Rheological Properties of Fruits and Vegetables: A Review

Abstract

Recently, published values of rheological properties of fruit- and vegetable-based products are presented, concerning shear stress, consistency coefficient, flow behaviour index, Bingham plastic viscosity, and activation energy as function of soluble solids content and temperature. The Herschel–Bulkley model was used to describe most of the products showing a pseudoplastic behaviour, whilst the Power law and the Bingham model were successfully fitted to the others. The clarified and depectinated fruit juices as well as carrot juice showed a Newtonian behaviour.

Keywords:

• Rheology
• Consistency coefficient
• Shear stress
• Flow behaviour index
• Newtonian fluid
• Non-Newtonian fluid

INTRODUCTION

Rheological study of foods is important to the handling and processing, quality control, and sensory evaluation.^[1] Knowledge of rheological characterisation is essential for the prediction of engineering parameters, such as heat and mass transfer coefficients for product development, design and evaluation of manufacturing processes, as well as packaging and storage strategies.^[2,3] An appropriate design of operating units is required for optimum processing to prevent facilities becoming over-dimensioned and to subsequently reduce the wasteful use of economic resources.^[4] With the world’s increased interest in human health and diet, fruits and vegetables are in demand due to their nutritional properties. As well as providing the basic nutrition, it has been shown that fruits and vegetables provide an additional physiological benefit, which is referred to as functional foods. Their rich bioactive compounds, such as polyphenols and carotenoids, can supply protection against the risk of certain diseases.^[5,6] As a result, there has been a great expansion of research, product development, and industrial processing of fruits and vegetables. The rheological behaviour of fruit- and vegetable-derived products, such as juice and puree, is fundamentally influenced by their qualitative and quantitative composition.^[6] As the plant-based dispersions are composed of insoluble particles and aqueous solution, the solids content, particle size distribution of solids, and serum viscosity play important roles.^[7] The manufacturing processes, including heating and cooling and mechanical treatments, also relate to the rheological behaviour.^[8] There have been a number of studies carried out to determine rheological properties of fruit purees, fruit juices, vegetable purees, and vegetable suspensions. Regardless of the numbers of papers published on the rheological behaviours of different fruits and vegetables, there has been only a couple of reviews on the rheological properties of fruit and vegetable products.^[9,10] The current article aims at giving a thorough overview of the most recent findings on the rheological properties of fruit- and vegetable-based products.

MATHEMATICAL MODEL

Different equations have been used to describe the flow behaviour of liquid foods.^[11] The simplest form of rheological behaviour is the linear relationship between shear stress and shear rate called Newtonian. In this case, the slope value is the viscosity of the sample according to Newton’s equation:

(1)

where = shear stress (Pa), μ = absolute viscosity (Pa.s), and = shear rate (s⁻¹). However, most fluid foods, including the fruit and vegetable derivatives, do not display the simple Newtonian behaviour. When the fruit and vegetable derivatives are assumed to behave as non-Newtonian fluids, the shear stress and shear rate data are fitted into some of the common non-Newtonian models, such as power-law, Herschel–Bulkley, and Bingham model. The power law model is:

(2)

where = shear stress (Pa), k = consistency coefficient (Pa.sⁿ), γ = shear rate (s⁻¹), and n = flow behaviour index (dimensionless). In the power law model, the constants k and n are required to characterise the flow behaviour. The k value corresponds to the absolute viscosity of Newtonian fluids. The Herschel–Bulkley model is derived from the power-law model by adding σ_o, yield stress (Pa):

(3)

Based on the magnitude of n and _o, the Herschel–Bulkley model is able to describe the general flow properties within a certain shear range. The Bingham model is derived from the Newton’s equation by adding _o, Bingham yield stress, shear stress at zero shear rate (Pa):

(4)

where = shear stress (Pa), μ_B = Bingham plastic viscosity (Pa.s), and = shear rate (s⁻¹). The effect of temperature on the viscosity follows the Arrhenius equation, which can be used to calculate the activation energy for the viscous flow:^[12,13]

(5)

where μ = absolute viscosity (Pa.s), μ_o = constant (Pa.s), Ea = flow activation energy (J.mol⁻¹), R = gas constant (8.3144 J.mol⁻¹.K⁻¹), and T = temperature (K). For the consistency coefficient,

(6)

where k = consistency coefficient (Pa.sⁿ), k_o = constant (Pa.s).

RHEOLOGICAL PROPERTIES OF SELECTED FRUITS AND VEGETABLES

A total number of more than 30 publications were retrieved from the literature. The gathered data along with the additional information, such as the soluble solids content, percentage of total solids, and temperature were tabulated into six different categories of berry, stone fruit, pome, citrus, and other fruits and vegetables. The Herschel–Bulkley model was used to describe most of the products, whilst the Power law and the Bingham model were successfully fitted to the others.

Berry Fruits

All the selected berry fruit products were fitted with the Herschel–Bulkley model, showing a pseudoplastic behaviour with n < 1 presented in Table 1.^[14−18] The general trend of decreasing yield stress (σ_o) with the increase in the temperature was observed. The consistency coefficient (k) displayed a decreasing trend with temperature except for the açai berry pulp, which demonstrated an increase in the consistency coefficient.^[14] This tendency was not verified in the study carried out by Haminiuk et al.^[15] for the 65°C sample of blueberry puree.^[16] According to Krokida et al.,^[9] the temperature affects the consistency coefficient (k) of the non-Newtonian fluid foods significantly. The flow behaviour index (n) was in the range of 0.25 to 0.6 for most of the berry products. There was a tendency for the flow behaviour index (n) to increase with temperature in raspberry and strawberry products. This was an opposite behaviour shown in the other berry products. The activation energy ranged from 4.18 to 18.27 kJ.mol⁻¹. Açai berry pulp had a low activation energy value of 4.18 kJ.mol⁻¹, which indicates that there was a less pronounced effect of temperature on the viscosity of açai pulp.^[14] It has been documented that the viscosity of fruit purees displays a lesser dependence on the temperature than clarified juices, and this is due to the presence of pulp or fibres in the purees.^[9] Açai berries are naturally high in fibre content. The fibre content of the pulp was approximately 31% dry basis and the difference in the activation energy is due to the considerable amount of fibre present in the pulp.^[14]

Stone Fruits

The general trend of the rheological properties of the selected stone fruit products was the decrease in yield stress (σ_o) and consistency coefficient (k) and the increase in flow behaviour index (n) with temperature increase, shown in Table 2.^[18−25] The Herschel–Bulkley model was fitted except for the cherry juice and sloe juice, which were described by the Power law and Bingham model, respectively. The pseudoplastic behaviour was observed for all the products fitted with Herschel–Bulkley models. The cherry juice was found to be a Newtonian fluid whereas the sloe juice was found to be non-Newtonian with a yield stress in contrast. It was discovered for the sloe juice that the higher the temperature, the higher the yield stress (σ_o) and the lower the Bingham plastic viscosity (μ_B).^[24] The Bingham model was also fitted to the pineapple juice, which also displayed the increase in the yield stress (σ_o) and the decrease in the Bingham plastic viscosity (μ_B) with temperature increase.^[26] Fruit juices are composed of an insoluble phase of the pulp dispersed in a viscous solution of the serum. The dispersed phase is the fruit tissue cells and their fragments, including the cell walls, insoluble polymer clusters, and chains, whereas the serum includes soluble polysaccharides, sugars, salts, and acids.^[27] Therefore, the interaction between the pulp and the serum defines the different fruit juice rheological properties. The activation energy ranged from the lowest of 3.99 kJ.mol⁻¹ to the highest of 44 kJ.mol⁻¹ within the selected stone fruit products. The sloe juice exhibited low activation energy values less than 10 kJ.mol⁻¹ across the different total soluble solid contents. The low activation energy values were observed for the pineapple juice and the quince nectar at 6.80 kJ.mol⁻¹ and 9.88 kJ.mol⁻¹, respectively. Suspensions with high insoluble solid content are more likely to have a lower activation energy value than the flow of water (14.4 kJ.mol⁻¹).^[9] The juices contained pulps, which resulted in the low activation energy values.

TABLE 1 Rheological parameters of selected berry fruit products

	C	Total						γ min	γ max	Ea,	Sugar content
Product	°Brix	% solids	Temp., °C	o, Pa	k, Pa.s^n	n	μB, Pa.s	s^−1	s^−1	kJ.mol^−1	g/100 g fruit	Reference
Açai berry pulp	—	—	10	4.740	0.170	0.790	—	0.0	300	4.18		[14]
Açai berry pulp	—	—	25	3.530	0.370	0.660	—	0.0	300
Açai berry pulp	—	—	40	3.270	0.360	0.620	—	0.0	300
Açai berry pulp	—	—	55	3.140	0.510	0.510	—	0.0	300
Açai berry pulp	—	—	70	2.290	1.280	0.390	—	0.0	300
Blackberry pulp	5.37	—	10	0.350	1.950	0.380	—	2.8	70	18.27		[15]
Blackberry pulp	5.37	—	20	0.290	1.120	0.440	—	2.8	70
Blackberry pulp	5.37	—	30	1.000	0.240	0.700	—	2.8	70
Blackberry pulp	5.37	—	40	0.570	0.440	0.550	—	2.8	70
Blackberry pulp	5.37	—	50	0.450	0.450	0.500	—	2.8	70
Blackberry pulp	5.37	—	60	0.540	0.090	0.770	—	2.8	70
Blueberry puree	14.46	—	5	31.760	14.817	0.341	—	0.0	300	9.36	10.67	[16]
Blueberry puree	14.46	—	25	17.465	17.196	0.276	—	0.0	300
Blueberry puree	14.46	—	45	9.837	13.604	0.270	—	0.0	300
Blueberry puree	14.46	—	65	37.015	0.519	0.696	—	0.0	300
Golden berry juice	16.42	21	5	3.038	8.198	0.269	—	0.3	100	13.49		[17]
Golden berry juice	16.42	21	20	2.244	7.877	0.266	—	0.3	100
Golden berry juice	16.42	21	40	1.150	7.036	0.258	—	0.3	100
Golden berry juice	16.42	21	60	0.573	5.418	0.259	—	0.3	100
Golden berry juice	16.42	21	80	0.427	3.812	0.257	—	0.3	100
Golden berry juice	16.42	21	100	0.366	2.162	0.255	—	0.3	100
Golden berry juice	30.00	—	5	3.043	17.330	0.356	—	0.3	100	11.48
Golden berry juice	30.00	—	20	2.106	15.860	0.337	—	0.3	100
Golden berry juice	30.00	—	40	1.503	13.420	0.333	—	0.3	100
Golden berry juice	30.00	—	60	0.792	11.400	0.332	—	0.3	100
Golden berry juice	30.00	—	80	0.455	9.148	0.314	—	0.3	100
Golden berry juice	30.00	—	100	0.426	7.514	0.305	—	0.3	100
Golden berry juice	30.00	—	5	3.931	21.760	0.580	—	0.3	100	10.07
Golden berry juice	40.00	—	20	3.146	18.900	0.564	—	0.3	100
Golden berry juice	40.00	—	40	3.047	17.960	0.566	—	0.3	100
Golden berry juice	40.00	—	60	2.776	15.250	0.534	—	0.3	100
Golden berry juice	40.00	—	80	2.3350	13.640	0.529	—	0.3	100
Golden berry juice	40.00	—	100	1.5130	9.836	0.509	—	0.3	100
Raspberry jam	—	—	20	12.6180	15.240	0.328	—	17.8	445		47	[18]
Raspberry jam	—	—	25	9.5005	12.600	0.335	—	17.8	445
Raspberry jam	—	—	30	6.5172	11.200	0.340	—	17.8	445
Raspberry jam	—	—	35	3.6583	10.040	0.345	—	17.8	445
Raspberry jam	—	—	40	1.6574	8.800	0.352	—	17.8	445
Raspberry puree	—	—	20	3.5300	4.268	0.362	—	17.8	445		7	[18]
Raspberry puree	—	—	25	2.8621	3.659	0.367	—	17.8	445
Raspberry puree	—	—	30	2.7175	3.029	0.374	—	17.8	445
Raspberry puree	—	—	35	2.3309	2.578	0.380	—	17.8	445
Raspberry puree	—	—	40	1.9906	1.985	0.387	—	17.8	445
Strawberry jam	—	—	20	3.8970	36.920	0.280	—	17.8	445		45	[18]
Strawberry jam	—	—	25	3.2200	21.450	0.327	—	17.8	445
Strawberry jam	—	—	30	2.5500	15.590	0.357	—	17.8	445
Strawberry jam	—	—	35	1.8940	10.590	0.393	—	17.8	445
Strawberry jam	—	—	40	1.4700	6.627	0.452	—	17.8	445
Strawberry puree	—	—	20	5.1190	5.770	0.261	—	17.8	445		7	[18]
Strawberry puree	—	—	25	4.5240	5.650	0.262	—	17.8	445
Strawberry puree	—	—	30	3.4010	5.522	0.263	—	17.8	445
Strawberry puree	—	—	35	3.2350	5.432	0.264	—	17.8	445
Strawberry puree	—	—	40	2.7750	5.346	0.265	—	17.8	445

TABLE 2 Rheological parameters of selected stone fruit products

	C	Total						γ min	γ max	Ea,	Sugar content
Product	°Brix	% solids	Temp., °C	o, Pa	k, Pa.s^n	n	μB, Pa.s	s^−1	s^−1	kJ.mol^−1	g/100 g fruit	Reference
Apricot puree for baby	—	—	5	3.710	31.100	0.202	—	0.1	100			[19]
Apricot puree for baby	—	—	20	7.410	13.700	0.283	—	0.1	100
Apricot puree for baby	—	—	35	7.560	11.800	0.222	—	0.1	100
Apricot puree for baby	—	—	50	4.240	8.380	0.351	—	0.1	100
Apricot puree for baby	—	—	65	0.650	6.970	0.355	—	0.1	100
Apricot puree for baby	—	—	80	0.952	3.150	0.372	—	0.1	100
Cherry juice	50.00	—	20	—	0.016	1.000	—	1.0	300	24.68		[20]
Cherry juice	55.00	—	20	—	0.029	1.000	—	1.0	300	28.78
Cherry juice	60.00	—	20	—	0.056	1.000	—	1.0	300	33.72
Cherry juice	63.80	—	20	—	0.107	1.000	—	1.0	300	38.48
Cherry juice	63.80	—	10	—	0.213	1.000	—	1.0	300
Cherry juice	63.80	—	20	—	0.108	1.000	—	1.0	300
Cherry juice	63.80	—	30	—	0.060	1.000	—	1.0	300
Cherry juice	63.80	—	40	—	0.040	1.000	—	1.0	300
Cherry juice	63.80	—	50	—	0.025	1.000	—	1.0	300
Cherry juice	63.80	—	60	—	0.016	1.000	—	1.0	300
Mango pulp (Fresh)	16.00	18.7	25	3.700	6.550	0.383	—	0.0	1000			[21]
Mango pulp (Fresh)	23.12	—	20	6.242	8.820	0.338	—	0.1	100			[22]
Mango pulp (Tinned)	27.10	—	20	3.805	11.330	0.309	—	0.1	100
Peach jam	—	—	20	8.080	18.410	0.326	—	0.1	300		44	[18]
Peach jam	—	—	25	6.104	11.580	0.349	—	0.1	300
Peach jam	—	—	30	4.806	7.725	0.419	—	0.1	300
Peach jam	—	—	35	3.041	4.543	0.473	—	0.1	300
Peach jam	—	—	40	1.845	3.114	0.528	—	0.1	300
Peach puree	—	—	20	12.681	6.774	0.360	—	0.1	300		10.0	[18]
Peach puree	—	—	25	12.094	6.395	0.362	—	0.1	300
Peach puree	—	—	30	11.421	6.005	0.363	—	0.1	300
Peach puree	—	—	35	10.773	5.596	0.365	—	0.1	300
Peach puree	—	—	40	10.149	5.331	0.367	—	0.1	300
Prune jam	—	—	20	7.791	59.100	0.216	—	10.0	290		40	[18]
Prune jam	—	—	25	6.001	40.920	0.238	—	10.0	290
Prune jam	—	—	30	4.258	33.500	0.255	—	10	290
Prune jam	—	—	35	2.403	28.590	0.276	—	10	290
Prune jam	—	—	30	4.258	33.500	0.255	—	10	290
Prune jam	—	—	35	2.403	28.590	0.276	—	10	290
Prune jam	—	—	40	1.065	23.500	0.295	—	10	290
Prune puree	—	—	20	3.810	6.609	0.308	—	10	290		12	[18]
Prune puree	—	—	25	3.109	5.771	0.311	—	10	290
Prune puree	—	—	30	2.643	5.349	0.314	—	10	290
Prune puree	—	—	35	2.202	4.630	0.318	—	10	290
Prune puree	—	—	40	1.772	4.291	0.323	—	10	290
Siriguela pulp	10.9	15.8	0	11.240	21.540	0.250	—	0.01	100	17.51		[23]
Siriguela pulp	10.9	15.8	20	13.260	15.220	0.300	—	0.01	100
Siriguela pulp	10.9	15.8	40	12.560	11.220	0.340	—	0.01	100
Siriguela pulp	10.9	15.8	60	1.500	3.010	0.440	—	0.01	100
Siriguela pulp	10.9	15.8	80	1.370	1.710	0.480	—	0.01	100
Sloe juice	25.0	—	5	1.740	—	—	9.1	0.01	512	3.99		[24]
Sloe juice	25.0	—	15	2.060	—	—	6.8	0.01	512
Sloe juice	25.0	—	25	2.140	—	—	5.2	0.01	512
Sloe juice	25.0	—	35	2.250	—	—	4.0	0.01	512
Sloe juice	25.0	—	45	1.740	—	—	3.6	0.01	512
Sloe juice	25.0	—	55	2.150	—	—	2.9	0.01	512
Sloe juice	25.0	—	65	2.420	—	—	2.5	0.01	512
Sloe juice	35.0	—	5	4.300	—	—	21.7	0.01	512	4.32
Sloe juice	35.0	—	15	3.910	—	—	14.2	0.01	512
Sloe juice	35.0	—	25	3.460	—	—	10.7	0.01	512
Sloe juice	35.0	—	35	3.260	—	—	8.1	0.01	512
Sloe juice	35.0	—	45	2.720	—	—	6.8	0.01	512
Sloe juice	35.0	—	55	2.090	—	—	6.0	0.01	512
Sloe juice	35.0	—	65	2.200	—	—	5.3	0.01	512
Sloe juice	40.0	—	5	4.830	—	—	34.9	0.01	512	4.64
Sloe juice	40.0	—	15	4.570	—	—	24.4	0.01	512
Sloe juice	40.0	—	25	4.100	—	—	17.8	0.01	512
Sloe juice	40.0	—	35	2.970	—	—	13.6	0.01	512
Sloe juice	40.0	—	45	3.260	—	—	11.0	0.01	512
Sloe juice	40.0	—	55	3.160	—	—	9.10	0.01	512
Sloe juice	40.0	—	65	3.040	—	—	7.90	0.01	512
Sloe juice	45.0	—	5	8.330	—	—	59.9	0.01	512	4.70
Sloe juice	45.0	—	15	6.260	—	—	41.0	0.01	512
Sloe juice	45.0	—	25	5.550	—	—	29.4	0.01	512
Sloe juice	45.0	—	35	4.590	—	—	22.3	0.01	512
Sloe juice	45.0	—	45	4.140	—	—	18.0	0.01	512
Sloe juice	45.0	—	55	4.290	—	—	14.9	0.01	512
Sloe juice	45.0	—	65	4.530	—	—	13.5	0.01	512
Sloe juice	50.0	—	5	7.570	—	—	120.2	0.01	512	5.87
Sloe juice	50.0	—	15	7.350	—	—	79.9	0.01	512
Sloe juice	50.0	—	25	8.860	—	—	45.2	0.01	512
Sloe juice	50.0	—	35	6.430	—	—	34.1	0.01	512
Sloe juice	50.0	—	45	5.790	—	—	26.3	0.01	512
Sloe juice	50.0	—	55	5.330	—	—	21.9	0.01	512
Sloe juice	50.0	—	65	5.150	—	—	18.7	0.01	512
Sloe juice	58.5	—	5	11.190	—	—	772.4	0.01	512	8.76
Sloe juice	58.5	—	15	10.280	—	—	383.3	0.01	512
Sloe juice	58.5	—	25	12.310	—	—	201.0	0.01	512
Sloe juice	58.5	—	35	10.240	—	—	118.9	0.01	512
Sloe juice	58.5	—	45	11.830	—	—	84.5	0.01	512
Sloe juice	58.5	—	55	11.130	—	—	56.7	0.01	512
Sloe juice	58.5	—	65	9.590	—	—	48.3	0.01	512
Umbu pulp	10.0	—	30	3.175	14.122	0.300	—	0.10	300			[25]
Umbu pulp	15.0	—	30	4.490	23.617	0.293	—	0.10	300
Umbu pulp	20.0	—	30	4.696	30.560	0.280	—	0.10	300
Umbu pulp	25.0	—	30	8.064	37.744	0.289	—	0.10	300

Pome Fruits

The apple and pear juices showed a Newtonian behaviour whilst the apple puree was all classified as non-Newtonian fluid (Table 3).^[19,28] The viscosity values for the apple and pear juices decreased with temperature and the soluble solid content. The effect of the temperature was analysed by the comparison of the flow activation energy. The values of the flow activation energy displayed an increase with the concentration of the soluble solids, and the constant η_o showed an inverse trend. Consequently, the effect of the temperature in the decreasing viscosity is considered as more prominent as soluble solid content increases.^[28] This tendency was shown across the values obtained for the fluid with Newtonian model fitted, including cherry juice, as shown in Table 2.^[20] It is possible to classify fruit juices into three groups according to Ibarz et al.^[29] The groups are clarified and depectinated, clarified and non-depectinated, and concentrates with suspended solids. Generally, the first group exhibits Newtonian behaviour, whereas the latter two behave as non-Newtonian fluids. The apple, pear, and cherry juices were clarified and depectinated. In Newtonian fluids, the activation energy has been found to increase from 14.4 kJ.mol⁻¹ for water to more than 60 kJ.mol⁻¹ for concentrated juices and sugar solutions.^[9] The flow activation energy for the Newtonian fluid behaving products ranged from 3.66 to 91 kJ.mol⁻¹. The activation energy calculated for the carrot juice was very low at 3.66 kJ.mol⁻¹.^[6] In contrast to the fruit juices, the carrot juice was only filtered through a mesh cloth without clarification or depectination. It has been shown that the presence of suspended solids and long-chain polysaccharides has a decreasing effect on flow activation energy.^[13] Therefore, the low activation energy of the carrot juice is most likely a result of the presence of fibres in the product.

Citrus Fruits

The citrus fruit juices were described by the Power law displaying a pseudoplastic characteristic.^[4,30] The selected citrus products, including mandarin and pummelo juices, are tabulated in Table 4. The consistency coefficient (k) followed a decreasing pattern with the rise of temperature. However, the flow behaviour index (n) increased in the mandarin juice and decreased in the pummelo juice with temperature. The effect of temperature in reducing pseudoplasticity is more prominent to juices at lower soluble solid concentration. The 20 °Brix pummelo juice displayed the flow behaviour index (n) of approximately 1 above 60°C, proposing a Newtonian characteristic of the juice at high temperature.^[30] A similar behaviour was observed in the beetroot juice of 67.1 °Brix above 60°C.^[31] Saravacos^[13] discovered that filtered orange juices of 10 and 18 °Brix exhibited a Newtonian fluid. The pummelo juice was filtered to remove the pulp from the serum and concentrated by freeze drying. The activation energy of 20 °Brix pummelo juice was 34.02 kJ.mol⁻¹, which is significantly higher than the value determined by Saravacos^[13] for the 10 and 18 °Brix filtered orange juices, 5.8 and 5.3 kJ.mol⁻¹, respectively. Higher activation energy suggests that the apparent viscosity is more prone to temperature change. The high activation energy of the pummelo juice is close to the values obtained for other concentrated fruit juices, such as mandarin juice^[4] and kiwifruit juice, as shown in Table 5.^[32] The filtered concentrated citrus fruit juices with low soluble solid content in conjunction with the high temperature applied may exhibit a Newtonian behaviour.

TABLE 3 Rheological parameters of selected pome fruit products

	C	Total						γ min	γ max	Ea,	Sugar content
Product	°Brix	% solids	Temp., °C	o, Pa	k, Pa.s^n	n	μB, Pa.s	s^−1	s^−1	kJ.mol^−1	g/100 g fruit	Reference
Apple juice	10	—	−1	—	0.007	1.000	—	0.0	400			[28]
Apple juice	20	—	−1	—	0.008	1.000	—	0.0	400
Apple juice	30	—	−3	—	0.013	1.000	—	0.0	400
Apple juice	30	—	−1	—	0.012	1.000	—	0.0	400
Apple juice	40	—	−6	—	0.019	1.000	—	0.0	400
Apple juice	40	—	−3	—	0.017	1.000	—	0.0	400
Apple juice	40	—	−1	—	0.015	1.000	—	0.0	400
Apple juice	50	—	−12	—	0.080	1.000	—	0.0	400	39
Apple juice	50	—	−9	—	0.065	1.000	—	0.0	400
Apple juice	50	—	−6	—	0.051	1.000	—	0.0	400
Apple juice	50	—	−3	—	0.046	1.000	—	0.0	400
Apple juice	50	—	−1	—	0.043	1.000	—	0.0	400
Apple juice	60	—	−18	—	0.895	1.000	—	0.0	400	49
Apple juice	60	—	−15	—	0.630	1.000	—	0.0	400
Apple juice	60	—	−12	—	0.432	1.000	—	0.0	400
Apple juice	60	—	−9	—	0.331	1.000	—	0.0	400
Apple juice	60	—	−6	—	0.257	1.000	—	0.0	400
Apple juice	60	—	−3	—	0.197	1.000	—	0.0	400
Apple juice	60	—	−1	—	0.167	1.000	—	0.0	400
Apple juice	70	—	−18	—	34.250	1.000	—	0.0	400	88
Apple juice	70	—	−15	—	19.360	1.000	—	0.0	400
Apple juice	70	—	−12	—	11.620	1.000	—	0.0	400
Apple juice	70	—	−9	—	7.189	1.000	—	0.0	400
Apple juice	70	—	−6	—	5.095	1.000	—	0.0	400
Apple juice	70	—	−3	—	3.474	1.000	—	0.0	400
Apple juice	70	—	−1	—	2.625	1.000	—	0.0	400
Apple puree for baby	—	—	5	1.56	3.230	0.331	—	0.1	100			[19]
Apple puree for baby	—	—	20	3.38	4.760	0.384	—	0.1	100
Apple puree for baby	—	—	35	2.68	2.700	0.378	—	0.1	100
Apple puree for baby	—	—	50	3.75	2.060	0.413	—	0.1	100
Apple puree for baby	—	—	65	2.74	3.360	0.304	—	0.1	100
Apple puree for baby	—	—	80	6.90	3.220	0.433	—	0.1	100
Pear juice	10	—	−1	—	0.007	1.000	—	0.0	400			[28]
Pear juice	20	—	−1	—	0.008	1.000	—	0.0	400
Pear juice	30	—	−3	—	0.013	1.000	—	0.0	400
Pear juice	30	—	−1	—	0.012	1.000	—	0.0	400
Pear juice	40	—	−6	—	0.020	1.000	—	0.0	400
Pear juice	40	—	−3	—	0.018	1.000	—	0.0	400
Pear juice	40	—	−1	—	0.016	1.000	—	0.0	400
Pear juice	50	—	−12	—	0.088	1.000	—	0.0	400	41
Pear juice	50	—	−9	—	0.071	1.000	—	0.0	400
Pear juice	50	—	−6	—	0.057	1.000	—	0.0	400
Pear juice	50	—	−3	—	0.047	1.000	—	0.0	400
Pear juice	50	—	−1	—	0.041	1.000	—	0.0	400
Pear juice	60	—	−18	—	0.860	1.000	—	0.0	400	46
Pear juice	60	—	−15	—	0.643	1.000	—	0.0	400
Pear juice	60	—	−12	—	0.474	1.000	—	0.0	400
Pear juice	60	—	−9	—	0.381	1.000	—	0.0	400
Pear juice	60	—	−6	—	0.283	1.000	—	0.0	400
Pear juice	60	—	−3	—	0.219	1.000	—	0.0	400
Pear juice	60	—	−1	—	0.183	1.000	—	0.0	400
Pear juice	70	—	−18	—	67.300	1.000	—	0.0	400	91
Pear juice	70	—	−15	—	30.150	1.000	—	0.0	400
Pear juice	70	—	−12	—	19.670	1.000	—	0.0	400
Pear juice	70	—	−9	—	12.440	1.000	—	0.0	400
Pear juice	70	—	−6	—	8.300	1.000	—	0.0	400
Pear juice	70	—	−3	—	5.730	1.000	—	0.0	400
Pear juice	70	—	−1	—	4.700	1.000	—	0.0	400

TABLE 4 Rheological parameters of selected citrus fruit products

	C	Total						γ min	γ max	Ea,	Sugar content
Product	°Brix	% solids	Temp., °C	o, Pa	k, Pa.s^n	n	μB, Pa.s	s^−1	s^−1	kJ.mol^−1	g/100 g fruit	Reference
Mandarin juice	63.3	—	−12	—	8.9400	0.730	—	0.01	400	32.00		[4]
Mandarin juice	63.3	—	−9	—	6.9100	0.746	—	0.01	400
Mandarin juice	63.3	—	−6	—	5.3800	0.742	—	0.01	400
Mandarin juice	63.3	—	−3	—	3.9800	0.721	—	0.01	400
Mandarin juice	63.3	—	0	—	3.7600	0.724	—	0.01	400
Mandarin juice	63.3	—	3	—	3.6600	0.718	—	0.01	400
Mandarin juice	63.3	—	6	—	3.9700	0.699	—	0.01	400
Pummelo juice	20.0	—	6	—	0.0710	0.741	—	1.00	400	34.02		[30]
Pummelo juice	20.0	—	20.0	—	0.0410	0.771	—	1.00	400
Pummelo juice	20.0	—	30.0	—	0.0221	0.851	—	1.00	400
Pummelo juice	20.0	—	40	—	0.0111	0.948	—	1.00	400
Pummelo juice	20.0	—	60	—	0.0066	1.008	—	1.00	400
Pummelo juice	20.0	—	75	—	0.0042	1.055	—	1.00	400
Pummelo juice	30.0	—	6	—	0.6621	0.504	—	1.00	400	42.06
Pummelo juice	30.0	—	20.0	—	0.4193	0.530	—	1.00	400
Pummelo juice	30.0	—	30.0	—	0.2072	0.602	—	1.00	400
Pummelo juice	30.0	—	40	—	0.1284	0.647	—	1.00	400
Pummelo juice	30.0	—	60	—	0.0418	0.743	—	1.00	400
Pummelo juice	30.0	—	75	—	0.0217	0.837	—	1.00	400
Pummelo juice	50.0	—	6	—	3.7564	0.504	—	1.00	400	22.12
Pummelo juice	50.0	—	20.0	—	2.4023	0.515	—	1.00	400
Pummelo juice	50.0	—	30.0	—	1.9646	0.514	—	1.00	400
Pummelo juice	50.0	—	40	—	1.5045	0.521	—	1.00	400
Pummelo juice	50.0	—	60	—	0.9900	0.532	—	1.00	400
Pummelo juice	50.0	—	75	—	0.4983	0.566	—	1.00	400

TABLE 5 Rheological parameters of selected other fruit products

	C	Total						γ min	γ max	Ea,	Sugar content
Product	°Brix	% solids	Temp., °C	o, Pa	k, Pa.s^n	n	μB, Pa.s	s^−1	s^−1	kJ.mol^−1	g/100 g fruit	Reference
Banana puree for baby	—	—	5	8.090	27.600	0.173	—	0.1	100			[19]
Banana puree for baby	—	—	20	6.120	17.600	0.184	—	0.1	100
Banana puree for baby	—	—	35	5.670	18.900	0.202	—	0.1	100
Banana puree for baby	—	—	50	0.410	10.300	0.302	—	0.1	100
Banana puree for baby	—	—	65	0.020	5.780	0.334	—	0.1	100
Banana puree for baby	—	—	80	0.760	3.640	0.345	—	0.1	100
Banana puree	—	23.70	30	81.040	4.670	0.442	—	2.8	70			[33]
Banana puree	—	23.70	40	82.200	3.150	0.457	—	2.8	70
Banana puree	—	23.70	50	74.760	1.060	0.614	—	2.8	70
Banana puree	—	23.70	60	68.980	4.920	0.412	—	2.8	70
Banana puree	—	23.70	70	56.300	2.020	0.542	—	2.8	70
Banana puree	—	23.70	80	56.350	1.710	0.523	—	2.8	70
Banana puree	—	23.70	90	54.930	0.320	0.701	—	2.8	70
Banana puree	—	23.70	100	50.860	0.170	0.809	—	2.8	70
Banana puree	—	23.70	110	30.850	0.060	0.871	—	2.8	70
Banana puree	—	23.70	120	40.940	0.030	0.966	—	2.8	70			[33]
Brazilian cherry	7.97	8.88	20	1.674	0.163	0.627	—	0.0	300	12.47		[34]
Brazilian cherry	7.97	8.88	83	0.621	0.179	0.479	—	0.0	300
Brazilian cherry	7.97	8.88	85	0.301	0.189	0.448	—	0.0	300
Brazilian cherry	7.97	8.88	90	0.351	0.091	0.558	—	0.0	300
Brazilian cherry	7.97	8.88	95	0.291	0.100	0.545	—	0.0	300
Brazilian cherry	7.97	8.88	97	0.299	0.095	0.553	—	0.0	300
Guava jam	65.04	63.66	25	—	344.610	0.320	—	0.1	10	8.16		[5]
Guava jam	65.04	63.66	35	—	347.650	0.290	—	0.1	10
Guava jam	65.04	63.66	45	—	308.480	0.300	—	0.1	10
Guava jam	65.04	63.66	55	—	285.490	0.300	—	0.1	10
Guava puree	10.2	—	10	—	127.000	0.110	—	0.0	185	16.73		[35]
Guava puree	10.20	—	16	—	120.000	0.126	—	0.0	185
Guava puree	10.20	—	20	—	92.000	0.131	—	0.0	185
Guava puree	10.20	—	30	—	88.000	0.159	—	0.0	185
Guava puree	10.20	—	40	—	87.000	0.162	—	0.0	185
Guava puree	10.2	—	50	—	85.000	0.175	—	0.0	185
Guava puree	10.2	—	60	—	81.000	0.182	—	0.0	185
Jaboticaba pulp	13.0	—	25	1.55	0.477	0.599	—	0.0	300	13.00		[36]
Kiwifruit juice	13.5	—	25	—	0.357	0.359	—	0.3	100	24.78		[32]
Kiwifruit juice	13.5	—	35	—	0.298	0.357	—	0.3	100
Kiwifruit juice	13.5	—	45	—	0.233	0.394	—	0.3	100
Kiwifruit juice	13.5	—	55	—	0.189	0.402	—	0.3	100
Kiwifruit juice	13.5	—	65	—	0.145	0.387	—	0.3	100
Kiwifruit juice	15.0	—	25	—	0.713	0.374	—	0.3	100	24.97
Kiwifruit juice	15.0	—	35	—	0.586	0.385	—	0.3	100
Kiwifruit juice	15.0	—	45	—	0.475	0.379	—	0.3	100
Kiwifruit juice	15.0	—	55	—	0.276	0.390	—	0.3	100
Kiwifruit juice	15.0	—	65	—	0.152	0.389	—	0.3	100
Kiwifruit juice	20.0	—	25	—	1.471	0.367	—	0.3	100	24.73
Kiwifruit juice	20.0	—	35	—	1.186	0.362	—	0.3	100
Kiwifruit juice	20.0	—	45	—	0.917	0.362	—	0.3	100
Kiwifruit juice	20.0	—	55	—	0.653	0.362	—	0.3	100
Kiwifruit juice	20.0	—	65	—	0.487	0.377	—	0.3	100
Kiwifruit juice	25.0	—	25	—	3.373	0.387	—	0.3	100	26.99
Kiwifruit juice	25.0	—	35	—	2.660	0.360	—	0.3	100
Kiwifruit juice	25.0	—	45	—	2.147	0.380	—	0.3	100
Kiwifruit juice	25.0	—	55	—	1.514	0.379	—	0.3	100
Kiwifruit juice	25.0	—	65	—	1.086	0.367	—	0.3	100
Kiwifruit juice	30.0	—	25	—	5.560	0.399	—	0.3	100	34.30
Kiwifruit juice	30.0	—	35	—	4.972	0.389	—	0.3	100
Kiwifruit juice	30.0	—	45	—	4.171	0.380	—	0.3	100
Kiwifruit juice	30.0	—	55	—	3.726	0.406	—	0.3	100
Kiwifruit juice	30.0	—	65	—	3.240	0.399	—	0.3	100
Pineapple juice	—	—	5	0.0184	—	—	0.0093	10.0	290	6.80		[26]
Pineapple juice	—	—	10	0.0339	—	—	0.0090	10.0	290
Pineapple juice	—	—	15	0.0252	—	—	0.0089	10.0	290
Pineapple juice	—	—	20	0.0847	—	—	0.0079	10.0	290
Pineapple juice	—	—	25	0.0966	—	—	0.0077	10.0	290

Other studies are required to understand the high temperature influence on the rheological properties of filtered concentrated citrus juices.

Other Fruits

The other fruit-based products, including banana puree, guava products, and kiwifruit juice, are shown in Table 5.^{[19,26,32−36]} The tendency of the flow behaviour index (n) increasing with increasing temperature was also found in banana puree.^[33] At 120°C, the flow behaviour index was found to be 0.966 with the consistency coefficient (k) of 0.03 Pa.sⁿ displaying that the behaviour became a Bingham fluid with a yield stress (Table 5). More significantly, the change in the flow behaviour index (n) and the consistency coefficient (k) between 50 and 60°C was prominent in the banana puree. The starch content of bananas is approximately 0.9% and the pasting temperature for banana starch varies from 49.8 to 51.8°C.^[37] A structure change in the puree was observed, most likely due to the starch gelation, which occurs within this temperature interval.^[33] This trend was not observed for the banana puree for baby,^[19] although the flow behaviour index (n) and the consistency coefficient (k) followed the same pattern as reported by Ditchfield et al.^[33] with temperature increase. The pasteurisation process before the bottling of the baby puree would have caused the starch gelation. Therefore, the pasting temperature did not affect the rheological behaviour of the baby puree. The interaction of polysaccharides in starchy fruits, such as bananas, above the gelation temperature should be analysed in further studies to determine the exact rheological behaviour.

The power law model was fitted to guava products and kiwifruit juice showing a pseudoplastic behaviour (Table 5). There was a decrease of the consistency coefficient (k) with a temperature increase across those products. However, the increase in the flow behaviour index (n) was observed only in the guava puree and the kiwifruit juice, while the flow behaviour index (n) in the guava jam was not influenced significantly with temperature.^[5] It has also been reported that the temperature did not significantly influence the flow behaviour index for guava puree in another study.^[38] This trend of the flow behaviour index (n) unaffected by the temperature was also observed in the pummelo juice of 50 °Brix at a similar range of temperature (Table 4), which was also described with the power law model.^[30] The constant flow behaviour index with temperature was also observed in the tomato juice presented in Table 6.^[39] In non-Newtonian fluid foods, the flow behaviour index is assumed to be affected by temperature only slightly.^[9] The activation energy of the guava jam was 8.16 kJ.mol⁻¹, while the guava puree displayed 16.73 kJ.mol^−1.[5,35] In pseudoplastic fruit products, the activation energy is directly proportional to the flow behaviour index. The higher the flow behaviour index, the less the effect of temperature on its apparent viscosity.^[13] As the guava jam indicated higher flow behaviour index compared to the guava puree, the activation energy appeared higher; thus, temperature had a greater influence on the viscosity.

Vegetables

The pseudoplastic behaviour was observed for vegetable products except for the carrot juice (Table 6).^{[6,27,31,40−43]} The power law was fitted for beetroot juice, fenugreek paste, and tomato ketchup, while the other vegetable products were described by the Herschel–Bulkely model. The general trend of decreasing consistency coefficient (k) was observed with temperature increase apart from the fenugreek paste. The structure of polysaccharides highly present in fenugreek, galactomannnan, consists of galactose and mannose residues in the ratios of 1:1 or 1:2 in a few cases.^[44] The galactomannan acquires the high water binding capacity and the formation of very viscous solutions when blended with water by swelling. As the fenugreek paste was prepared by suspending 10% dried ground fenugreek in water, the distinct behaviour of the consistency coefficient can be explained by the increase of the water solubility of higher molecular mass compounds with

TABLE 6 Rheological parameters of selected vegetable products

	C	Total						γ min	γ max	Ea,	Sugar content
Product	°Brix	% solids	Temp., °C	o, Pa	k, Pa.s^n	n	μB, Pa.s	s^−1	s^−1	kJ.mol^−1	g/100 g fruit	Reference
Beetroot juice	67.10	—	10	—	0.3324	4.124	—	1.0	300	39.960		[31]*
Beetroot juice	67.10	—	20	—	0.1793	1.534	—	1.0	300
Beetroot juice	67.10	—	30	—	0.1054	1.259	—	1.0	300
Beetroot juice	67.10	—	40	—	0.0567	1.145	—	1.0	300
Beetroot juice	67.10	—	50	—	0.0398	1.109	—	1.0	300
Beetroot juice	67.10	—	60	—	0.0279	1.083	—	1.0	300
Beetroot juice	50.00	—	20	—	0.0150	1.025	—	1.0	300	24.680
Beetroot juice	55.00	—	20	—	0.0234	1.044	—	1.0	300	26.760
Beetroot juice	60.00	—	20	—	0.0519	1.100	—	1.0	300	30.480
Beetroot juice	65.00	—	20	—	0.1054	1.259	—	1.0	300	36.070
Carrot juice	7.57	8.94	8	—	0.0014	1.061	—	0.0	1600	3.660		[6]
Carrot juice	7.57	8.94	15	—	0.0010	1.080	—	0.0	1600
Carrot juice	7.57	8.94	25	—	0.0005	1.133	—	0.0	1600
Carrot juice	7.57	8.94	35, 45	—	0.0004	1.129	—	0.0	1600
Carrot juice	7.57	8.94	55–85	—	0.0001	1.066	—	0.0	1600
Coriander puree	4.30	8.95	30	36.66	20.7500	0.455	—	1.0	300	23.990		[40]
Coriander puree	4.30	8.95	80	11.65	5.7030	0.735	—	1.0	300
Fenugreek paste	—	—	10	—	3.7490	0.595	—	0.0	25	39.650		[41]
Fenugreek paste	—	—	15	—	5.1410	0.542	—	0.0	25
Fenugreek paste	—	—	20	—	5.3440	0.567	—	0.0	25
Fenugreek paste	—	—	25	—	7.6120	0.522	—	0.0	25
Fenugreek paste	—	—	30	—	12.4200	0.515	—	0.0	25
Mint puree	1.80	8.39	30	147.25	344.0200	0.137	—	0.1	300	32.620		[40]
Mint puree	1.80	8.39	80	24.45	50.9700	0.451	—	0.1	300
Tamarind juice	71.00	—	10	3.88	9.2800	0.780	—	0.1	100	35.090		[42]
Tamarind juice	71.00	—	30	1.46	4.3200	0.590	—	0.1	100
Tamarind juice	71.00	—	50	0.69	0.5200	0.590	—	0.1	100
Tamarind juice	71.00	—	70	0.53	0.4900	0.430	—	0.1	100
Tamarind juice	71.00	—	90	0.91	0.2700	0.510	—	0.1	100
Tomato juice	5.40	5.96	0	0.93	0.2700	0.560	—	50.0	500	7.353		[27]
Tomato juice	5.40	5.96	20	0.94	0.1900	0.560	—	50.0	500
Tomato juice	5.40	5.96	40	0.73	0.1600	0.560	—	50.0	500
Tomato juice	5.40	5.96	60	0.56	0.1400	0.560	—	50.0	500
Tomato juice	5.40	5.96	80	0.48	0.1300	0.580	—	50.0	500
Tomato juice	4.50	—	25	5.38	0.9200	0.440	—	0.1	300
Tomato ketchup	—	—	25	—	19.3400	0.228	—	0.0	300	21.470		[43]
Tomato ketchup	—	—	35	—	11.3800	0.225	—	0.0	300
Tomato ketchup	—	—	45	—	9.5300	0.219	—	0.0	300
Tomato ketchup	—	—	55	—	8.4200	0.213	—	0.0	300

*Data derived from the graph.

temperature and the change in the soluble mass ratio of galactose and mannose in the aqueous suspension was affected.^[41] The unsystematic trend of flow behaviour index was observed in coriander puree, fenugreek puree, mint puree, and tamarind juice. Tomato ketchup displayed a decreasing flow behaviour index with temperature, showing the tendency to have higher pseudoplasticity at higher temperature in contrast (Table 6). The activation energy values obtained for the vegetable products were mostly above 20 kJ.mol⁻¹ except for the carrot juice and tomato juice. The activation energy values for the two juice products were 3.66 and 7.353 kJ.mol⁻¹, respectively.^[6,27] The presence of fibres in the juice was considered to affect the activation energy values, which was also shown in açai berry pulp.^[14]

Impact of Total Soluble Solids on Rheological Properties

The impact of total soluble solids on the rheological parameters of different products has been studied in a number of literatures. According to Krokida et al.,^[9] concentration of soluble solids with insoluble solid contents has a strong non-linear effect on the viscosity of Newtonian fluid foods, the consistency coefficient (k), and the apparent viscosity of non-Newtonian foods. The increase in the consistency coefficient (k) was observed in all data fitted with the power law or Herschel–Bulkey model. On the other hand, the increase in Bingham plastic viscosity (μ_B) was displayed in sloe juice. The general tendency of activation energy value increase with higher soluble solids content was observed.^{[20,24,25,28,31,32]} This shows that the dependence of viscosity on temperature is greater when the soluble solids content of the products is higher. Activation energy is the energy that must be overcome to start a reaction process and the viscosity is the resistance of a fluid that is being deformed. Even with the same soluble solids content, it was reported by Falguera et al.^[28] that the variations in reducing and non-reducing sugar content of the products were considered to affect the flow activation energy depending on the temperature. Although it has been widely acknowledged that the viscosity is affected by the molecular weight of the sugars contained in the sample, the effect of the different compositions of monosaccharides in fruit juices and vegetables has not been established and this is a field of which the rheological study can possibly expand into.

CONCLUSION

Data from over 30 recent publications on the rheological properties of fruit- and vegetable-based products were compiled and analysed. The Herschel–Bulkley model was used to describe most of the products showing a pseudoplastic behaviour with n < 1, whilst the Power law and the Bingham model were successfully fitted to the others. The clarified and depectinated fruit juices, apple and pear juice and cherry juice as well as the carrot juice, showed a Newtonian behaviour whilst the other products were all classified as non-Newtonian. The general trend of the rheological properties of the selected berry and stone fruit products was the decrease in yield stress (σ₀) and consistency coefficient (k) and the increase in flow behaviour index (n) with temperature increase. The citrus fruit juices showed the consistency coefficient (k) following a decreasing pattern with the rise of temperature. The constant flow behaviour index with temperature was observed in the tomato juice, guava puree, and pummelo juice of 50 °Brix. The general trend of decreasing consistency coefficient (k) was observed in vegetable products with temperature increase. The unsystematic trend of flow behaviour index was observed in coriander puree, fenugreek puree, mint puree, and tamarind puree. The increase in the consistency coefficient (k) was observed with the increase in soluble solid content. The effect of the temperature was analysed by the comparison of the flow activation energy. The values of the flow activation energy displayed an increase with the concentration of the soluble solids. The presence of soluble solids content and non-soluble solids content in the products was considered to affect the activation energy values. The general tendency of activation energy value increase with higher soluble solid content was observed, showing that the dependence of viscosity on temperature is greater when the soluble solids content of the products is higher. The filtered concentrated citrus fruit juices with low soluble solid content in conjunction with the high temperature applied may exhibit a Newtonian behaviour. Other studies are required to understand the high temperature influence on the rheological properties of filtered concentrated citrus juices. The interaction of polysaccharides in starchy fruits, such as bananas, above the gelation temperature should be analysed in the further studies to determine the exact rheological behaviour. This review puts emphasis on the recently studied rheological properties of different fruit and vegetable products as function of temperature and soluble solids contents. Further developments in the analysis of rheological properties in relation to the influence of different unit operations and change of biochemical compounds present in the products should increase the understanding and performance of appropriate process design.