layer of the tofu (∼ 0.4 cm) was peeled off using a sharp knife due to its potential unique dense structure caused from mechanical pressure during its processing. Disc samples (diameter: 57 mm, height: 10 mm) were prepared using a sharp cylindrical cutter and a slicer. The average initial chemical composition (w/w) of the samples was 71.9% water, 15.9% protein, 8.75% fat, 2.0% carbohydrates, 1.1% fiber, and 0.3% ash. Moisture and fat contents were determined by drying and Soxhlet method, respectively.[10] Other compositions were from chemical analysis provided by the manufacturer.

Deep Fat Frying

An electric powered fryer (T-fal Supercontrol home deep fryer, SEB Canada Inc., Scarborough, ON) was used for frying. The oil temperature was maintained at desired temperatures within ± 0.7°C with the help of an additional proportional temperature controller (CN3910AJC/S, OMEGA Inc., Laval, QC). The fryer was equipped with a metal mesh basket in which the sample was placed. The basket moved up and down easily and instantly by a switch outside the fryer. A sample holder was specially designed to ensure complete immersion of the sample below the oil surface at the same frying position and angle. The frame was made of stainless steel, and the sample holding parts were made of Teflon. The tofu disc was ∼4 cm below the oil surface and ∼4 cm above the bottom of fryer. The frying medium used in this study was fresh hydrogenated vegetable oil. To minimize variations of oil properties due to degradation, the oil was changed after 3 hours of frying. Oil temperatures were 147, 160, and 172°C, which were measured about 1.5 cm above sample’s surface using a T-type thermocouple with a junction diameter of 0.5 mm.

Stress Relaxation

Cylindrical specimens measuring 20 mm in diameter and 10 mm in length were prepared by a cork borer. The samples were positioned parallel to the compression plates. Stress relaxation tests were performed on a universal testing machine (Model 4204, Instron Corp., Burlington, ON, Canada). Crosshead speed was 50 mm/min. The specimens were compressed to 90% of their original height for 9 min. Up to the strain level of 10%, all of the samples showed a linear viscoelastic behavior in our preliminary tests. The force decaying-time curves were recorded at intervals of 5 points/s, using a PC-based data acquisition software (Labview version 6.0, National Instruments Co., Austin, TX). The stress relaxation data were fitted using a discrete linear-Maxwell model:[11]

(1)

where E_t is the modulus of elasticity at time, t, N; E₀ and E_i are the elastic moduli of the spring, N; τ_i is the relaxation times of Maxwell elements, i.e. η_i/Ei, s; η_i is the apparent viscosities of Maxwell elements, N.s. A computer program[12] was used for the fitting, which was based on the successive residual method. The number of Maxwell elements was determined based on the fitness of the model tested; the details will be discussed later.

Volume Average Temperature

A tofu disc was immersed in oil with several thermocouple (TC) probes (TMQSS-020-6, T-type subminiature, OD: 0.508 mm, OMEGA Inc., Laval, QC) inserted into the tofu at 1 mm and 3 mm, from top and bottom surfaces, and at the product center. For the measurement of surface temperatures, two T-type thermocouples were fixed at the surfaces using alligator clips. The tip (∼2 cm) of the TC was bent and made contact with the surface. The thermocouple was positioned slightly below (∼0.2 mm) the tofu surface. After frying, the TC contacts were verified again. If the TC tip became embedded in the crust or pushed beyond the surface, the data set was discarded. The temperature acquisition system consisted of a data-logger (LabMate model 902 CPU, Sciemetric Instruments, Nepean, ON), and a portable computer. A BASIC program was used to collect data on the portable computer from the data acquisition system. Temperature data were recorded at 5 s intervals during the experiment. All TC probes and wires used in this study were calibrated using boiling water and ice water. The volume average temperature was calculated by taking temperature gradients (temperature vs. distance) within the product at a given time. Temperature locations at 7 locations as a function of time were used. Then the curve was numerically integrated (50 space intervals), and the volume average temperature was then calculated by dividing area by sample thickness.

Kinetics Modeling

The changes of stress relaxation properties were modeled using reaction kinetics and the Arrhenius equation. The ratios of viscoelastic parameters, E₀, E₁, E₂, τ₁, and τ₂ were defined as follows:

(2)

where, subscripts, max, min, and t represent maximum, minimum, and specific values at time, t, respectively. The change rate of viscoelastic parameters (P = A, B, C, I, and J) can be modeled using the following reaction kinetics equation:

(3)

where k is reaction rate constant, s⁻¹; n is the order of reaction. The temperature dependence of the reaction rate constant can be expressed using Arrhenius’ relationship:

(4)

where k₀ is frequency factor, s⁻¹; E_a is activation energy, kJ/mol; R is gas constant, 8.314 kJ/ (K.mol); and T is absolute temperature, K. The volume average temperature was used to relate the reaction rate constant with reaction system temperature. Eqs. (2, 3, and 4) were solved using a simulation language, ISIM[13] with the Runge-Kutta method of fourth order. The k₀, E_a, and n were obtained by minimizing the root mean square of deviations (σ) between predicted and observed data using the pattern search algorithm.[14]

(5)

where N is the number of data set.

Data Analysis

The data were analyzed using SAS/ANOVA.[15] Duncan’s multiple range tests were also performed to compare means.

RESULTS AND DISCUSSION

Volume Average Temperature (VAT)

Fig. 1 shows the volume average temperatures of the tofu during frying at 147, 160, and 172°C. The volume average temperatures rose rapidly up to 85–103°C until the frying time of 120–180 s then gradually increased with maximum 105.0–110.6°C during frying. The average coefficients of variance (CV) of the VAT for frying replication were 2.8%, 2.8%, and 6.3% at 147, 160, and 172°C, respectively. The average CVs for post-150 s frying were lower as 1.4%, 2.5%, and 3.6%, respectively. The VAT data were fitted into polynomial equations of third order (Eqs. 6–8) to be used in the kinetic simulation of viscoelastic parameters of tofu during frying.

(6)

(7)

(8)

where T_{k, vol} is volume average temperature, K.

Figure 1. Volume average temperatures of tofu during frying at 147–172°C.

Stress Relaxation Model

A model with two Maxwell elements and a residual spring in parallel was most acceptable for the characterization of the viscoelastic properties of the tofu. The model (Eq. 9), thus, includes three elastic spring components (E₀, E₁, and E₂) and two time constants (τ₁ and τ₂).

(9)

After adding two Maxwell elements, an increase in the number of Maxwell elements in the model did not affect the fitness of the relaxation data significantly (ΔR² < 0.05). In our preliminary tests, samples with various frying levels were exposed to a very long relaxation duration (about 5 hours), and none of the samples relaxed completely showing residual stresses was zero. E₀, the elastic spring element, in parallel with the Maxwell elements accounts for this residual stress in the tofu. The correlation coefficient between model and experimental data averaged 0.99, which suggested that the selected model was acceptable to represent the stress relaxation properties of the tofu samples during frying. A typical plot of calculated stress from the model and measured data with relaxation time is shown in Fig. 2. In spite of the experimental noises, both curves overlapped with each other.

Figure 2. Experimental and calculated stress relaxation curves of fresh tofu.

Modulus of elasticity

The initial time-dependent modulus of elasticity of fresh tofu, E_t at t = 0, was 11.6 N. According to the model, the initial time-dependent modulus is equal to the sum of the elastic moduli of the three Maxwell springs (E₀ + E₁ + E₂). Before frying, E₀, E₁, and E₂ of the tofu were 2.8, 3.8, and 4.9 N, respectively. The value of elastic modulus increases for stiffer materials. During 5 minutes of frying at 147, 160, and 172°C, E₀, E₁, and E₂ increased to 5.6–8.1 N, 8.0–11.9 N, and 9.4–13.9 N, respectively with non-linear fashion depending on frying temperatures (Fig. 3). The effect of replication was not significant at the 5% level for each elastic modulus. The effects of frying temperature and frying time, however, were significant (p < 0.01 for both). Higher frying temperature, consequently higher product temperature caused higher elastic modulus of the product suggesting the tofu became stiffer and more elastic during frying.

Figure 3. Changes of elastic moduli, E₀, E₁, and E₂ of tofu during frying at 147–172°C.

The order of kinetic reaction was zero for all viscoelastic parameters. With zero order kinetics and constant k, the viscoelastic parameters change linearly with time. In this study, reaction rate constant, k was temperature dependent, thus the non-linear fashion in Fig. 2 was from the reflection of the product temperature changes during frying. Root Mean Square (RMS) values between calculated data and measured data were 0.264, 0.297, and 0.280 N for E₀, E₁, and E₂, respectively (Table 1).

Table 1 Summary of viscoelastic properties kinetics of tofu during frying

Parameters	Ea (J/mol)	k0	R^2	RMS ^a	d.f. ^b
E0	1.49 × 10^5	1.55 × 10^18	0.976	0.264	15
E1	1.31 × 10^5	5.02 × 10^15	0.984	0.297	15
E2	1.00 × 10^5	2.71 × 10^11	0.988	0.280	15
τ1	1.01 × 10^5	3.70 × 10^11	0.978	2.07	15
τ2	–	–	–	–	15
^aRMS = root mean square of deviation, Eq. 5.
^bd.f. = degree of freedom for error.
n = order of reaction, 0 for all parameters.

The apparent activation energies for the elastic modulus dynamics during frying were 149, 131, and 100 kJ/mol for E₀, E₁, and E₂, respectively. As moisture variation in the product was associated with kinetic parameters, the term “apparent” was used. These values are comparable with those for texture changes of peas during cook-chill processes [traditional cook-chill (CC) and sous vide cook-chill (SVCC)].[16] The activation energies were 147 kJ/mol (CC) and 126 kJ/mol (SVCC) for peak compression force and 112 kJ/mole (CC) and 168 kJ/mol (SVCC) for peak puncture force. Activation energies in our study were higher than those (40–98 kJ/mol) for thermal degradation of green asparagus texture at 70–100°C heating[17] and lower than those (393–786 kJ/mol) for the shear change of beef semitendinosus muscle.[18] Correia and Mittal[8] characterized kinetics of viscoelastic properties of meat batters during smokehouse cooking. They applied Eyring’s absolute reaction rate theory (Eq. 10) for temperature dependency of reaction rate constant, k.

(10)

Where, R is the gas constant, 8.314 kJ/ (kg.mol.K); K is the Boltzman’s constant, 1.38 × 10⁻²³ J/K; h is the Planck’s constant, 6.625 × 10⁻³⁴ J.s; ΔS is the entropy change of activation, kJ/ (kg.mol.K); and ΔH is the enthalpy change of activation, kJ/(kg.mol). For the comparison between the activation energies of tofu frying and those of meat batter cooking, the ΔH was converted to E_a using the following relationship.[19]

(11)

At average product temperature, 50°C, the converted E_a were 21.5–59.0 kJ/mol and 6.69–79.3 kJ/mol for E₁ and E₂, respectively. This suggested that hardening of tofu by frying is less temperature-sensitive than that of meat during smokehouse cooking.

Relaxation Times

Relaxation times represent viscous behavior, a measure of how fast the stress decays and are frequently used rather than the quantity, η _i /E_i .[8] A compressive force applied to a tofu during stress relaxation was assumed to split into two parallel forces: one through continuous phase (i.e. aqueous protein matrix), and the other through both the continuous phase as well as discrete phase (i.e. tofu-protein and fat globules). The relaxation time, τ₁, representing both the continuous and discrete phases, was 100 s at the frying time zero and maintained up to the frying time 120 s, then it increased 1.3–1.5 fold at the end (Fig. 4). A material that has a longer relaxation time 1 (τ₁) indicates that the dashpot in the Maxwell element-1 cannot quickly dissipate the stress exerted by the spring, thus less viscous than elastic in nature. Lima and Singh[7] studied viscoelastic properties of fried potato crust. The applied frying temperatures were 170–190°C and frying time 5, 10, and 15 min. There were no results shown for their fresh potato (at the frying time of 0 minutes). From 5 to 10 minutes frying, relaxation time decreased and then slightly increased or tapered off from 10 to 15 minutes frying. As frying progresses, bigger pore sizes develop at the crust, which holds more oil. The oil contributes a viscous component to the overall viscoelastic behavior of the crust and possibly allows a faster recovery of stress. Stress relaxation in a fried crust might be due to many factors, such as slippage of the dispersed oil through the solid crust matrix, or/and from rearrangements of the void structures.[7]

Figure 4. Changes of relaxation times, τ₁ and τ₂ of tofu during frying at 147–172°C.

In our study, the whole products were subjected to stress relaxation. Assuming that the tofu crust relaxed in the similar manner of potato crust, the increase in the relaxation time of whole tofu during frying suggested that the viscoelastic properties of whole tofu largely depends on those of crumb.

The apparent activation energy of τ₁ changes during frying of tofu was 101 kJ/mol. This value was much higher than that (−2.7–3.2 kJ/mol), calculated from ΔH using Labuza’s equation for average product temperature of 50°C of meat batters during smokehouse cooking by Correia and Mittal.[8] This implies that viscous factors of the tofu cannot easily change compared to that of the meat batter during thermal processes. Except the study with meat batters, there is no traceable information on the activation energy of relaxation time changes during heating processes of other food materials.

The τ₂, representing the continuous phase, were 7.7–8.6 s during frying (Fig. 4). The τ₂ values are associated with liquid behavior of the sample; consequently, they were much smaller than the τ₁ values, which are associated with the solid behavior. Due to no discernable increase in τ₂ with frying time and temperature (p > 0.05), no kinetic model was established to predict τ₂.

CONCLUSIONS

The dynamics of viscoelastic properties of tofu during frying was characterized with reaction kinetics and Arrhenius equation. Reasonable prediction was possible for elastic moduli, E₁, E₂, E₃ and relaxation time, τ₁ with zero order reaction kinetics and activation energy of 100–149 kJ/mol. No model was established for τ₂ since there were no significant changes with frying time and the temperatures applied. Coupling with transport phenomena, the developed kinetic models would be useful for predicting viscoelastic properties of tofu during frying.

ACKNOWLEDGMENTS

The authors gratefully acknowledge Fond FCAR (Le Fonds pour la Formation de Chercheurs et l’Aide à la Recherche), NSERC (Natural Science and Engineering Research Council of Canada), and OMAFRA (Ontario Minister of Agriculture, Food and Rural Affairs) for research funding.