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Application of multiple component constraint mixture design for studying the
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      International Food Research Journal 20(2): 811-818 (2013)
Journal homepage: http://www.ifrj.upm.edu.my
Application of multiple component constraint mixture design for studying the 
effect of ingredient variations on the chemical composition and physico-chemical 
properties of soy-peanut-cow milk
*Kpodo, F. M., Afoakwa, E. O., Amoa B. B., Saalia, F. K. S. and Budu, A. S. 
Department of Nutrition and Food Science, University of Ghana, P. O. Box LG 134
Legon-Accra, Ghana
Article history Abstract
Received: 20 May 2012 Investigations were conducted employing a three-component constrained mixture design 
Received in revised form: to formulate milk blends from soy milk, peanut milk and cow milk. Variations in chemical 
9 August 2012 composition and physico-chemical properties of 10-soy-peanut-cow milk (SPCM) formulations 
Accepted: 15 August 2012 were studied. Variations in soy-peanut-cow milk (SPCM) concentrations influenced to varying 
levels the chemical composition and physico-chemical properties of blends. SPCM formulations 
containing significant amounts of all three ingredients used (60-70% soy milk, 20-27% peanut 
Keywords milk and 7-20% cow milk) had high crude protein and fat values ranging from 2.20-2.51% and 
5.00-6.35% respectively. Increasing soy concentrations caused relative increases in protein 
Composite milk blend content while fat content increased with increasing peanut concentrations. SPCM formulations 
nutritive value were high in the minerals Fe and Mn relative to cow milk which was high in Ca and Zn content. 
functionality Trends in pH were contrary to titratable acidity and increased with increasing soy milk content 
rheology but decreasing cow milk content. SPCM formulations demonstrated acceptable non-Newtonian 
non-Newtownian fluids behaviour and consistency indices. 
 flow behaviour
© All Rights Reserved
Introduction quantities, milk products from a vegetable source is 
an excellent alternative to help remedy the problem 
Milk is an oil-in-water emulsion containing fat of protein deficiency. 
droplets and protein aggregates (Cruz et al., 2009). Functional properties of food proteins are essential 
Milk-like beverages manufactured from legumes factors to consider in the formulation of new food 
such as soya beans and peanut have been noted products (Yu et al., 2007). Proteins impart desirable 
as potential nutritional substitutes to cow milk physicochemical and rheological properties like water 
(Beasley et al., 2003; Isanga and Zhang, 2009). Soy and oil holding capacities, viscosity, emulsification, 
protein has been noted as an advantage over animal gelation, foam formation and whipping capacity to 
protein as it does not raise serum cholesterol values food systems (Moure et al., 2006; Yu et al., 2007). 
(Fukushima, 2001) and hence, is useful for people The presence of soy proteins, peanut proteins and 
suffering from cardiovascular disorders (De Kleijn casein in food systems and their interactions can 
et al., 2002). Soybean milk also has a number of influence physicochemical and rheological properties 
phytochemicals found to be effective in fighting of such food products.
osteoporosis (Anderson and Garner, 1997), obesity, Soy-peanut-cow milk is a composite milk product 
cancer (Messina, 1999) and postmenopausal problems formulated by mixing the three basic ingredients; 
(Albertazzi et al., 1998). Soy milk is used in cases of peanut milk (PM), soy milk (SM) and cow milk (CM). 
lactose intolerance. Peanut milk also has nutritional The proportions of these ingredients were obtained 
benefits because of its richness in protein, minerals using a three component, constrained mixture design 
and essential fatty acids such as linoleic and oleic (Cornell, 1983). A mixture design was used for this 
acids which are considered to be highly valuable in study because components of a mixture are limited by 
human nutrition (Isanga and Zhang, 2009). In some an implicit constraint that the sum of all components 
developing countries where dairy and dairy products must be -1 (100%) (Leardi, 2009). Components 
are usually priced too high for low income earners cannot be varied independently because by varying 
and are also invariably produced in insufficient the percentage of one component, percentages of the 
*Corresponding author. 
Email: fideliskpodo@yahoo.com/
           eafoakwa@ug.edu.gh
812 Kpodo et al./IFRJ 20(2): 811-818
other components change (Leardi, 2009). The essence Table 1. Design matrix for ingredient formulations of SPCM
of combining milk from two vegetable sources is Formulation Soy milk Peanut milk Cow milk
guided by the fact that no single vegetable milk can F1 0.60 0.40 0.00F2 0.70 0.20 0.10
adequately resemble milk from a dairy source in its F3 0.63 0.33 0.03F4 0.60 0.20 0.20
nutritional and physico-chemical attributes. Thus, F5 0.80 0.20 0.00
the objective of the study was to apply multiple F6 0.63 0.23 0.13F7 0.70 0.30 0.00
component constraint mixture design in combining F8 0.73 0.23 0.03F9 0.60 0.30 0.10
milk from three different sources and investigate F10 0.67 0.27 0.07
the effect of ingredient variations on the chemical 
composition and physico-chemical properties of the 
milk blends.
Materials and Methods
Materials
Red-skinned peanut seeds (Chinese variety) and 
soya bean seeds (Jenguma variety) were purchased 
from a registered seed grower in Tamale, Northern 
region of Ghana. Care was taken to ensure that good 
quality and mould-free seeds were selected. Cow 
milk used for the study was obtained from Amrahia Figure 1. constrained simplex design used in formulating ingredients for 
Dairy Farms, Amrahia, Ghana. vegetable milk yoghurt
Milk preparation
Peanut milk and soy milk were prepared by a mixture design (centroid design) was used to obtain 
modifying the method reported by Aidoo et al. (2010). 10 design points from three components. The lower 
Sorted peanut seeds were blanched by submerging in limit (soy milk - 0.6; peanut milk - 0.2; cow milk 
boiling water for 10 minutes to inactivate the enzyme - 0.0) and upper bound constraints (soy milk - 0.8; 
lypoxygenase known for its ability to cause oxidation peanut milk - 0.4; cow milk - 0.2) for each mixture 
which leads to the production of beany flavour. The component were used to generate the design (Figure 
seeds were then de-skinned, weighed and soaked 1).
in 2% NaHCO3 for 18 hours. To remove residual Analytical methods
NaHCO3, the peanut kernels were washed with hot 
 o Proximate composition water (70 C). Soy beans were also steeped in boiling 
o Proximate analysis was done on the ten different water (100 C) for about 10 minutes, dehulled, formulations of soya-peanut-cow milk. Moisture, 
weighed and then steeped in water for 16hrs, and total nitrogen and ash were determined according 
then in 2% NaHCO3 for 2 hours. Soaking in NaHCO3 to AOAC methods 925.09, 920.105 and 923.03 
was to soften the seeds and also reduce the beany respectively (AOAC, 1990). Protein was calculated 
flavour. The beans were then washed in hot water. from total nitrogen using the conversion factor 6.25 
The dehulled peanut and soya beans were separately for the vegetable milk. Fat content was determined 
mixed with water in a ratio of 1:5 [oilseed (g): water by the Gerber method (AOAC, 1990). Carbohydrate 
(ml)] and then milled to obtain the slurry (Isanga was determined by difference. The calorific values 
and Zhang, 2009). The slurry was filtered to obtain were calculated using the expression:
a smooth, fine, homogenized milk. Cow milk was 
added to the prepared soy milk and peanut milk in EV (Kj/100g) = [(%AC X 17) + (%P X 17) + (%F X 37)] 
proportions determined by a mixture design (Table 1) 
to obtain the soy-peanut-cow milk blend. where: EV = Energy value of food; %AC = Percentage 
available carbohydrates; %P = Percentage protein; 
Experimental design %F = Percentage fat (Isanga and Zhang, 2009). 
Ten milk formulations were processed by mixing 
the three basic ingredients; peanut milk (PM), soy milk Mineral determination
(SM) and cow milk (CM). The proportions of these The ash from proximate analysis was dissolved 
ingredients were obtained using a three component, in 10 ml of 10% (v/v) nitric acid and 10% (v/v) 
constrained mixture design (Cornell, 1983). Using hydrochloric acid and made up to volume with distilled 
design of experiments software, Minitab version 14, 
Kpodo et al./IFRJ 20(2): 811-818 813
water in a 25 ml volumetric flask (Isanga and Zhang, 
2009). Calcium, magnesium, copper, manganese, zinc 
and iron in the prepared samples were determined by SM0.8
atomic absorption spectrophotometry (Perkin Elmer 
Analyst 400. Tokyo, Japan). 8.8
Titratable acidity and pH 
Titratable acidity was determined using AOAC 0.0 0.29.2
method 947.05 (AOAC, 1990) by titration with 0.1N 
NaOH solution and expressed as percent lactic acid 
while the pH of the samples was measured using a 9.0
pH meter (Hanna Instrument pH 210, microprocessor 0.4 0.6 0.2
pH meter, Duisburg, Germany). PM CM
Figure 2. contour plot of total solids content of SPCM formulations        
Apparent viscosity
The apparent viscosity of the 10 soy-peanut-cow 
milk formulations were measured at 10°C using a 
Brook-field viscometer (Brook-field model LVDVI, SM
0.8
AE42086, Springfield, MA, USA). The flow curves 
of the milk were obtained by varying the shear rate 
from 10 to 60 s−1 and the corresponding viscosity 91.2
91.0
values measured (Isanga and Zhang, 2009). 
0.0 0.2
Statistical analysis
Data obtained from the analysis was analyzed 90.8
using MINITAB and Statgraphics (Graphics 0.4 0.6 0.2PM CM
Software System, STCC, Inc. U.S.A). Comparisons 
between the 10 Soy-peanut-cow milk formulations Figure  3. contour plot of moisture content of SPCM formulations
were done using analysis of variance (ANOVA) 
with a probability, p < 0.05. All treatments and solids content 8.47 to 8.94% relative to formulations 
measurements were carried out in duplicates and the that had cow milk. Cow milk generally has been 
mean values reported. observed to have higher total solids content than other 
aqueous extracts of oil seeds (Schaffner and Beuchat, 
Results and Discussion 1986; Vargas et al., 2008). Hence it is expected 
that as the proportion of cow milk increases in a 
Proximate composition of soy-peanut-cow milk mixture relative to vegetable milk, moisture content 
(SPCM) correspondingly decreases. The moisture content 
The proximate composition of the 10 soy-peanut- of formulations increased with increasing soy milk 
cow milk formulations were determined. The solids content (Figure 3). Since the vegetable milk was an 
content of the soy-peanut-cow milk formulations aqueous plant seed extract it contained more moisture 
ranged from 8.47 to 9.68% and decreased with as compared to cow milk. The solids content of 
increasing soymilk content (Figure 2). SPCM SPCM formulations with different proportions of soy 
formulations did not show any great difference in milk and peanut milk were different but formulations 
solids content when compared with other soy milk. without cow milk did not differ significantly (p > 
Fávaro-Trindade et al. (2001) and Gatade et al. 0.05). Among formulations that had cow milk ranging 
(2009) observed high moisture content above 90% in from 3-10%, there were no significant differences (p 
soy milk. However Isanga and Zhang (2009) reported > 0.05) between their solids content.
lower moisture content (87.15%) peanut milk. Since Crude protein content of the formulations ranged 
the formulations used in this study generally had from 1.77% to 2.59% and the values were significantly 
high amounts of soy milk than peanut milk, moisture different for all samples which contained varied 
content of samples were high and comparable to that proportions of soy milk, peanut milk and cow milk. 
of soy milk (Fávaro-Trindade et al., 2001; Gatade et In this study formulations which contained significant 
al., 2009). Formulations without cow milk had lower amounts of all three components: 60 to 70% soy 
814 Kpodo et al./IFRJ 20(2): 811-818
SM
SM
0.8 0.8
2.0 2.2
5.4
0.0 0.2 0.0 0.2
2.4 5.8
5.6
2.1
2.3 2.4 6.0
0.4 0.6 0.2 0.4 0.6 0.2
PM CM PM CM
Figure 4. contour plot of protein content of SPCM formulations Figure 5. contour plot of fat content of SPCM formulations
SM SM
0.8 0.8
245
1.0
250
0.0 0.2 0.0 0.2255
260
0.6
0.8
0.2
265 0.4
0.4 0.6 0.2 0.4 0.6 0.2
PM CM PM CM
Figure 6. contour plot of energy value of SPCM formulations   Figure 7. contour plot of carbohydrate content of SPCM formulations
SM SM
0.8 0.8
0.55
12.5
0.50
0.45
0.0 0.2 0.0 17.5 0.2
0.40
22.5
0.45
15.0 20.0
0.4 0.6 0.2 0.4 0.6 0.2
PM CM PM CM
Figure  8. contour plot of ash content of SPCM formulations Figure 9. Mixture contour plot of Ca content of SPCM formulations 
milk; 20 to 27% peanut milk and 7 to 20% cow milk (Figure 5). Values obtained for fat content were lower 
generally had high crude protein values ranging than the value of 8% reported by Isanga and Zhang 
from 2.20 to 2.51%. The crude protein content of (2009) for peanut milk prepared from roasted peanut 
the samples increased when all components of the seeds. Since the fat content of peanut is greater than 
mixture were present in high amounts (Figure 4). the other components of the mixture (soy beans and 
Crude protein content of soy milk (4.8%) and peanut cow milk), an increase in peanut content expectedly 
milk (3.71%) were generally higher than cow milk increased the fat content of the formulations. The 
(2.84%) primarily because these oil seeds are the energy value of formulations ranged from 238.45 
most abundant sources of proteins (Gatade et al., to 274.70 KJ/100g and increased with increasing 
2009; Isanga and Zhang, 2009). peanut milk but decreasing soy milk content (Figure 
The fat content of soy-peanut-cow milk samples 6). The high fat content of peanut milk might have 
ranged from 5.00 to 6.35%. The fat content increased contributed to the high energy values recorded for the 
with increasing peanut content in the formulations high peanut containing formulations.
Kpodo et al./IFRJ 20(2): 811-818 815
SM SM
0.8 0.8
0.37 0.70
0.0 0.39 0.2 0.0 0.80 0.2
0.38
0.75 0.85
0.40
0.4 0.6 0.2 0.4 0.6 0.2
PM CM PM CM
Figure 10: Mixture contour plot of Zn content of SPCM formulations Figure 11. Mixture contour plot of Mn content of SPCM formulations  
SM SM
0.8 0.8
0.11
8.8
0.12
0.0 0.2
0.0 0.2
0.13
8.4
0.11 0.12 8.6
0.4 0.6 0.2
0.4 0.6 0.2 PM CM
PM CM
Figure 12. contour plot of Fe content of SPCM formulations Figure 13. contour plot of pH of SPCM formulations                                 
SM
SM 0.8
0.8
0.010
0.0 800 0.2
0.0 0.2 400
0.020
600
200 1000
0.015 0.025
0.4 0.6 0.2
0.4 0.6 0.2
PM
PM CM CM
Figure 14. contour plot of titratable acidity of SPCM formulations Figure 15.contour plot of consistency index of SPCM formulations 
The carbohydrate content in the formulations residue remaining after the organic material has 
ranged between 0.10 to 2.09%. The carbohydrate been burnt off. The importance of ash content is that 
content of samples increased as proportions of soy it gives an idea of the amount of mineral elements 
milk and cow milk increased in samples (Figure present in the food sample. The ash content of SPCM 
7). The carbohydrate content of aqueous extracts mixtures ranged from 0.38 to 0.61%, and the values 
of oil seeds is usually low due to their high protein did not differ significantly (p > 0.05) between all 
and fat content. However, soy milk generally has the 10 formulations. However increasing soymilk 
higher carbohydrate content than peanut milk. Values and cow milk in formulations increased ash content 
between 1.5 to 2.0% for soy milk (Gatade et al., (Figure 8).
2009) and 0.84 to 0.95% for peanut milk (Schaffner 
and Beuchat, 1986; Isanga and Zhang, 2009) have Mineral composition of soy-peanut-cow milk 
been reported. samples
The ash content of a food material is the inorganic The formulations generally had high Fe and Mn 
816 Kpodo et al./IFRJ 20(2): 811-818
without cow milk did not differ significantly (p > 
0.05). 
SM
0.8
Rheological characterization of SPCM
Viscosity is an important property of fluid foods 
0.6
that affects mouth feel and consistency. The flow 
0.0 0.6 0.2 behavior of fluid foods affects the efficacy of unit 
operations in the food industry, notably pumping, 
extrusion, filling, drying and evaporation. Viscosity 
0.4
0.7
0.5 measurements are therefore routinely performed in 
0.4 0.6 0.2 the food industry and research laboratories, primarily 
PM CM
Figure 16.contour plot of flow behaviour indices of SPCM formulations as part of quality control or product development (Yu 
et al., 2007). 
content compared to the control, cow milk, which had Data obtained from apparent viscosity 
high Ca and Zn content. As expected, formulations determination of the formulations at varying shear 
without cow milk were low in Ca content. Ca and Zn rates were fitted to the power law model to obtain 
content increased in formulations as cow milk content the consistency and flow behaviour indices of SPCM 
increased (Figures 9 and 10). Manganese increased formulations. The consistency index of SPCM 
with increasing peanut milk content and decreasing formulations increased with increasing cow milk 
soy milk content (Figure 11). Increasing soymilk content and decreased as peanut milk increased in 
content also increased Fe content of formulations samples (Figure 15). SPCM formulations without 
(Figure 12). cow milk generally had low consistency indices. 
Since the total solid content of cow milk is higher 
Titratable acidity and pH of soy-peanut-cow milk than that of vegetable milk, an increase in cow milk 
(SPCM) content should increase the consistency/viscosity of 
Titratable acidity of a food system is indicative the milk products. It had been reported that higher 
of the total acid concentration within a food and it is total solids content in milk usually increases the 
a better predictor of an acid’s impact on flavour than viscosity and consistency of the end product (Tamime 
pH (Nielsen, 1998). The ability of microorganisms and Robinson, 1999). Yoghurt manufacturers in 
to grow in a specific food is dependent on the an attempt to develop yoghurt products with high 
hydroxonium ion concentration of the food system viscosities and better consistencies would usually 
(Nielsen, 1998). pH values ranged from 8.06 to 9.08 add powdered milk to the raw material to increase 
and titratable acidity was between 0.005 and 0.027%. the total solids content and produce yoghurts with 
The results of the pH measurements were contrary to improved consistencies and viscosities. The flow 
trends observed for titratable acidity measurements. behaviour indices for all the soy-peanut-cow milk 
As the acidity increased, the pH decreased (Figures formulations showed them to have non-Newtonian 
13 and 14). The pH of soy milk ranges between flow behaviour. Unlike cow milk that has been 
6.5 to 6.8 (Pinthong et al., 1980; Buono et al., established to be Newtonian, the flow characteristics 
1990; Park et al., 2010). However the pH of SPCM of the formulations were pseudoplastic, with the 
formulations observed in this study were far higher apparent viscosities decreasing as the shear rates 
than those reported in literature. This could be due were increased. The flow behaviour of the mixtures 
to the fact that the seeds were soaked in a solution gradually moved towards Newtonian flow (with the 
of NaHCO  prior to milk extraction and the NaHCO  flow behavior indices approaching unity) as cow milk 3 3
solution might have increased the pH of the aqueous in the formulation increased (Figure 16).
extracts from these seeds. The pH values of SPCM 
formulations differed significantly (p < 0.05). pH Conclusion
values generally increased with increasing soy milk 
content and decreasing cow milk content (Figure 13). Variations in soy-peanut-cow milk (SPCM) 
Formulations with either no or low amount of cow concentrations influenced the chemical composition 
milk had high pH values in the range of 8.7 to 8.8 and and physico-chemical properties of blends. SPCM 
low total acid content ranging from 0.005 to 0.016%. formulations containing significant amounts of all 
Formulations with cow milk content ranging from 10 three ingredients used (60 – 70% soy milk, 20 – 27% 
to 20% recorded low pH and high titratable acidity peanut milk and 7 – 20% cow milk) had high crude 
values. The titratable acidity of SPCM formulations protein and fat values ranging from 2.20 to 2.51% 
and 5.00 to 6.35% respectively. Increasing soy 
Kpodo et al./IFRJ 20(2): 811-818 817
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