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Rheological Modelling of Red Cherry Tomato Puree at Varying Concentration Levels

S
Sandeep Yadav1
J
Joyita Mali1
S
Supriti Haldar1
A
Arina Mondal1
A
Anindita Karmakar1,*
S
Subrata Karmakar2
I
Ivi Chakraborty3
1Department of Post Harvest Engineering, Faculty of Agricultural Engineering, Bidhan Chandra Krishi Viswavidyalaya, Nadia-741 252, West Bengal, India.
2Department of Farm Machinery and Power, Faculty of Agricultural Engineering, Bidhan Chandra Krishi Viswavidyalaya, Nadia-741 252, West Bengal, India.
3Department of Post Harvest Management, Faculty of Horticulture, Bidhan Chandra Krishi Viswavidyalaya, Nadia-741 252, West Bengal, India.

ABSTRACT

Background: Understanding the rheological behaviour of fruit and vegetable purees is essential for optimizing processing, handling and product quality. Rheological properties are strongly influenced by factors such as soluble solid concentration and temperature, which affect flow behavior, viscosity and structural stability. This study aimed to investigate the rheological characteristics of red cherry tomato puree under varying total soluble solids (TSS) concentrations and temperatures.

Methods: Red cherry tomato puree samples were prepared with TSS levels ranging from 15 to 27oBrix and evaluated at temperatures between 20 and 50oC. The flow behavior, in terms of shear stress, shear rate and viscosity measured using an Anton Paar rheometer (MCR 92), was analyzed using the Power Law, Herschel-Bulkley and Casson models. The temperature dependence of apparent viscosity was described using the Arrhenius model. Oscillatory rheological measurements were performed to assess viscoelastic properties within the linear viscoelastic region (LVR).

Result: All three rheological models exhibited high coefficients of determination (R2) and low RMSE values, indicating excellent agreement with experimental data. Increasing TSS led to higher consistency index (k) values and lower flow behavior index (n), reflecting enhanced pseudoplastic behavior. Apparent viscosity decreased with increasing temperature for all samples and Arrhenius model fitting yielded high R2 values (up to 0.989). Oscillatory tests revealed dominant elastic behavior within the linear viscoelastic region (LVR). The most concentrated sample (27oBrix) showed higher storage modulus, loss modulus and yield points, indicating greater structural stability and deformation resistance, while the most dilute sample (15oBrix) exhibited no yield point within the tested strain range. Overall, red cherry tomato puree behaved as a pseudoplastic, temperature-sensitive and viscoelastic material, with rheological properties strongly governed by soluble solid concentration.

INTRODUCTION

Cherry tomato (Solanum lycopersicum var. cerasiforme), belonging to the Solanaceae family and sometimes referred to as pearl tomatoes, is among the most widely grown tomato cultivars worldwide. Fresh cherry tomatoes are round in shape, rich in nutrients and bioactive compounds and are well-known for their flavor, texture and colour (Tang et al., 2020; Chang et al., 2014). It serves as an essential raw material for producing a wide range of processed items such as juice, ketchup, sauces, pickles, chutneys, canned fruits, puree and paste (Thakur et al., 2026). This is a warm season crop that requires a long growing period to achieve higher yields and is considered one of the most promising crops for cultivation under protected structures (Vidyadhar et al., 2015). Intense sunlight, heat stress, drought, drying winds and hailstorms are some of the key environmental factors that limit the productivity and nutritional quality of cherry tomatoes grown in open fields (Kannaujia et al., 2025).
       
Ascorbic acid (AA), lycopene, beta-carotene, organic acids and other minerals are more abundant in cherry tomatoes than in regular tomatoes; for example, the AA content of cherry tomatoes is 1.7 times higher than that of regular tomatoes (Wang et al., 2022; Zeng et al., 2020; Yun et al., 2015). Cherry tomatoes offer several health benefits, including enhancement of immune function, delayed aging, reduction of blood pressure, lowering of cholesterol levels and potential cancer-preventive effects (Chang et al., 2024). However, as a climacteric and highly perishable fruit, cherry tomatoes typically have a short shelf life, usually lasting around 2-3 weeks (Anubha et al., 2024). The main factors that reduce the commercial value of tomatoes after harvest include softening due to impact damage or over-ripening, cracking, moisture loss, chilling injury, compositional changes and decay. Temperature and humidity influence the ripening process, determining how quickly the fruit matures and softens, eventually making it unfit for consumption (Razali et al., 2021). India’s cherry tomato production has increased due to rising demand for salads and healthy foods. Their high lycopene and colour value suit natural colorants and antioxidants.
       
Processing surplus and rejected fruits into purees reduces postharvest losses and improves farmers’ income. Despite the common perception that processed foods are inferior than unprocessed foods, “processing” is not always a bad thing and processed foods are not consistently sickly or inadequately nourished (Maity et al., 2025). The pureeing process helps preserve the nutritional value of cherry tomatoes while extending their shelf life. While fresh tomatoes spoil quickly, purees can be stored for months or even longer through canning or freezing, ensuring year-round access to their health benefits. The rheological behavior of fruit purees is crucial in both research and engineering applications, particularly for the design and optimization of processing operations such as evaporation, concentration, pasteurization and pumping (Sakhare et al., 2016; Martinez-Padilla, 2024). Key rheological parameters, including viscosity, consistency and flow behavior serve as important indicators of the physical characteristics of fruit purees (Stanciu, 2022). Viscosity is influenced by factors such as temperature, pH, shear rate, water content and sugar concentration (Ramzi et al., 2015). Liquid foods often exhibit a transition from Newtonian to non-Newtonian flow behaviour depending on their composition and conditions. Dynamic frequency sweep analysis is commonly used to evaluate viscoelastic properties by measuring storage modulus (G′) and loss modulus (G″) as functions of frequency (Liu et al., 2023). Under small deformations G′  and G″ represent the elastic and viscous behaviour of food materials without disrupting its structure. Understanding these properties is essential for optimizing processing conditions and ensuring product quality. Although several studies have examined the rheological properties of tomato pulp (Fang et al., 2021; Liu et al., 2023; Toth and Hajos, 2019; Gao et al., 2021; Augusto et al., 2011) limited research has specifically addressed the rheological behaviour of red cherry tomato puree, particularly under varying temperature and total soluble solids conditions. Therefore, the present study aims to investigate the effects of temperature and total dissolved solids on the rheological behaviour of red cherry tomato puree.

MATERIALS AND METHODS

The study was conducted during 2025 at the Department of Post Harvest Engineering, Bidhan Chandra Krishi Viswavidyalaya, Mohanpur, Nadia, West Bengal.

Preparation of the puree
 
The puree was prepared from the ripened red cherry tomatoes following the standard procedure of grading, cleaning, chopping, blanching and heating as described by Srivastava and Kumar (2014). The flowchart followed for preparation of puree is presented in Fig 1.


Fig 1: Flow-chart followed for preparation of puree.


 
Physicochemical analysis
 
The TSS content of puree samples was measured by using Parisa Digital Refractometer at room temperature (25±5oC) and expressed in oBrix. Moisture content significantly affected the physical properties of a substance such as density, viscosity, refractive index and many more. Therefore, it plays a crucial role in determining standard product characteristics such as storability, concentration or purity and commercial grade. Moisture content of puree samples was determined using a Citizen Digital Moisture Analyzer. The pH of puree samples was determined using a Labard digital pH meter (Model: LI-1122pH). Prior to measurement, the electrode was washed with distilled water and gently dried with a soft tissue. The instrument was calibrated using a standard pH 7 buffer solution before each set of measurements. Each sample was measured in triplicate to ensure accuracy. The estimation of titratable acidity and Vitamin C (Ascorbic acid) of prepared puree sample were carried out using the standard procedure described by Sadasivam and Manickam (2023).
 
Rheological measurements
 
Rheological measurements of red cherry tomato puree were carried out using an Anton Paar Rheometer (Model: MCR-92) provided with a parallel plate measuring system (PP50, SN000000). The viscosity curve test was performed by applying a logarithmic ramp of shear rates ranging from 0.01 s-1 to 200 s-1 at varying temperatures of 20 to 50oC. The test was performed to obtain data at 50 points.
       
The shear stress versus shear rate data were analyzed to evaluate the flow behavior of the tomato puree. The Power law (Equation 1), Herschel-Bulkley (Equation 2) and Casson Model (Equation 3) were applied to the rheological data in order to fit the best representative model. The Arrhenius equation (Equation 4) was used to describe the effect of temperature on viscosity of red cherry tomato puree.
 
τ = Kγn                    (1)
 
τ = τ o + Kγn                (2)
 
                      √τ = √τ o + ηca  √γo               (3)                


 
Where,
τ = Shear stress (Pa).
K = Consistency index (pa sn). 
γ = Shear rate (s-1).
n = Flow behavior index.
τ o = Yield stress (pa).
ηca = Casson Plastic Viscosity (Pa-s). 
μ = Apparent viscosity (mPa-s).
A = Arrhenius constant.
Ea = Activation energy (kJ mol-1).
R = Universal gas constant (J. K-1.mol-1).
T = Temperature (K).
       
An amplitude sweep test was performed to determine the linear viscoelastic region (LVR) of red cherry tomato puree. The test was conducted at a constant angular frequency of 10 rad s-1. Shear strain was varied logarithmically from 0.01% to 100% over 40 measurement points.

RESULTS AND DISCUSSION

Physicochemical properties
 
The variations in total soluble solids (TSS), moisture content, pH, titratable acidity and vitamin C of red cherry tomato puree were presented in Table 1. The puree samples were adjusted to TSS levels of 15, 19, 23 and 27oBrix by drying or dilution with distilled water. An inverse relationship was observed between TSS and moisture content, with TSS increasing from 15 to 27oBrix, moisture content decreased from 74.22% to 57.1%. The pH decreased from 6.08 to 5.47 as TSS increased showing acidification during concentration. These values were slightly higher than the common pH range (4.0-4.6) reported for commercial tomato products (Aykas et al., 2020). Titratable acidity increased steadily with higher TSS, likely due to concentration of organic acids such as citric and malic acids. Vitamin C increased from 8.5 mg (100 g)-1 at 15oBrix to 11 mg (100 g)-1 at 27oBrix, consistent with Haseen et al. (2019) and Koh et al. (2012), who reported that higher TSS can help protect ascorbic acid from enzymatic breakdown. This relative stability at higher concentrations also agrees with Vigneshwaran et al. (2022), showing that although thermal processing causes some initial vitamin C loss, further concentration does not substantially increase its degradation (Dippong et al., 2025).

Table 1: Physicochemical properties of red cherry tomato puree.


 
Rheological properties
 
The shear stress and viscosity data at different temperatures and shear rate for lowest and highest concentration levels were presented in Table 2. The rheogram in Fig 2 showed the relationship between shear stress and shear rate for red cherry tomato puree at four concentrations of 15o, 19o, 23o and 27o Brix.

Table 2: Viscosity curve test parameters for lowest and highest concentration levels.



Fig 2: Rheogram of concentrated red cherry tomato puree for 15, 19, 23 and 27oBrix.


       
For all the samples, shear stress increased as shear rate increased, showing a non-Newtonian, shear-thinning (pseudoplastic) behaviour as also reported by Stanciu (2022), (Fadeyibi et al., 2024) for tomato sauce. Samples with higher TSS had higher shear stress at the same shear rate indicating that more soluble and structural solids increased resistance to flow and raised apparent viscosity also reported by Evangelista et al. (2020). Among the samples the puree at 27oBrix showed the highest shear stress of 3.708 Pa at 0.1 s-1 while the 15oBrix sample recorded the lowest value of 3.0008 Pa at 200 s-1, confirming that concentration strongly affected rheological properties.
   
The variation of apparent viscosity with shear rate for red cherry tomato puree samples was shown in Fig 3. All samples exhibited a marked decrease in viscosity with increasing shear rate, confirming a shear-thinning (pseudoplastic) behaviour typical of fruit purees. This rheological behaviour was attributed to the breakdown of internal structure and alignment of particles under shear. Furthermore, at any given shear rate, samples with higher TSS showed significantly higher viscosity values. The puree at 27oBrix demonstrated the highest viscosity (37.18 Pa. s) at shear rate of 0.1 s-1, while the 15oBrix sample had the lowest (0.02 Pa. s) at shear rate of 0.1 s-1 indicating that increased soluble solids contribute to greater resistance to flow and structural rigidity.

Fig 3: Viscosity vs shear rate.


       
Both temperature and total soluble solid (TSS) content had a significant effect on the viscosity of red cherry tomato puree, consistent with observations reported for persimmon puree (Mazlum and Lodos, 2025) and pomelo juice concentrate (Keshani et al., 2012). An increase in temperature enhances molecular mobility and intermolecular spacing thereby reducing flow resistance. Consequently, the viscosity of red cherry tomato puree decreased markedly with increasing temperature, as shown in Fig 4. This effect was more pronounced at higher TSS levels.

Fig 4: The effect of temperature and TSS on viscosity of red cherry tomato puree.


       
In contrast, TSS concentration exhibited a strong positive influence on viscosity which is characteristic of non-Newtonian fluids. Increasing soluble solid content alters the degree of hydration of solute molecules and promotes hydrogen bonding between hydroxyl groups, leading to reduced intermolecular spacing and increased resistance to flow. As a result, the viscosity of red cherry tomato puree increased significantly with increasing TSS.

Rheological models
 
One of the most widely used models for describing viscosity data is the power law model which contains only two parameters (K and n) to represent shear stress-shear rate behaviour. Due to its simplicity and ability to express rheological behaviour as a linear relationship under shear, it has been extensively applied to fluid foods. The flow behavior index reflects the deviation from Newtonian flow and quantifies the non-Newtonian nature of fluids (Pang et al., 2020). A value of 1 indicates Newtonian behaviour, whereas values greater than 1 signify dilatant flow (Gao et al., 2021). In this study shear stress and shear rate data were fitted to Equation 1 and the resulting parameters are presented in Table 3. The consistency index (K) increased from 0.85 at 15oBrix to 4.8 at 27oBrix, while the flow behavior index (n) decreased from 0.22 to 0.13, indicating shear-thinning (pseudoplastic) behaviour. The Herschel-Bulkley model, which combines power law and Bingham characteristics and is widely used for non-Newtonian fluids, was also fitted using Equation 2, with parameters reported in Table 3. The model similarly indicated pseudoplastic behaviour as reflected by flow behavior index values below 1 (0.44 to 0.82). The consistency index increased (0.03 to 0.48) with increasing concentration. Yield stress defined as the minimum shear stress required to initiate flow, is an important property of multiphase systems (González-Montemayor et al., 2022). In this study, yield stress increased with concentration, reaching a maximum value of 5.3 Pa at 27oBrix. The Casson model commonly applied to concentrated fruit and vegetable purées exhibiting yield stress, effectively described the non-Newtonian behaviour of the samples. Parameters (Table 3) obtained from Equation 3 showed that Casson yield stress increased with total soluble solids and was comparable to the Herschel-Bulkley yield stress values. Casson plastic viscosity decreased with increasing concentration, suggesting possible particle rearrangement or reduced inter-particle friction after yielding. Overall, regression analysis based on R2 and RMSE indicated that all three models-Power Law, Herschel-Bulkley and Casson-provided a good fit to the experimental data, confirming consistent pseudoplastic behaviour of red cherry tomato puree across different concentrations and temperatures. Among these, the Power Law model showed the highest R2 and the lowest RMSE, indicating superior fitting performance. However, the presence of yield stress at low shear rates suggests that models incorporating yield stress (Herschel-Bulkley and Casson) may better represent the initial flow behaviour. Similar results were obtained during measurement of rheological behaviour of yoghurt at 10-85 s-1 shear rate using a rotational viscometer (Karmakar et al., 2025).

Table 3: Model parameters, R2 and RMSE values.


 
Effect of temperature on apparent viscosity
 
The temperature dependence of the apparent viscosity of red cherry tomato puree was evaluated using the Arrhenius model (Equation 4). A linear relationship was observed between the natural logarithm of apparent viscosity (ln μ) and the reciprocal of absolute temperature (1/T), confirming the suitability of the Arrhenius equation for describing the thermal behavior of the puree. As shown in Fig 5, the apparent viscosity decreased with increasing temperature for all Brix levels, indicating a typical pseudoplastic and temperature-sensitive nature of the product which was also reported by (Hopper et al., 2025 and Ali et al., 2024).

Fig 5: Apparent viscosity at different temperatures and concentrations.


       
The calculated slopes from the linear equations allowed for the determination of activation energy (Ea). The activation energies and the Arrhenius constants (A) determined from the curve were listed in Table 4. The increasing trend in activation energy with higher TSS levels suggests that the puree becomes more sensitive to temperature changes at higher concentrations also observed by (Mazlum and Lodos, 2025). This behaviour could be attributed to the greater presence of soluble solids such as sugars and pectins, which form more structured networks that resist flow at lower temperatures but break down more rapidly with heat. The regression equations derived from the experimental data yielded high coefficients of determination (R2) with the highest being 0.989 at 27oBrix demonstrating excellent model fit. A molecule needs activation energy to move and when the temperature rises, the liquid flowed more readily because of the higher activation energy in high temperatures. Furthermore, the increased alignment of constituent molecules was linked to the decrease in viscosity with an increase in shear rate (Haminiuk et al., 2006).

Table 4: Parameters for Arrhenius model.


 
Viscoelastic behaviour
 
The amplitude sweep test was conducted to determine the linear viscoelastic region (LVR) of red cherry tomato puree at different TSS levels by applying oscillatory shear with increasing strain at a constant angular frequency as shown in Fig 6, 7, 8 and 9. The amplitude sweep test parameters of lowest and highest TSS levels were listed in Table 5.

Fig 6: Amplitude sweep curve for 15oBrix.



Fig 7: Amplitude sweep curve for 19oBrix.



Fig 8: Amplitude sweep curve for 23oBrix.



Fig 9: Amplitude sweep curve for 27oBrix.



Table 5: Amplitude sweep test parameters for lowest and highest TSS levels.


       
The storage modulus represented elastic portion and the loss modulus characterize viscous portion. The results revealed that the storage modulus (G′) was consistently higher than the loss modulus (G″) within the LVR, indicating that the puree exhibited predominantly elastic or solid-like behavior under small deformations, aligning with finding by Wan et al., (2025); Fadeyibi et al., (2024); Giura et al., (2022); Augusto et al., (2011). Beyond the LVR, all samples showed a gradual decrease in both G′ and G″ with increasing strain (strain-softening). At larger strains, G′ and G″ approached each other and crossed over (G′ =G″), marking the transition from solid-dominated to liquid-dominated behaviour (flow point), signifying the breakdown of the internal structure and a transition from elastic to viscous behavior. The point where G″ cross over G′ was known as the yield point or critical strain. Based on the graph, the yield point occurred at higher strain for the more concentrated Purees (23 and 27oBrix) than for the diluted one (15oBrix). However, no yield point was observed for 15oBrix sample in the range of applied strain. The amplitude sweep test provided critical insights into the viscoelastic strength and deformation tolerance of tomato puree under different compositional conditions.

CONCLUSION

Red cherry tomato purée exhibited clear pseudoplastic behavior across all concentrations, as confirmed by the Power Law, Herschel-Bulkley and Casson models, which all showed strong fits to the shear stress-shear rate data. Higher TSS increased consistency and yield stress while reducing flow behavior index. Apparent viscosity decreased with temperature, with activation energy rising at higher concentrations. Viscoelastic tests revealed dominant elastic behavior within the linear viscoelastic region and higher yield strain for concentrated samples, indicating stronger structural networks at elevated TSS levels.

CONFLICT OF INTEREST

I, on behalf of all the authors, declare that there are no conflicts of interest regarding the publication of this manuscript. All co-authors have reviewed and approved the contents of the manuscript, and there are no financial interests to disclose.

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    Rheological Modelling of Red Cherry Tomato Puree at Varying Concentration Levels

    S
    Sandeep Yadav1
    J
    Joyita Mali1
    S
    Supriti Haldar1
    A
    Arina Mondal1
    A
    Anindita Karmakar1,*
    S
    Subrata Karmakar2
    I
    Ivi Chakraborty3
    1Department of Post Harvest Engineering, Faculty of Agricultural Engineering, Bidhan Chandra Krishi Viswavidyalaya, Nadia-741 252, West Bengal, India.
    2Department of Farm Machinery and Power, Faculty of Agricultural Engineering, Bidhan Chandra Krishi Viswavidyalaya, Nadia-741 252, West Bengal, India.
    3Department of Post Harvest Management, Faculty of Horticulture, Bidhan Chandra Krishi Viswavidyalaya, Nadia-741 252, West Bengal, India.

    ABSTRACT

    Background: Understanding the rheological behaviour of fruit and vegetable purees is essential for optimizing processing, handling and product quality. Rheological properties are strongly influenced by factors such as soluble solid concentration and temperature, which affect flow behavior, viscosity and structural stability. This study aimed to investigate the rheological characteristics of red cherry tomato puree under varying total soluble solids (TSS) concentrations and temperatures.

    Methods: Red cherry tomato puree samples were prepared with TSS levels ranging from 15 to 27oBrix and evaluated at temperatures between 20 and 50oC. The flow behavior, in terms of shear stress, shear rate and viscosity measured using an Anton Paar rheometer (MCR 92), was analyzed using the Power Law, Herschel-Bulkley and Casson models. The temperature dependence of apparent viscosity was described using the Arrhenius model. Oscillatory rheological measurements were performed to assess viscoelastic properties within the linear viscoelastic region (LVR).

    Result: All three rheological models exhibited high coefficients of determination (R2) and low RMSE values, indicating excellent agreement with experimental data. Increasing TSS led to higher consistency index (k) values and lower flow behavior index (n), reflecting enhanced pseudoplastic behavior. Apparent viscosity decreased with increasing temperature for all samples and Arrhenius model fitting yielded high R2 values (up to 0.989). Oscillatory tests revealed dominant elastic behavior within the linear viscoelastic region (LVR). The most concentrated sample (27oBrix) showed higher storage modulus, loss modulus and yield points, indicating greater structural stability and deformation resistance, while the most dilute sample (15oBrix) exhibited no yield point within the tested strain range. Overall, red cherry tomato puree behaved as a pseudoplastic, temperature-sensitive and viscoelastic material, with rheological properties strongly governed by soluble solid concentration.

    INTRODUCTION

    Cherry tomato (Solanum lycopersicum var. cerasiforme), belonging to the Solanaceae family and sometimes referred to as pearl tomatoes, is among the most widely grown tomato cultivars worldwide. Fresh cherry tomatoes are round in shape, rich in nutrients and bioactive compounds and are well-known for their flavor, texture and colour (Tang et al., 2020; Chang et al., 2014). It serves as an essential raw material for producing a wide range of processed items such as juice, ketchup, sauces, pickles, chutneys, canned fruits, puree and paste (Thakur et al., 2026). This is a warm season crop that requires a long growing period to achieve higher yields and is considered one of the most promising crops for cultivation under protected structures (Vidyadhar et al., 2015). Intense sunlight, heat stress, drought, drying winds and hailstorms are some of the key environmental factors that limit the productivity and nutritional quality of cherry tomatoes grown in open fields (Kannaujia et al., 2025).
           
    Ascorbic acid (AA), lycopene, beta-carotene, organic acids and other minerals are more abundant in cherry tomatoes than in regular tomatoes; for example, the AA content of cherry tomatoes is 1.7 times higher than that of regular tomatoes (Wang et al., 2022; Zeng et al., 2020; Yun et al., 2015). Cherry tomatoes offer several health benefits, including enhancement of immune function, delayed aging, reduction of blood pressure, lowering of cholesterol levels and potential cancer-preventive effects (Chang et al., 2024). However, as a climacteric and highly perishable fruit, cherry tomatoes typically have a short shelf life, usually lasting around 2-3 weeks (Anubha et al., 2024). The main factors that reduce the commercial value of tomatoes after harvest include softening due to impact damage or over-ripening, cracking, moisture loss, chilling injury, compositional changes and decay. Temperature and humidity influence the ripening process, determining how quickly the fruit matures and softens, eventually making it unfit for consumption (Razali et al., 2021). India’s cherry tomato production has increased due to rising demand for salads and healthy foods. Their high lycopene and colour value suit natural colorants and antioxidants.
           
    Processing surplus and rejected fruits into purees reduces postharvest losses and improves farmers’ income. Despite the common perception that processed foods are inferior than unprocessed foods, “processing” is not always a bad thing and processed foods are not consistently sickly or inadequately nourished (Maity et al., 2025). The pureeing process helps preserve the nutritional value of cherry tomatoes while extending their shelf life. While fresh tomatoes spoil quickly, purees can be stored for months or even longer through canning or freezing, ensuring year-round access to their health benefits. The rheological behavior of fruit purees is crucial in both research and engineering applications, particularly for the design and optimization of processing operations such as evaporation, concentration, pasteurization and pumping (Sakhare et al., 2016; Martinez-Padilla, 2024). Key rheological parameters, including viscosity, consistency and flow behavior serve as important indicators of the physical characteristics of fruit purees (Stanciu, 2022). Viscosity is influenced by factors such as temperature, pH, shear rate, water content and sugar concentration (Ramzi et al., 2015). Liquid foods often exhibit a transition from Newtonian to non-Newtonian flow behaviour depending on their composition and conditions. Dynamic frequency sweep analysis is commonly used to evaluate viscoelastic properties by measuring storage modulus (G′) and loss modulus (G″) as functions of frequency (Liu et al., 2023). Under small deformations G′  and G″ represent the elastic and viscous behaviour of food materials without disrupting its structure. Understanding these properties is essential for optimizing processing conditions and ensuring product quality. Although several studies have examined the rheological properties of tomato pulp (Fang et al., 2021; Liu et al., 2023; Toth and Hajos, 2019; Gao et al., 2021; Augusto et al., 2011) limited research has specifically addressed the rheological behaviour of red cherry tomato puree, particularly under varying temperature and total soluble solids conditions. Therefore, the present study aims to investigate the effects of temperature and total dissolved solids on the rheological behaviour of red cherry tomato puree.

    MATERIALS AND METHODS

    The study was conducted during 2025 at the Department of Post Harvest Engineering, Bidhan Chandra Krishi Viswavidyalaya, Mohanpur, Nadia, West Bengal.

    Preparation of the puree
     
    The puree was prepared from the ripened red cherry tomatoes following the standard procedure of grading, cleaning, chopping, blanching and heating as described by Srivastava and Kumar (2014). The flowchart followed for preparation of puree is presented in Fig 1.


    Fig 1: Flow-chart followed for preparation of puree.


     
    Physicochemical analysis
     
    The TSS content of puree samples was measured by using Parisa Digital Refractometer at room temperature (25±5oC) and expressed in oBrix. Moisture content significantly affected the physical properties of a substance such as density, viscosity, refractive index and many more. Therefore, it plays a crucial role in determining standard product characteristics such as storability, concentration or purity and commercial grade. Moisture content of puree samples was determined using a Citizen Digital Moisture Analyzer. The pH of puree samples was determined using a Labard digital pH meter (Model: LI-1122pH). Prior to measurement, the electrode was washed with distilled water and gently dried with a soft tissue. The instrument was calibrated using a standard pH 7 buffer solution before each set of measurements. Each sample was measured in triplicate to ensure accuracy. The estimation of titratable acidity and Vitamin C (Ascorbic acid) of prepared puree sample were carried out using the standard procedure described by Sadasivam and Manickam (2023).
     
    Rheological measurements
     
    Rheological measurements of red cherry tomato puree were carried out using an Anton Paar Rheometer (Model: MCR-92) provided with a parallel plate measuring system (PP50, SN000000). The viscosity curve test was performed by applying a logarithmic ramp of shear rates ranging from 0.01 s-1 to 200 s-1 at varying temperatures of 20 to 50oC. The test was performed to obtain data at 50 points.
           
    The shear stress versus shear rate data were analyzed to evaluate the flow behavior of the tomato puree. The Power law (Equation 1), Herschel-Bulkley (Equation 2) and Casson Model (Equation 3) were applied to the rheological data in order to fit the best representative model. The Arrhenius equation (Equation 4) was used to describe the effect of temperature on viscosity of red cherry tomato puree.
     
    τ = Kγn                    (1)
     
    τ = τ o + Kγn                (2)
     
                          √τ = √τ o + ηca  √γo               (3)                


     
    Where,
    τ = Shear stress (Pa).
    K = Consistency index (pa sn). 
    γ = Shear rate (s-1).
    n = Flow behavior index.
    τ o = Yield stress (pa).
    ηca = Casson Plastic Viscosity (Pa-s). 
    μ = Apparent viscosity (mPa-s).
    A = Arrhenius constant.
    Ea = Activation energy (kJ mol-1).
    R = Universal gas constant (J. K-1.mol-1).
    T = Temperature (K).
           
    An amplitude sweep test was performed to determine the linear viscoelastic region (LVR) of red cherry tomato puree. The test was conducted at a constant angular frequency of 10 rad s-1. Shear strain was varied logarithmically from 0.01% to 100% over 40 measurement points.

    RESULTS AND DISCUSSION

    Physicochemical properties
     
    The variations in total soluble solids (TSS), moisture content, pH, titratable acidity and vitamin C of red cherry tomato puree were presented in Table 1. The puree samples were adjusted to TSS levels of 15, 19, 23 and 27oBrix by drying or dilution with distilled water. An inverse relationship was observed between TSS and moisture content, with TSS increasing from 15 to 27oBrix, moisture content decreased from 74.22% to 57.1%. The pH decreased from 6.08 to 5.47 as TSS increased showing acidification during concentration. These values were slightly higher than the common pH range (4.0-4.6) reported for commercial tomato products (Aykas et al., 2020). Titratable acidity increased steadily with higher TSS, likely due to concentration of organic acids such as citric and malic acids. Vitamin C increased from 8.5 mg (100 g)-1 at 15oBrix to 11 mg (100 g)-1 at 27oBrix, consistent with Haseen et al. (2019) and Koh et al. (2012), who reported that higher TSS can help protect ascorbic acid from enzymatic breakdown. This relative stability at higher concentrations also agrees with Vigneshwaran et al. (2022), showing that although thermal processing causes some initial vitamin C loss, further concentration does not substantially increase its degradation (Dippong et al., 2025).

    Table 1: Physicochemical properties of red cherry tomato puree.


     
    Rheological properties
     
    The shear stress and viscosity data at different temperatures and shear rate for lowest and highest concentration levels were presented in Table 2. The rheogram in Fig 2 showed the relationship between shear stress and shear rate for red cherry tomato puree at four concentrations of 15o, 19o, 23o and 27o Brix.

    Table 2: Viscosity curve test parameters for lowest and highest concentration levels.



    Fig 2: Rheogram of concentrated red cherry tomato puree for 15, 19, 23 and 27oBrix.


           
    For all the samples, shear stress increased as shear rate increased, showing a non-Newtonian, shear-thinning (pseudoplastic) behaviour as also reported by Stanciu (2022), (Fadeyibi et al., 2024) for tomato sauce. Samples with higher TSS had higher shear stress at the same shear rate indicating that more soluble and structural solids increased resistance to flow and raised apparent viscosity also reported by Evangelista et al. (2020). Among the samples the puree at 27oBrix showed the highest shear stress of 3.708 Pa at 0.1 s-1 while the 15oBrix sample recorded the lowest value of 3.0008 Pa at 200 s-1, confirming that concentration strongly affected rheological properties.
       
    The variation of apparent viscosity with shear rate for red cherry tomato puree samples was shown in Fig 3. All samples exhibited a marked decrease in viscosity with increasing shear rate, confirming a shear-thinning (pseudoplastic) behaviour typical of fruit purees. This rheological behaviour was attributed to the breakdown of internal structure and alignment of particles under shear. Furthermore, at any given shear rate, samples with higher TSS showed significantly higher viscosity values. The puree at 27oBrix demonstrated the highest viscosity (37.18 Pa. s) at shear rate of 0.1 s-1, while the 15oBrix sample had the lowest (0.02 Pa. s) at shear rate of 0.1 s-1 indicating that increased soluble solids contribute to greater resistance to flow and structural rigidity.

    Fig 3: Viscosity vs shear rate.


           
    Both temperature and total soluble solid (TSS) content had a significant effect on the viscosity of red cherry tomato puree, consistent with observations reported for persimmon puree (Mazlum and Lodos, 2025) and pomelo juice concentrate (Keshani et al., 2012). An increase in temperature enhances molecular mobility and intermolecular spacing thereby reducing flow resistance. Consequently, the viscosity of red cherry tomato puree decreased markedly with increasing temperature, as shown in Fig 4. This effect was more pronounced at higher TSS levels.

    Fig 4: The effect of temperature and TSS on viscosity of red cherry tomato puree.


           
    In contrast, TSS concentration exhibited a strong positive influence on viscosity which is characteristic of non-Newtonian fluids. Increasing soluble solid content alters the degree of hydration of solute molecules and promotes hydrogen bonding between hydroxyl groups, leading to reduced intermolecular spacing and increased resistance to flow. As a result, the viscosity of red cherry tomato puree increased significantly with increasing TSS.

    Rheological models
     
    One of the most widely used models for describing viscosity data is the power law model which contains only two parameters (K and n) to represent shear stress-shear rate behaviour. Due to its simplicity and ability to express rheological behaviour as a linear relationship under shear, it has been extensively applied to fluid foods. The flow behavior index reflects the deviation from Newtonian flow and quantifies the non-Newtonian nature of fluids (Pang et al., 2020). A value of 1 indicates Newtonian behaviour, whereas values greater than 1 signify dilatant flow (Gao et al., 2021). In this study shear stress and shear rate data were fitted to Equation 1 and the resulting parameters are presented in Table 3. The consistency index (K) increased from 0.85 at 15oBrix to 4.8 at 27oBrix, while the flow behavior index (n) decreased from 0.22 to 0.13, indicating shear-thinning (pseudoplastic) behaviour. The Herschel-Bulkley model, which combines power law and Bingham characteristics and is widely used for non-Newtonian fluids, was also fitted using Equation 2, with parameters reported in Table 3. The model similarly indicated pseudoplastic behaviour as reflected by flow behavior index values below 1 (0.44 to 0.82). The consistency index increased (0.03 to 0.48) with increasing concentration. Yield stress defined as the minimum shear stress required to initiate flow, is an important property of multiphase systems (González-Montemayor et al., 2022). In this study, yield stress increased with concentration, reaching a maximum value of 5.3 Pa at 27oBrix. The Casson model commonly applied to concentrated fruit and vegetable purées exhibiting yield stress, effectively described the non-Newtonian behaviour of the samples. Parameters (Table 3) obtained from Equation 3 showed that Casson yield stress increased with total soluble solids and was comparable to the Herschel-Bulkley yield stress values. Casson plastic viscosity decreased with increasing concentration, suggesting possible particle rearrangement or reduced inter-particle friction after yielding. Overall, regression analysis based on R2 and RMSE indicated that all three models-Power Law, Herschel-Bulkley and Casson-provided a good fit to the experimental data, confirming consistent pseudoplastic behaviour of red cherry tomato puree across different concentrations and temperatures. Among these, the Power Law model showed the highest R2 and the lowest RMSE, indicating superior fitting performance. However, the presence of yield stress at low shear rates suggests that models incorporating yield stress (Herschel-Bulkley and Casson) may better represent the initial flow behaviour. Similar results were obtained during measurement of rheological behaviour of yoghurt at 10-85 s-1 shear rate using a rotational viscometer (Karmakar et al., 2025).

    Table 3: Model parameters, R2 and RMSE values.


     
    Effect of temperature on apparent viscosity
     
    The temperature dependence of the apparent viscosity of red cherry tomato puree was evaluated using the Arrhenius model (Equation 4). A linear relationship was observed between the natural logarithm of apparent viscosity (ln μ) and the reciprocal of absolute temperature (1/T), confirming the suitability of the Arrhenius equation for describing the thermal behavior of the puree. As shown in Fig 5, the apparent viscosity decreased with increasing temperature for all Brix levels, indicating a typical pseudoplastic and temperature-sensitive nature of the product which was also reported by (Hopper et al., 2025 and Ali et al., 2024).

    Fig 5: Apparent viscosity at different temperatures and concentrations.


           
    The calculated slopes from the linear equations allowed for the determination of activation energy (Ea). The activation energies and the Arrhenius constants (A) determined from the curve were listed in Table 4. The increasing trend in activation energy with higher TSS levels suggests that the puree becomes more sensitive to temperature changes at higher concentrations also observed by (Mazlum and Lodos, 2025). This behaviour could be attributed to the greater presence of soluble solids such as sugars and pectins, which form more structured networks that resist flow at lower temperatures but break down more rapidly with heat. The regression equations derived from the experimental data yielded high coefficients of determination (R2) with the highest being 0.989 at 27oBrix demonstrating excellent model fit. A molecule needs activation energy to move and when the temperature rises, the liquid flowed more readily because of the higher activation energy in high temperatures. Furthermore, the increased alignment of constituent molecules was linked to the decrease in viscosity with an increase in shear rate (Haminiuk et al., 2006).

    Table 4: Parameters for Arrhenius model.


     
    Viscoelastic behaviour
     
    The amplitude sweep test was conducted to determine the linear viscoelastic region (LVR) of red cherry tomato puree at different TSS levels by applying oscillatory shear with increasing strain at a constant angular frequency as shown in Fig 6, 7, 8 and 9. The amplitude sweep test parameters of lowest and highest TSS levels were listed in Table 5.

    Fig 6: Amplitude sweep curve for 15oBrix.



    Fig 7: Amplitude sweep curve for 19oBrix.



    Fig 8: Amplitude sweep curve for 23oBrix.



    Fig 9: Amplitude sweep curve for 27oBrix.



    Table 5: Amplitude sweep test parameters for lowest and highest TSS levels.


           
    The storage modulus represented elastic portion and the loss modulus characterize viscous portion. The results revealed that the storage modulus (G′) was consistently higher than the loss modulus (G″) within the LVR, indicating that the puree exhibited predominantly elastic or solid-like behavior under small deformations, aligning with finding by Wan et al., (2025); Fadeyibi et al., (2024); Giura et al., (2022); Augusto et al., (2011). Beyond the LVR, all samples showed a gradual decrease in both G′ and G″ with increasing strain (strain-softening). At larger strains, G′ and G″ approached each other and crossed over (G′ =G″), marking the transition from solid-dominated to liquid-dominated behaviour (flow point), signifying the breakdown of the internal structure and a transition from elastic to viscous behavior. The point where G″ cross over G′ was known as the yield point or critical strain. Based on the graph, the yield point occurred at higher strain for the more concentrated Purees (23 and 27oBrix) than for the diluted one (15oBrix). However, no yield point was observed for 15oBrix sample in the range of applied strain. The amplitude sweep test provided critical insights into the viscoelastic strength and deformation tolerance of tomato puree under different compositional conditions.

    CONCLUSION

    Red cherry tomato purée exhibited clear pseudoplastic behavior across all concentrations, as confirmed by the Power Law, Herschel-Bulkley and Casson models, which all showed strong fits to the shear stress-shear rate data. Higher TSS increased consistency and yield stress while reducing flow behavior index. Apparent viscosity decreased with temperature, with activation energy rising at higher concentrations. Viscoelastic tests revealed dominant elastic behavior within the linear viscoelastic region and higher yield strain for concentrated samples, indicating stronger structural networks at elevated TSS levels.

    CONFLICT OF INTEREST

    I, on behalf of all the authors, declare that there are no conflicts of interest regarding the publication of this manuscript. All co-authors have reviewed and approved the contents of the manuscript, and there are no financial interests to disclose.

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