Rheological behaviour of enzyme clarified sapota (Achras sapota L) juice at different concentration and temperatures

Abstract

Rheological behaviour of enzyme clarified sapota (Achras sapota L.) juice at different temperatures (10 to 85 °C) and total soluble solid content (10.2 to 55.6 °brix) corresponding to a water activity (a_w) (0.986 to 0.865) was studied using controlled stress rheometer by coaxial cylinders attachment. The rheological parameter shear stress (Pa) was measured upto a shear rate of 1,000 s⁻¹. The investigation showed that the enzyme clarified sapota juice and its concentrates behaved like a Newtonian liquid and the viscosity (η) values were in the range 4.340 to 56.418 mPa s depending upon temperature and concentration studied. The temperature dependency of viscosity of enzyme clarified sapota juice was described by Arrhenius equation (r > 0.94) and activation energy (E_a) for viscous flow was in the range 5.218 to 25.439 KJ/mol depending upon concentration. The effect of total soluble solid content on flow activation energy was described by exponential relationship (r > 0.95, rmse% <13.5, p < 0.01) and that of water activity was described by power law relation (r > 0.99, rmse% <5.80, p < 0.01). The effect of total soluble solid content on viscosity of enzyme clarified sapota juice followed second order exponential type relationship (r > 0.99, rmse% < 3.53) at the temperature used. The effect of water activity on viscosity of enzyme clarified sapota juice followed power law equation (r > 0.98, rmse% < 4.38). A single equation representing combined effect of temperature and total soluble solid content/water activity on viscosity of enzyme clarified sapota was established.

Introduction

In recent developments in the design and control of food processes, utilization of computer aided designing, modelling and simulation require extensive data on the physical and engineering properties of foods. The rheological properties of fluid food is an important aspect in the field of food processing and engineering such as, in developing food process techniques, design of processing equipments, structural understanding and quality evaluation of food and raw agricultural materials in the field of food science and technology. Due to the complex physical, chemical and biological structures of food material it is difficult to arrive at theoretical prediction of rheological properties of foods. Therefore, experimental determination of rheological properties is important in the understanding and characterisation of food. The rheological properties of fluid food products are important in determining the power requirements for unit operations such as, pumping, sizing of pipes, design of processing equipment of heat exchangers, chilling, evaporation, concentration, mixing, filling, agitation etc. It is also important in calculation of heat, mass and momentum transfer phenomena during food processing (Krokida et. al 2001; Rao 2007; Steffe 1992; Telis-Romero et al. 1999). The quality parameter of fluid food which is related to rheology is known as mouth-feel, is defined as the mingled experience deriving from the sensation of skin of the mouth after ingestion of a food or beverage and is related to physical properties such as viscosity, density, surface tension and other related properties of the fluid foods. The physical properties of fluid foods have gained more importance as rheological attributes of fluid foods have been developed and quantified (Ingate and Christensen 1981). Fluid foods were subjected to different temperatures and concentrations during processing, storage, transportation, marketing etc. where the rheological properties were more essential in handling and processing of the liquid food material. Among the liquid foods, fruit products such as pulp, juice, concentrate, serum and filtered/clarified juices are of commercial importance. The development of concentrated fluid foods is more advantageous than single strength liquid as concentration of liquid foods lead to decrease in water content and water activity. The reduction in water activity of food helps its stability and makes it convenient during storage, handling, transportation and preparation of novel products with suitable dilution/modifications to make convenient products such as ready to serve (RTS) beverage, squash and concentrates etc.

Water activity of food is defined as the ratio of the equilibrium vapour pressure exerted in the food to the vapour pressure of pure water at constant temperature and also measure of the amount of water available for microbial growth. It is also refered as the ratio of escaping tendency of water fugacity in the system to the escaping tendency of pure water. The fugacity of food system was closely approximated by vapour pressur of food. The water activity is a measure of the energy state of the water in the system and it is measure of free, unbound and available water in the food system. There are several factors that control the water activity in a food system, the colligative effect of dissolved species (salts, sugars and acids) interact with water through dipole-dipole, ionic and hydrogen bonds. Influence of water activity may induce profound changes in the quality and stability of a food product and is also an important requirement for packaging of food material. Water activity is a critical factor that determines the shelf life of the food. The water activity of food is a more important factor than total moisture content for deciding the quality and stability of food (Fennema 2005).

The rheological behaviour of fluid foods is evaluated by the measurement of shear stress, shear rate data and representing the experimental data by rheograms and empirical equations as a function of concentration, temperature, particle size, processing techniques etc. These properties are very much helpful in understanding the flow mechanism of complex fluid systems. The viscosity of fluid is markedly affected by temperature, concentration of solute, its molecular weight, pressure and suspended matter (Bourne 2002). The relationship between shear stress and shear rate was described by Ostwald-De-Waele model or power law equation (Tavares et al. 2007; Sanchez et al. 2009)

$$\sigma =K_{\gamma }^n$$ 1

where σ is shear stress (Pa), K is consistency index (Pa sⁿ), γ is shear rate (s⁻¹) and n is flow behaviour index (-). If the fluid is Newtonian in nature, n = 1 and hence K becomes viscosity η (Pa s) of the fluid. In general, liquid food such as fruit and vegetable juices behave like Newtonian fluids; so their flow behaviour would be Newtonian in nature. Several investigators reported that clarified and depectinated juices and their concentrates exhibit Newtonian flow behaviour. (Juszczak and Fortuna 2004; Cepeda and Villaran 1999; Ibarz et al. 1992a, b, 1987)

$$\sigma =\eta \gamma$$ 2

where σ is shear stress (Pa), η is coefficient of viscosity (Pa s) and γ is the shear rate (s⁻¹). Several authors have used Newtonian equation for describing rheological behaviour of liquid food products like pomegranate juice (Altan and Maskan 2005; Kaya and Sozer 2005), Pekmez (Kaya and Belibagli 2002), lime juice (Manjunatha et al. 2012a), gooseberry juice (Manjunatha et al. 2012b), Tender coconut water (Manjunatha and Raju 2013), liquorice extract (Maskan 1999).

Enzyme clarification is one of the most important techniques to enhance qualitative and quantitative characteristics of juice. Several authors studied the effect of enzyme clarification on physicochemical characteristics of fruit juices were reported (Rai et al. 2004; Lee et al. 2006; Sin et al. 2006; Abdullah et al. 2007). The effect of the enzyme pectinase, incubation time and temperature on rheological characteristics of mango pulp was studied (Bhattacharya and Rastogi 1998). The effect of temperature, total soluble solid content, pH and α-amylase concentration on rheological properties of papaya puree was studied using response surface methodology (Ahmed and Ramaswamy 2004). The rheological behavior of enzyme treated goldenberry (Physalis peruviana) juice was studied at two concentrations and at wide range of temperatures (Sharoba and Ramadan 2011). There are several studies reported that depectinisation using enzymatic treatment such as pectinase enzymes, which could effectively clarify the fruit juices (Chamchong and Noomhorm 1991; Ceci and Lozano 1998; Brasil et al. 1995; Kashyap et al. 2001; Vaillant et al. 2001; Yusof and Ibrahim, 1994; Aliaa et al. 2010; Matta et al. 2004; Singh and Gupta 2004; Cassano et al. 2007; Vandana and Das Gupta 2006).

Sapota (Achras sapota L.) is a tropical fruit belonging to the family Sapotaceae native to Mexico, Central America, and is extensively grown in other parts of world such as southern Florida in the U.S., India, Sri Lanka, Indonesia, Philippines and Caribbean Islands (Salunkhe and Desai 1984). The chemical composition and antioxidant activity of sapota juice was reported by Kulkarni et al. (2007). The phenolic content and antioxidant activity of mamey sapota (pouteria sapota) in postharvest were evaluated and hydrophilic extract of sapota fruit showed higher antioxidant capacity than that of lipophilic portion. The appreciable amount of total soluble phenolic content which contain mainly p-hydroxy benzoic acid had been reported (Rodriguez et al. 2011; Yahia et al. 2011). The sapota juice can be used as nutritional and nutraceutical health beverage, which contains large amount of polyphenols. Sapota juice can be used as a health-promoting beverage due to its multifunctional properties. There is a lack of information on rheological characteristics of enzyme clarified sapota juice and its concentrates, which is essentially required for development of novel sapota juice products on large scale commercial production. The present investigation was aimed at studying the rheological behaviour of enzyme clarified sapota juice and its concentrate at different temperatures and modeling of these properties.

Material and methods

Raw material

The sapota fruits were purchased from local market in Mysore, India and allowed 24 h to ripen at room temperature

Juice extraction

Fruits were washed with water twice and allowed to dry at room temperature. The washed and dried fruits were peeled, deseeded and blended using a waring blender (Model:W, Waring Laboratory, Torrington, CT) for 5 min until a homogenous fruit pulp was obtained. The sapota pulp was pasteurized in water bath at 95 °C for 5 min to inactivate the enzymes. The enzyme based clarification was carried out using commercial enzyme, pectinex ultra SPL (Novozyme, Denmark). The concentration of enzyme, incubation temperature and time was fixed and clarification carried out as reported (Sin et al. 2006). The enzyme was inactivated by placing the material in water bath maintained at temperature 95 °C for 3 min and quickly cooled in ice cold water. The sapota pulp was filtered with four fold muslin cloth and pressed in tincture press (Hafio, West Germany). The filtered sapota juice was centrifuged at a relative centrifugal force of 15,000 rpm using continuous centrifuge (Model: LE 711368, CEPA, Lahr/Baden, and West Germany). The clarified sapota juice was subjected to various concentrations.

Juice concentration

The enzyme clarified sapota juice was concentrated by vacuum evaporation technique using laboratory rotary vacuum evaporator (Model: Laborata 4001, Heidolph, Germany) with reduced pressure, at temperature of 60 °C and rotation speed of 60 rpm. Sapota juice was concentrated to different concentration levels and subjected to rheological measurements.

Rheological measurements

The rheological measurements were carried out using MCR100 controlled stress rheometer (Paar Physica, Anton paar, Gmbh, Austria) equipped with coaxial cylinders (CC 27) and the radii ratio of coaxial cylinders was 1.08477. The rheometer was equipped with an electric temperature controlled peltier system (TEZ-15P-C) to control the experimental temperature with an accuracy of 0.01 °C and a circulating water bath was used (Viscotherm VT-2, Paar Physica, Anton paar Gmbh, Austria). The rheological parameter shear stress (Pa) was measured linearly increasing up to a shear rate of 1,000 s⁻¹ with 10 min duration and 30 shear stress-shear rate data points were collected and analyzed using universal software US200 (Paar Physica, Anton paar Gmbh, Austria). The shear rate range used encompasses most of the food processing applications such as pumping, in-pipe flow, mixing, stirring and grinding (Steffe 1992). The rheological measurements were carried out at different temperatures. All the measurements were done in triplicate and fresh sample was used in each measurement.

Total soluble solid content

The total soluble solids content of sapota juice was determined using digital hand-held refractometer (Model: PAL-1, Atago co, Ltd., Tokyo, Japan) with an accuracy of 0.1 and calibrated using distilled water and total soluble solid content was expressed as °brix.

pH

A digital pH meter was used to measure the pH of sapota juice (Model: pH tutor, P/N 54X002606, Cyber scan, India) at 25 °C with an accuracy of 0.01. The instrument was calibrated using standard buffers provided by manufacturer.

Moisture

Moisture content of enzyme clarified sapota juice was carried out by vacuum oven method as reported (Ranganna 1986).

Ash

The ash content of the juice was measured gravimetrically by drying the juice in hot air oven in silica crucible, ignited in hot plate and placed in muffle furnace at 550 °C for 16 h and the ash content was calculated by difference in weight and expressed as % (Ranganna 1986).

Protein

The protein content of enzyme clarified sapota juice was estimated by micro-Kjeldahl method as reported (Ranganna 1986).

Water activity

The water activity of sapota juice at different concentration was measured using digital water activity meter at 25 °C (Aqua Lab, model: 3 T E, Decagon devices, USA). The water activity meter was calibrated using standard solutions at water activity levels of 0.250, 0.500, 0.760 and 0.984 obtained from original manufacturers (Decagon, Pullman WA, USA).

Acidity

The acidity of enzyme clarified sapota juice was determined by titration method with standard 0.01 N NaOH solution using phenolphthalein as indicator and expressed as % citric acid (Ranganna 1986).

Sugars

Reducing sugar and total sugar of enzyme clarified sapota juice were determined colorimetrically using 3–5, dinitro salicylic acid reagent and expressed as percentage (Miller 1959).

Ascorbic acid

Ascorbic acid content of the juice was determined by titration method using 2, 6 - dichloro-phenol Indo-phenol dye as indicator and expressed as mg/100 ml of juice (Ranganna, 1986).

Total phenolics

The total phenolics content of the enzyme clarified sapota juice was determined spectrophotometrically using Folin-Ciocalteu reagent and expressed as mg/100 ml as gallic acid equivalent (Singleton et al. 1999).

Total flavonoids

The total flavonoids content of the enzyme clarified sapota juice was determined spectrophotometrically using the method and expressed as mg/100 ml as catechin equivalent (Zhishen et al. 1999).

Colour measurement

The color parameters of clarified sapota juice were measured using Hunter color meter (Mini scan XE plus, model 45/0-S Hunter laboratory Inc, Baton). Measurement was carried out at 10° observations, D65 illuminant source and instrument was calibrated using standard black and white tile provided by manufacturer. The colour values were expressed in CIE scale. where L^* refers to lightness, a^* refers to redness, -a^* refers to greenness, b^* refers to yellowness and ‘-b’ refers to blueness. The saturation index (Chroma) C* and hue angle h* were calculated using following equations:

$$\begin{array}{c}\hfill \mathrm{Saturation}\mathrm{index}\left(\mathrm{Chroma}\right):{\mathrm{C}}^{*}={\left({\mathrm{a}}^{*2}+{\mathrm{b}}^{*2}\right)}^{0.5}\hfill \\ \hfill \mathrm{hue}\mathrm{angle}:{\mathrm{h}}^{*}={tan}^{-1}\left({\mathrm{b}}^{*}/{\mathrm{a}}^{*}\right)\hfill \end{array}$$ 3

Statistical analysis

The experimental results and data analysis was carried out using statistical software (Statistica 7.0, Stat Soft Tulsa, USA). The fitting and estimates were calculated at p ≤ 0.05 significance level. The suitability of the models fitting was evaluated by determining the correlation coefficient (r) and root mean square error percent (rmse %) which was evaluated by the following equation:

$$\mathrm{rmse}\%=100/\mathrm{n}{\left[{\displaystyle \sum {\left({\mathrm{W}}_{\exp }-{\mathrm{W}}_{\mathrm{cal}}/{\mathrm{W}}_{\exp }\right)}^2}\right]}^{1/2}$$ 4

where W_exp is the experimental value, W_cal is the calculated value and n is number of data sets. The suitability of the model was decided based on higher correlation coefficient (r) and low percent root mean square error (rmse %) values and level of significance (p < 0.05).

Results and discussion

Physicochemical characteristics

The physicochemical characteristics of enzyme clarified sapota (Achras sapota L.) juice is reported in Table 1. The moisture content was found to be 81.31 % (wet basis) and total soluble solid content was about 18.0 °brix. The solid content of enzyme clarified sapota juice was mainly of soluble solids, which constitutes mainly sugars and marginally organic acids. The protein and ash content was 0.093 % and 0.446 % respectively. The sapota juice had appreciable amount of minerals mainly potassium, calcium and sodium. The pH and acidity of sapota juice was 4.72 and 0.196 % as citric acid respectively. The reducing sugar and total sugars was found to be 11.17 % and 17.03 % respectively. The ascorbic acid content of sapota juice was 3.72 mg/100 ml which was low compared to reported values. This may be due to heat treatment during pasteurization and clarification processes, the ascorbic acid being heat sensitive and water soluble in nature. The enzyme clarified sapota juice had good amount of phenolics and flavonoids, which accounts for appreciable amounts of antioxidant potential. The CIE colour values such as lightness (L^*), redness (a^*) and yellowness (b^*) were very low which indicates appreciable extent of clarification. The chroma (C^*) and hue angle (h^*) were found to be 3.064 and 88.98 respectively. The values reported were within the range as reported with marginal variations. This deviation may be due to processing, varietals difference, agro climatic conditions, maturity level etc. (Kulkarni et al. 2007; Gopalan et al. 2000; Pawar et al. 2011; Ganjayal et al. 2005; Ahmed et al. 2011; Mahattanatawee et al. 2006; Ma et al. 2004; Jain and Jain 1998; Ilamaran and Amutha 2007; Rodriguez et al. 2011; Almeida et al. 2011).

Table 1.

Physico-chemical characteristics of enzyme clarified sapota (Achras sapota L.) juice

Parameter	Quantity
Moisture (%)	81.31 ± 0.060
Ash (%)	0.446 ± 0.047
Protein (%)	0.093 ± 0.001
TSS (ºBrix)	18.0 ± 0.05
Water activity (aw)	0.980 ± 0.001
pH	4.72 ± 0.01
Acidity (% citric acid)	0.196 ± 0.007
Ascorbic acid (mg/100 ml)	3.72 ± 0.06
Total phenolics (mg/100 ml Gallic acid)	48.91 ± 0.38
Flavonoids (mg/100 ml catechin)	7.52 ± 0.28
Reducing sugars (%)	11.17 ± 0.16
Total sugar (%)	17.03 ± 0.16
Colour values
L*	3.003 ± 0.001
a*	0.053 ± 0.025
b*	3.063 ± 0.189
c*	3.064 ± 0.189
h*	88.98 ± 0.54

Mean ± S D (n = 3)

* Indicate the colour values in CIE scale

Flow behaviour

Figure 1 shows the relation between shear stress and shear rate of enzyme clarified sapota juice of 55.6^o brix at different temperatures and Fig. 2 shows the relation between shear stress and shear rate of enzyme clarified sapota juice at 25 °C at different soluble solid contents. The rheograms of enzyme clarified sapota juice showed that there was linear increase in shear stress with respect to increase in shear rate, passed through origin while indicating the flow is Newtonian in nature. The Newtonian model was able to describe the relationship between shear stress and shear rate data. The viscosity of clarified sapota juice could be estimated using Newtonian model (σ = ηγ) and the correlation coefficient values were greater than 0.969. The viscosity values of enzyme clarified sapota juice and its concentrates vary from 4.340 mPa s to 56.416 mPa s at different temperatures and total soluble contents are reported in Table 2. The results showed that temperature and total soluble solid content or water activity had a marked and significant effect on viscosity of sapota juice. The viscosity of enzyme clarified sapota juice was increased significantly (p < 0.05) with the increase in soluble solid content, whereas a significant (p < 0.05) decrease was observed with increase in water activity. The water activity of juice was dependant on solid content, nature of solute, its physicochemical properties and solute-solvent interactions. The viscosity of enzyme clarified sapota juice decreased significantly (p < 0.05) with increase in temperature. The viscosity of liquid foods strongly depends on inter-molecular forces between molecules and water-solute (sugars and acids) interactions, which result from the inter-molecular spacing and strength of hydrogen bonds as both are strongly affected by temperature and concentration. An increased soluble solid content leads to increase in hydrated molecules and hydrogen bonding with hydroxyl groups of solute, which would increase the viscosity of juice. In case of enzyme clarified sapota juice soluble solids (sugars and acids) content plays a vital role in magnitude of viscosity. The increase in temperature significantly decreases the magnitude of viscosity, because of increase in thermal energy of the molecules which enhances mobility of molecules and increases inter-molecular spacing (Krokida et al. 2001; Steffe 1992; Rao 2007). Several authors have reported similar type of results with similar magnitude of viscosity values for different juices and other liquid food products such as cherry juice (Juszczak and Fortuna 2004), pineapple juice (Shamsudin et al. 2007), orange juice (Ibarz et al. 2009), pomegranate juice (Altan and Maskan 2005; Kaya and Sozer 2005), beetroot juice (Juszczak et al. 2010), lime juice (Manjunatha et al. 2012a), gooseberry juice (Manjunatha et al. 2012b), tender coconut water (Manjunatha and Raju 2013), kiwi fruit juice (Goula and Adamopoulos 2011), clarified fruit juices such as orange, black currant, peach, pear, cherry, banana (Ibarz et al. 1994; Ibarz et al. 1992a; 1992b; Ibarz et al. 1989; khalil et al. 1989), carrot juice (Vandresen et al. 2009), sole juice (Ibarz et al. 1996), blueberry and raspberry juices (Nindo et al. 2005), apple and pear juices (Ibarz et al. 1987), black chokeberry juice (Juszczak et al. 2009) Liquorice extract (Maskan 1999), aqueous carbohydrate solutions (Telis et al. 2007).. The consistency coefficient k is increased with total soluble solid content as well as particle size and is decreased with increase temperature of watermelon juice (Sogi et al. 2010). The viscosity of pomegranate juice is significantly affected by total soluble content and temperature while it was not affected by concentration method (Altan and Maskan 2005). The viscosity of goldenberry juice was markedly affected by enzyme treatment and as well as temperature (Sharoba and Ramadan 2011). Juszczak et al. (2010) reported that beetroot juice concentrate had a lower viscosity than concentrated fruit juices with same soluble solid content and at the same temperature studied. This deviation was due to its different levels of individual constituent sugars present in the juice. The viscosity of aqueous carbohydrate solutions such as sucrose, glucose and fructose were reported at different temperatures and concentrations and the aqueous solution behaved like a Newtonian liquid. The magnitude of viscosity decreased in following order of solutes; sucrose, glucose, and fructose at same temperature and concentration studied and these differences were reduced with increase in temperature and decreasing solution concentration (Telis et al. 2007) Chetana et al. (2004) reported that sugar and sorbital solutions behaved like Newtonian fluids while at other syrups such as polydextrose, maltodextrin and polydextrose combination behaved like shear thinning non-Newtonian flow behaviour with yield stress. The results showed that the flow behaviour of polydextrose and combination of maltodextrin + polydextrose syrups obeyed Hershel–Bulkley model. The viscosity of liquid depends on nature of solute, its molecular weight, molecular size and shape, solute-solvent interactions, and state of hydration (Nindo et al. 2005; Telis et al. 2007; Fennema 2005).

Fig. 1.

Rheogram of enzyme clarified sapota (Achras sapota L.) juice at constant total soluble solid content of 55.6 °B at temperature of 10 °C (black square), 25 °C(black up-pointing triangle), 40 °C(black diamond suit), 55 °C(white up-pointing triangle), 70 °C (white square) and 85 °C (Plus sign)

Fig. 2.

Rheogram of enzyme clarified sapota (Achras sapota L.) juice at constant temperature of 25 °C at total soluble solid content of 10.2 °brix (Plus sign), 18.0 °brix (white square), 28.5 brix (white up-pointing triangle), 38.9 °brix (black diamond suit), 49.4 °brix (black up-pointing triangle) and 55.6 °brix (black square)

Table 2.

Newtonian viscosity values of enzyme clarified sapota (Achras sapota L.) juice at different temperatures and total soluble solid content/water activity levels

Total soluble solid content (ºbrix)	Water activity (aw)	Temperature (°C)	Newtonian viscosity (η) (mPa s)	r
10.2	0.986	10	6.803 ± 0.002	0.9847
		25	5.828 ± 0.002	0.9880
		40	5.206 ± 0.002	0.9882
		55	4.808 ± 0.002	0.9888
		70	4.541 ± 0.003	0.9882
		85	4.340 ± 0.002	0.9878
18.0	0.980	10	7.910 ± 0.002	0.9788
		25	6.576 ± 0.003	0.9859
		40	5.773 ± 0.003	0.9877
		55	5.284 ± 0.005	0.9880
		70	4.942 ± 0.006	0.9888
		85	4.676 ± 0.005	0.9882
28.5	0.958	10	9.484 ± 0.003	0.9752
		25	7.981 ± 0.005	0.9792
		40	6.856 ± 0.006	0.9839
		55	6.083 ± 0.005	0.9878
		70	5.692 ± 0.003	0.9866
		85	5.425 ± 0.008	0.9857
38.9	0.937	10	12.487 ± 0.011	0.9967
		25	10.117 ± 0.012	0.9771
		40	9.034 ± 0.010	0.9734
		55	7.919 ± 0.002	0.9787
		70	7.154 ± 0.009	0.9829
		85	6.833 ± 0.002	0.9824
49.4	0.896	10	30.699 ± 0.029	0.9999
		25	16.446 ± 0.024	0.9993
		40	11.763 ± 0.015	0.9831
		55	10.595 ± 0.016	0.9738
		70	9.659 ± 0.009	0.9704
		85	9.362 ± 0.012	0.9696
55.6	0.865	10	56.416 ± 0.064	0.9999
		25	27.722 ± 0.017	0.9998
		40	17.067 ± 0.054	0.9992
		55	12.540 ± 0.023	0.9886
		70	11.304 ± 0.017	0.9748
		85	10.236 ± 0.004	0.9691

Mean ± SD (n = 3)

Effect of temperature

The temperature had a major effect on the Newtonian viscosity similar to the effect on the consistency coefficient for non-Newtonian fluids. The increase in temperature of fluid leads to increased in mobility of the molecules and increase in intermolecular spacing, which decreases the flow resistance. The viscosity of sapota juice decreased markedly with increase in temperature. The variation in viscosity of sapota juice with temperature was significantly high at higher soluble solid content. The effect of temperature on the viscosity of sapota juice with different soluble solid contents/water activity was described using the Arrhenius equation:

$$\eta ={\eta }_{\infty }\mathit{Exp}\left(E_a/RT\right)$$ 5

where η = Viscosity (Pa s), η_∞ = Material constant/pre-exponential coefficient/frequency factor (Pa s), E_a = Flow activation energy (J/mol), R = Gas constant (J/mol K) and T = Temperature (K).

The parameters of Arrhenius equation which was determined by least square approximation method is reported in Table 3. The correlation coefficient was greater than 0.96 and the activation energy for viscous flow was in the range 5.218 to 25.439 kJ/mol depending upon the soluble solid content. The flow activation energy (E_a) was defined as minimum energy required which overcomes the energy barrier before the elementary flow can occur. The viscous flow occurs as a sequence of events which are shift of particles in the direction of shear force action from one equilibrium position to another position by overcoming a potential energy barrier. The barrier height determines the free activation energy of viscous flow. Higher activation energy value indicates a greater influence of temperature on the viscosity, i.e. more rapid change in viscosity with temperature. The magnitude of energy of activation for viscous flow increased significantly (p < 0.05) with increase in soluble solid content of the sapota juice, indicating that higher energy was required to overcome potential energy barrier at higher soluble solids content, where as significant (p < 0.05) increase was observed with decrease in water activity. The frequency factor (η_∞) is significantly (p < 0.05) decreased with increase in total soluble solid content and reported in Table 3 Therefore, temperature had a greater effect on viscosity at higher soluble solid contents. When temperature increased, the thermal energy of the molecules and intermolecular spacing increased significantly, which lead to decrease in the magnitude of viscosity (Steffe 1992; Rao 2007). The magnitude of flow activation energy of Newtonian fluids increased significantly with increase in total soluble solid content (Krokida et al. 2001). The activation energy for viscous flow was markedly affected by enzyme treatment of goldenberry juice (Sharoba and Ramadan 2011). The magnitude of activation energy of viscous flow was in conforming to values reported for other fluid foods (Juszczak and Fortuna 2004; Juszczak et al. 2009; 2010; Altan and Maskan 2005; Kaya and Sozer 2005; Vandresen et al. 2009; Ibarz et al. 2009; Manjunatha et al. 2012a, 2012b; Manjunatha and Raju 2013; Telis et al. 2007; Chetana et al. 2004; Ibarz et al. 1994; Ibarz et al. 1992a; 1992b; Ibarz et al. 1989; Ibarz et al. 1996; khalil et al. 1989; Shamsudin et al. 2007; Sharoba and Ramadan 2011). The Arrhenius equation was satisfactorily described the temperature dependency of viscosity of model solutions such as sucrose, glucose, fructose and the flow activation energy was correlated with solute content by unique equation as a function of an effective volumetric fraction of solute (Telis et al. 2007). The flow activation energy of concentrated orange juice was increased marginally with shear rate and a logarithmic model was reported for variation of flow activation energy with shear rate (Falguera and Ibarz 2010).

Table 3.

Parameters of Arrhenius equation relating Newtonian viscosity of enzyme clarified sapota (Achras sapota L.) juice to temperature at different total soluble solid content and water activity levels

Total soluble solid content (TSS) (ºB)	Water activity (aw)	η∞ (mPa s)	Flow activation energy (Ea) (KJ/mol)	r
10.2	0.986	0.723a ± 0.001	5.218a ± 0.003	0.9879
18.0	0.980	0.572b ± 0.003	6.115b ± 0.013	0.9871
28.5	0.958	0.541c ± 0.003	6.693c ± 0.014	0.9904
38.9	0.937	0.600d ± 0.004	7.084d ± 0.019	0.9918
49.4	0.896	0.0202e ± 0.0001	17.051e ± 0.013	0.9474
55.6	0.865	0.00111f ± 0.00001	25.439f ± 0.001	0.9826

Mean ± SD (n = 3), Different superscripts in columns show significantly different at p < 0.05

Effect of soluble solid content and water activity on flow activation energy

The activation energy for viscous flow of sapota juice increased significantly (p < 0.05) with increase in soluble solid content whereas it decreased significantly (p < 0.05) with increase in water activity and both trends were non-linear in nature. The variation of activation energy with concentration and water activity could be described by different models, such as power law and exponential type relations

$$\begin{array}{c}\hfill E_a=a{\left(C\right)}^b\hfill \\ \hfill E_a=a\mathit{Exp}\left(bC\right)\hfill \\ \hfill E_a=a{\left(a_w\right)}^{b*}\hfill \\ \hfill E_a=a\mathit{Exp}\left(b^{*}{a}_w\right)\hfill \end{array}$$ 6

where E_a is activation energy (kJ/mol), a is empirical constant (kJ/mol), C is total soluble solid content (^obrix), a_w is the water activity (-), a, b,, b^* are empirical constants. These models were fitted with activation energy values which were obtained by Arrhenius equation with soluble solid content and water activity by the method of least square approximation at 5 % significant level (p < 0.05). The magnitudes of the parameters of above four models, correlation coefficient (r) and percent root mean square error (rmse%) are reported in Table 4. The results indicated that exponential model (r = 0.9588, rmse% = 13.44, p < 0.05) was more effective to describe the influence of total soluble solid content on flow activation energy of sapota juice. The power law model had lower values of correlation coefficient (r), higher root mean square error value. This indicated that the flow activation energy increased exponentially with total soluble solid content. The effect of water activity on flow activation energy was described by power law equation (r = 0.9909, rmse % = 5.80, p < 0.01), where as the exponential model the correlation coefficient was lower and the percent root mean square error values are higher. The results showed that the relation between activation energy for viscous flow of sapota juice with total soluble solid content/water activity was non-linear. The relationship between flow activation energy and total soluble solid content/water activity were given by

$$\begin{array}{ll}{E}_a=1.5603*\mathit{Exp}\left(0.049C\right),\hfill & \left(r=0.9588,\mathit{rmse\%}=13.44,p<0.05\right)\hfill \\ E_a=3.890{\left(a_w\right)}^{-12.985}\hfill & \left(r=0.9909,\mathit{rmse\%}=5.80,p<0.01\right)\hfill \end{array}$$

where E_a is the flow activation energy (kJ/mol), C is total soluble solid content (^obrix), a_w is the water activity (-). The variation of flow activation energy increased exponentially with total soluble solid content. Similar type of exponential relation was reported relating to flow activation energy to total soluble solid content. The magnitude of the coefficient concentration was found to be 0.049 and it was within the range as reported for different fruit juices such as pomegranate, pineapple, cherry, peach, chokeberry, lime, gooseberry and tender coconut water (Altan and Maskan 2005; Kaya and Sozer 2005; Shamsudin et al. 2007; Giner et al. 1996; Ibarz et al. 1992a; Juszczak et al. 2009: Manjunatha et al. 2012a; 2012b; Manjunatha and Raju 2013). It was reported that flow activation energy increased significantly with square of total soluble solid content for blue berry and raspberry juices, where as it increased quadratically with soluble solid content in case of liquorice (Glycyrrhiza glabra) extract (Nindo et al. 2005; Maskan 1999). The flow activation energy was increased linearly with total dissolved solid content in case of blueberry puree (Nindo et al. 2007). The deviation in models and model coefficient was due nature solute, size, shape, solute-solvent interactions, hydration state and range of temperature and soluble solid content studied. The flow activation decreased significantly (p < 0.05) with increased in water activity by power law relation and magnitude of decrease was high, which indicated that flow activation energy sensitive to water activity of sapota juice. Similar type of results was reported for different liquid foods. The magnitude of coefficient (b) of water activity was found to be −12.985 in case enzyme clarified sapota juice. The magnitude of power law coefficient (b) of variation with flow activation energy with water activity is comparable with values of lime juice and tender coconut water (Manjunatha et al. 2012a; Manjunatha and Raju 2013).

Table 4.

Parameters of different models relating to flow activation energy (E_a) with total soluble solid content and water activity of enzyme clarified sapota (Achras sapota L.) juice

Model	a (KJ/mol)	b (Brix−1)/(−)	r	rmse%
Ea = a(C)b	0.0055 ± 0.0001	2.079 ± 0.005	0.9089	20.44
Ea = a Exp (bC)	1.5603 ± 0.0031	0.0492 ± 0.0001	0.9588	13.44
Ea = a (aw)b	3.890 ± 0.002	−12.985 ± 0.005	0.9909	5.80
Ea = a Exp (b aw)	5795063.25 ± 31718.73	−14.260 ± 0.006	0.9903	6.20

Mean ± SD (n = 3)

Effect of total soluble solid content

The concentration of the soluble solids and insoluble solids had strong effect on the viscosity of the Newtonian fluids, where as consistency index and apparent viscosity of non-Newtonian fluids (Krokida et al. 2001). The viscosity of a liquid food depends on the nature of solvent, nature of solute, their interaction, and amount of solid content in solution, solute shape, size and state of hydration. The viscosity of sapota juice increased significantly (p < 0.05) with increase in total soluble solid content. The variation in viscosity with soluble solid content was due to variation in degree of hydration of solute molecules, increase in hydrogen bonding with hydroxyl groups of solute and decrease in inter-molecular spacing. The variation of viscosity of sapota juice with total soluble solid content was non-linear in nature. The different models namely power law and exponential model of different orders were used to investigate the variation in viscosity with soluble solid content at particular temperature used. Several investigators had used these models to investigate the effect of soluble solid content on viscosity of different fluids (Ibarz et al. 2009; Ibarz et al. 1989; Manjunatha et al. 2012a; 2012b; Manjunatha and Raju 2013; Altan and Maskan 2005; Kaya and Sozer 2005; Shamsudin et al. 2007; Giner et al. 1996; Juszczak et al. 2009; Ibarz et al. 1992a; Juszczak et al. 2010; Juszczak and Fortuna 2004; Nindo et al. 2005).

$$\begin{array}{ll}\mathrm{Power}\mathrm{law}\mathrm{type}:\hfill & \eta =a{\left(C\right)}^b\hfill \\ \mathrm{Exponential}\mathrm{type};\mathrm{First}\mathrm{order}:\hfill & \eta =a\mathit{Exp}\left(bC\right)\hfill \\ \mathrm{Exponential}\mathrm{type};\mathrm{second}\mathrm{order}:\hfill & \eta =a\mathit{Exp}\left(bC+c{C}^2\right)\hfill \end{array}$$ 7

where η is the viscosity (mPa s), a is constant (mPa s), b is constant (brix⁻¹), c is a constant (brix⁻²) and C is total soluble solid content (^o brix).

The parameters of the above models were estimated by least square approximation method at 95 % confidence level (p < 0.05). The parameters of variation in viscosity of sapota juice with soluble solid content by three models namely power law; exponential first order and exponential second order at different temperatures are shown in Tables 5, 6, and 7 respectively. The correlation coefficients were 0.9075 ≤ r ≤ 0.9614, 0.9612 ≤ r ≤ 0.9922 and 0.9944 ≤ r ≤ 0.9992 for power law, exponential first order and exponential second order models respectively. The root mean square error percentage values were 5.47 ≤ rmse% ≤ 24.4, 2.24 ≤ rmse% ≤ 17.02 and 0.52 ≤ rmse% ≤ 3.52 for power law, exponential first order and exponential second order models respectively. The parameter ‘b’ in power law and exponential models decreased significantly (p < 0.05) with increase in temperature. This indicated that at lower temperatures, the viscosity of sapota juice increases rapidly when concentration increases, which could be due to marked change in thermal energy of the molecules and inter-molecular spacing. The exponential type of second order was better to describe the influence of total soluble solid content on viscosity of sapota juice at different temperatures (r ≥ 0.99, rmse% ≤ 3.53). The parameters of second order exponential model are shown in Table 7 and parameter ‘a’ decreasing significantly with increasing temperature. The suggested model result indicated that the variation viscosity of sapota juice was sensitive to total soluble solid content because the parameter ‘c’ which relates the viscosity quadratically with concentration. The second order exponential model was better to describe the relation between total soluble solid content on viscosity of sapota juice at different temperatures. Similar type of results was reported for pear juice, lime juice and tender coconut water (Ibarz et al. 1989; Manjunatha et al. 2012a; Manjunatha and Raju 2013).

Table 5.

Parameters of power law model relating Newtonian viscosity with total soluble solid content of enzyme clarified sapota (Achras sapota L.) juice at different temperatures

Power law model: η = a (C)b
Temperature (°C)	a (mPa s)	b (Brix−1)	r	rmse%
10	1.088 × 10−5a ± 2.702 × 10−7	3.838a ± 0.007	0.9614	24.40
25	0.032b ± 0.001	1.645b ± 0.004	0.9075	15.83
40	0.376c ± 0.003	0.912c ± 0.002	0.9178	8.48
55	0.668d ± 0.006	0.709d ± 0.003	0.9460	6.10
70	0.709e ± 0.002	0.668e ± 0.001	0.9415	5.88
85	0.745f ± 0.001	0.638f ± 0.001	0.9476	5.47

Mean ± SD (n = 3), Different superscripts in columns show significantly different at p < 0.05

Table 6.

Parameters of first order exponential model relating Newtonian viscosity with total soluble solid content of enzyme clarified sapota (Achras sapota L.) juice at different temperatures

First order exponential model: η = a Exp (bC)
Temperature (°C)	a (mPa s)	b (%−1)	r	rmse%
10	0.815a ± 0.004	0.0755a ± 0.0001	0.9796	17.02
25	2.191b ± 0.004	0.0440b ± 0.0001	0.9612	9.40
40	3.136c ± 0.006	0.0284c ± 0.0012	0.9729	4.43
55	3.367d ± 0.007	0.0233d ± 0.0001	0.9922	2.48
70	3.218e ± 0.003	0.0222de ± 0.00003	0.9906	2.49
85	3.165f ± 0.001	0.0212e ± 0.00001	0.9907	2.24

Mean ± SD (n = 3), Different superscripts in columns show significantly different at p < 0.05

Table 7.

Parameters of second order exponential model relating Newtonian viscosity with total soluble solid content of enzyme clarified sapota (Achras sapota L.) juice at different temperatures

Second order exponential Model: η = a Exp (b C + c C2)
Temperature (°C)	a (mPa s)	b (Brix−1)	c (Brix−2)	r	rmse%
10	10.575a ± 0.007	−0.0479a ± 0.0001	0.00140a ± 0.00001	0.9990	3.53
25	8.201b ± 0.009	−0.0338b ± 0.0001	0.000996b ± 0.000001	0.9957	3.11
40	5.661c ± 0.024	−0.0092c ± 0.0003	0.000515c ± 0.000006	0.9944	1.78
55	4.367d ± 0.003	0.0060d ± 0.0001	0.000236d ± 0.000003	0.9992	0.63
70	4.205e ± 0.016	0.0043e ± 0.0003	0.000246d ± 0.000004	0.9992	0.52
85	3.755e ± 0.010	0.0097f ± 0.0002	0.000246d ± 0.000004	0.9945	1.24

Mean ± SD (n = 3), Different superscripts in columns show significantly different at p < 0.05

Effect of water activity

The water activity of fluid was dependent on amount of solid content, nature of solute, its physicochemical properties such as molecular weight, size, shape and solute-solvent interactions. The variation in viscosity of sapota juice to water activity was non linear in nature and several authors were suggested by two model equations namely power law and exponential type models as (Ibarz et al. 1992b; 1994; Manjunatha et al. 2012a; Manjunatha and Raju 2013)

$$\begin{array}{ll}\mathrm{Power}\mathrm{law};\hfill & \eta =a{\left(a_w\right)}^b\hfill \\ \mathrm{Exponential}\mathrm{type};\hfill & \eta =a\mathit{exp}\left(b{a}_w\right)\hfill \end{array}$$ 8

where η is the viscosity (mPa s), a is constant (mPa s), b is constant (-) and a_w is water activity (-). The parameters of the power law and exponential models were estimated by the method of least squares at 95 % confidence level (p < 0.05). The parameters of the models correlation coefficient and percent root mean square error and are shown in Tables 8 and 9 respectively. The correlation coefficient was in 0.9808 ≤ r ≤ 0.9985 and 0.9836 ≤ r ≤ 0.9981; whereas percent root mean square error values 1.46 ≤ rmse% ≤ 4.38 and 1.52 ≤ rmse% ≤ 5.19 for power law and exponential models respectively. The results indicated that power law model suitable for describing the viscosity of sapota juice with specific water activity level. The parameter ‘b’ of power law model was negative which indicated that the viscosity would decrease with increase in water activity as water activity mainly depends on solid content of the sapota juice. The water activity of liquid foods is dependent on concentration of the soluble solids, insoluble solids, nature of solute and solute-solvent interactions reported to have a strong non-linear effect on the viscosity of Newtonian fluids (Krokida et al. 2001). The magnitude of parameter ‘b’ of models decreased significantly (p < 0.05) with increase in temperature which indicated that the effect of water activity on viscosity markedly high at lower temperatures. At lower temperatures the change in viscosity of sapota juice was more rapid compared to that at higher temperatures. Similar type of results was reported for other liquid foods (Ibarz et al. 1994; Ibarz et al. 1992b; Manjunatha et al. 2012a; Manjunatha and Raju 2013). The second order polynomial equation was reported for variation of viscosity with water activity of some model solutions such as sodium chloride, glycerol, sucrose, and urea (Mazurkiewicz et al. 2001). These variations may be due nature of solute, its molecular weight, molecular size and shape, solute-solvent interactions, and state of hydration (Nindo et al. 2005; Telis et al. 2007; Fennema 2005).

Table 8.

Parameters of power law model relating Newtonian viscosity with water activity of enzyme clarified sapota (Achras sapota L.) juice at different temperatures

Power law Model : η = a (aw)b
Temperature (°C)	a (mPa s)	b (-)	r	rmse%
10	4.579a ± 0.004	−17.300a ± 0.014	0.9985	4.38
25	4.626b ± 0.002	−12.198b ± 0.009	0.9965	2.36
40	4.779c ± 0.005	−8.684c ± 0.022	0.9956	1.46
55	4.692d ± 0.004	−6.981d ± 0.019	0.9909	2.08
70	4.395e ± 0.003	−6.713e ± 0.012	0.9922	1.75
85	4.237f ± 0.001	−6.359f ± 0.001	0.9808	2.41

Mean ± SD (n = 3), Different superscripts in columns show significantly different at p < 0.05

Table 9.

Parameters of exponential model relating Newtonian viscosity with water activity of enzyme clarified sapota (Achras sapota L.) juice at different temperatures

Exponential Model : η = a exp (baw)
Temperature (°C)	a (mPa s)	b (-)	r	rmse%
10	849162102.2a ± 12773932.89	−19.112a ± 0.016	0.9981	5.19
25	2815305.33b ± 26342.11	−13.358b ± 0.010	0.9951	2.84
40	60603.79b ± 1370.57	−9.471c ± 0.024	0.9951	1.61
55	9365.69b ± 186.17	−7.618d ± 0.021	0.9928	1.85
70	6535.42b ± 79.00	−7.322e ± 0.013	0.9940	1.52
85	4344.59b ± 1.63	−6.942f ± 0.001	0.9836	2.18

Mean ± SD (n = 3), Different superscripts in columns show significantly different at p < 0.05

Combined effect of temperature and total soluble solid content

From the food process engineering point of view, it is important to obtain a single equation which describes both temperature and soluble solid content on viscosity of sapota juice. Several authors have used different equations to describe the combined effect of temperature and soluble solid content on viscosity of the fluids (Juszczak et al. 2009; Juszczak et al. 2010; Ibarz et al. 2009; Altan and Maskan 2005; Kaya and Sozer 2005; Giner et al. 1996; Ibarz et al. 1996; Nindo et al. 2005; Manjunatha et al. 2012a, 2012b; Manjunatha and Raju 2013; Juszczak and Fortuna 2004; Nindo et al. 2007). The model equations were

$$\begin{array}{ll}\mathrm{Power}\mathrm{law}\mathrm{type}:\hfill & \eta =a{\left(C\right)}^c*\mathit{Exp}\left(E_a/\mathit{RT}\right)\hfill \\ \mathrm{Exponential}\mathrm{type}\mathrm{first}\mathrm{order}:\hfill & \eta =a\mathit{Exp}\left(E_a/\mathit{RT}+cC\right)\hfill \\ \mathrm{Exponential}\mathrm{type}\mathrm{second}\mathrm{order}:\hfill & \eta =a\mathit{Exp}\left(E_a/\mathit{RT}+cC+d{C}^2\right)\hfill \end{array}$$ 9

where η is the viscosity (mPa s), a is pre-exponential constant (mPa s), b = E_a/R, E_a is the flow activation energy (J/mol), R is universal gas constant (J/mol K), T is absolute temperature (K), c is constant (brix⁻¹), d is constant (brix⁻²) and C is total soluble solid content (^obrix).

The values of viscosity shown in Table 2 were fitted to the above equations by the method of least squares using multiple regression analysis. The fits and estimates of the parameters were determined at 5 % significant level (p < 0.05). The suitability of the model was decided based on correlation coefficient (r) and percent root mean square error (rmse%) values. Table 10 shows the parameters for the different models, correlation coefficients and percent root mean square errors. The correlation coefficients were 0.9042, 0.9344 and 0.9553 for power law, exponential first order and exponential second order models, whereas percent root mean square error values 9.22, 7.22 and 5.90 respectively. The second order exponential equation was better to describe the combined effect of temperature and total soluble solid content on viscosity of sapota juice, because of high correlation coefficient and low percent root mean square error values, where the values of other models were low correlation coefficient (r) and high root mean square error percent (rmse%) compared to second order exponential model. The final equation which represents the combined effect of temperature and total soluble solid content on viscosity of enzyme clarified sapota juice was given by

$$\eta =2.809\times {10}^{-3}\mathit{Exp}\left(2382.48/T-0.0366C+0.0011C^2\right),\left(r=0.9553,\mathit{rmse\%}=5.90,p<0.05\right)$$

where η is viscosity in mPa s, T is temperature in Kelvin (K) and C is total soluble solid content in ^oBrix. The viscosity of enzyme clarified sapota juice was significantly (p < 0.05) affected by temperature and total soluble solid content of sapota juice. The surface plot that described the combined effect of temperature and total soluble solid content on viscosity of sapota juice at different temperatures and concentrations is shown in Fig. 3. The magnitude of viscosity depends on both temperature and total soluble solid content of sapota juice. At lower temperatures the magnitude of viscosity increased rapidly with soluble solid content and increased marginally at higher temperatures, this was due to increase in thermal energy of the molecules and increase in intermolecular spacing at higher temperatures this strongly affected the viscosity. Similar type of results was reported for other fluid foods (Nindo et al. 2005; Ibarz et al. 1989; Manjunatha et al. 2012a; Manjunatha and Raju 2013). Altan and Maskan (2005) reported that the viscosity of pomegranate juice was strongly depends on total soluble solid content and temperature irrespective of method of concentration. The viscosity of fluid depends on nature solute, size, and shape state of hydration of the molecules in juice. The solute and solvent interaction was different for different types of solutes. In case of sapota juice the soluble solids were mainly sugars, such as glucose, fructose and sucrose. The state of hydration was different for different sugars and magnitude of viscosity depends on type of sugar and fractions present in the juice (Nindo et al. 2005; Telis et al. 2007).

Table 10.

Parameters of different models relating combined effect of temperature and total soluble solid content on Newtonian viscosity of enzyme clarified sapota (Achras sapota L.) juice

Model	a (mPa s)	b = Ea/R (K)	c (Brix−1)	d (Brix−2)	r	rmse%
Power Law: η = a (C)c Exp(Ea/RT)	1.183 × 10−6 ± 3.465 × 10−8	2390.54 ± 1.72	2.244 ± 0.006	–	0.9042	9.22
First order exponential η = a Exp(Ea/RT + c C)	5.945 × 10−4 ± 4.618 × 10−6	2366.68 ± 1.36	0.0523 ± 0.0001	–	0.9344	7.22
Second order exponential η = a Exp(Ea/RT + c C + d C2)	2.809 × 10−3 ± 1.102 × 10−5	2382.48 ± 1.29	−0.0366 ± 0.0001	0.0011 ± 0.00001	0.9553	5.90

Mean ± SD (n = 3)

Fig. 3.

Surface plot for combined effect of total soluble solid content and temperature on viscosity of enzyme clarified sapota (Achras sapota L.) juice

Combined effect of temperature and water activity

It was also very important to establish a combined single equation relating temperature and water activity on viscosity of sapota juice. The two models were used to obtain a single equation for describing the combined effect of temperature and water activity on viscosity of sapota juice. Generally, power law and exponential type equation were used to describe the combined effect of temperature and water activity on viscosity of juices.

$$\begin{array}{ll}\mathrm{Power}\mathrm{law}\mathrm{model}:\hfill & \eta =a\mathit{Exp}\left(E_a/\mathit{RT}\right)*{\left(a_w\right)}^c\hfill \\ \mathrm{Exponential}\mathrm{model}:\hfill & \eta =a\mathit{Exp}\left(E_a/\mathit{RT}+c{a}_w\right)\hfill \end{array}$$ 10

where η is the viscosity (m Pa s), a is pre-exponential constant (m Pa s), b = E_a/R, E_a is flow activation energy (J/mol), R is the universal gas constant, T is absolute temperature (K), a_w is the water activity (-) and c is constant (-).

The viscosity of sapota juice at different temperature and water activity in Table 2 were fitted using multiple regression analysis by method of least squares at 5 % significant level. The parameters of combined effect of temperature and water activity were reported in Table 11. The correlation coefficients were 0.9553 and 0.9547 for power law and exponential models, whereas percent root mean square error was 5.93 and 5.98 respectively. Both the models were able to describe the combined effect of temperature and water activity on sapota juice, since the correlation coefficients and root mean square value were almost similar magnitude. The parameter ‘c’ of the model was negative, which indicated that viscosity of sapota juice decreased with increase in water activity. The water activity of fluid mainly depends on nature of solute and its concentration, solute-solvent interactions. The combined equations which related to temperature and water activity on viscosity of sapota juice were given by

$$\begin{array}{ll}\eta =1.513\times {10}^{-3}{\left(a_w\right)}^{-13.695}\mathit{Exp}\left(2380.02/T\right),\hfill & \left(r=0.9553,\mathit{rmse\%}=5.93\right)\hfill \\ \eta =4913.16*\mathit{Exp}\left(2379.47/T-15.040a_w\right),\hfill & \left(r=0.9547,\mathit{rmse\%}=5.98\right)\hfill \end{array}$$

where η is the viscosity (mPa s), a is pre-exponential constant (mPa s), T is temperature (K) and a_w is water activity (-). Figure 4 shows the surface plot for the combined effect of temperature and water activity on viscosity of sapota juice at different temperature and water activity levels. The magnitude of viscosity of sapota juice increased rapidly at lower water activities where as increased marginally at higher water activity levels. This indicated that both temperature and water activity had significant effect on viscosity of sapota juice and at higher temperatures the mobility of molecules was higher due to its higher kinetic energy and also increase in inter-molecular spacing. Similar types of results were reported for different fruit juices (Ibarz et al. 1994; Ibarz et al. 1992b; Manjunatha et al. 2012a; Manjunatha and Raju 2013). These results were very useful in processing, designing of equipments and up scaling of process of sapota juice and their concentrates in large scale commercial production.

Table 11.

Parameters of different models relating combined effect of temperature and water activity on Newtonian viscosity of enzyme clarified sapota (Achras sapota L.) juice

Model	a (mPa s)	b = Ea/R (K)	c (-)	r	rmse%
Power Law: η = a (aw)c Exp(Ea/RT)	1.513 × 10−3 ± 7.550 × 10−6	2380.02 ± 1.25	−13.695 ± 0.014	0.9553	5.93
Exponential model: η = a Exp(Ea/RT + c aw)	4913.16 ± 50.77	2379.47 ± 1.26	−15.040 ± 0.016	0.9547	5.98

Mean ± SD (n = 3)

Fig. 4.

Surface plot for combined effect of water activity and temperature on viscosity of enzyme clarified sapota (Achras sapota L.) juice

Conclusions

The enzyme clarified sapota juice and its concentrates behaved like Newtonian fluid. The Newtonian viscosity of enzyme clarified sapota juice and its concentrates were in the range 4.340 to 56.416 mPa s depending upon temperature (10 to 85 °C) and total soluble solid content (10.2 to 55.6 °brix) corresponding water activity (0.986 to 0.865). The viscosity of enzyme clarified sapota juice was increased significantly (p < 0.05) with increase in solid content whereas it decreased significantly (p < 0.05) with increase in water activity. The viscosity of sapota juice decreased significantly (p < 0.05) with increase in temperature. The effect of temperature on viscosity of enzyme clarified sapota juice followed Arrhenius equation (r > 0.94) and activation energy for viscous flow was in the range from 5.218 to 25.439 kJ/mol depending upon the total soluble solid content studied. The effect of total soluble solid content on flow activation energy followed exponential type relation (r > 0.95) where as it followed power law equation with water activity (r > 0.99). The effect of total soluble solid content on viscosity of enzyme clarified sapota juice followed by second order exponential type equation (r > 0.99) at temperature studied. The effect of water activity on viscosity of enzyme clarified sapota juice followed power law type equation (r > 0.98) at temperature studied. The combined effect of temperature and total soluble solid content/water activity on viscosity was described by the equations

$$\begin{array}{ll}\eta =2.809\times {10}^{-3}\mathit{Exp}\left(2382.48/T-0.0366C+0.0011C^2\right),\hfill & \left(r=0.9553,\mathit{rmse\%}=5.90\right)\hfill \\ \eta =1.513\times {10}^{-3}{\left(a_w\right)}^{-13.695}\mathit{Exp}\left(2380.02/T\right),\hfill & \left(r=0.9553,\mathit{rmse\%}=5.93\right)\hfill \\ \eta =4913.16*\mathit{Exp}\left(2379.47/T-15.040a_w\right),\hfill & \left(r=0.9547,\mathit{rmse\%}=5.98\right)\hfill \end{array}$$

where, η is the viscosity (mPa s), a is pre-exponential constant is mPa s, T is temperature in Kelvin (K) and C is the total soluble solid content in °brix, a_w is water activity (-).