Advances in Chemical Engineering and Science, 2012, 2, 444-452
http://dx.doi.org/10.4236/aces.2012.24054 Published Online October 2012 (http://www.SciRP.org/journal/aces)
A Laboratory Study of the Effect of Temperatur e on
Densities and Viscosities of Binary and Ternary Blends of
Soybean Oil, Soy Biodiesel and Petroleum Diesel Oil
Oluwafunmilayo A. Aworanti, Samuel E. Agarry*, Ayobami O. Ajani
Biochemical Engineering and Biotechnology Research Laboratory, Department of Chemical Engineering,
Ladoke Akintola University of Technology, Ogbomoso, Nigeria
Received April 20, 2012; revised May 25, 2012; accepted June 6, 2012
ABSTRACT
The depletion of world petroleum reserves and the increased environmental concerns have stimulated the search for
alternative sources for petroleum based fuel. The possibility of using vegetable oils as fuel has been recognized, how-
ever, due to its high viscosities and low volatilities makes it inefficient for most combustion en gines and thus th e need
to get them chemically altered or transesterified to obtain fatty alkyl esters of the oil (biodiesel). In this study, binary
and ternary blends of biodiesel were produced and the effect of temperature on their viscosity and density was investi-
gated. Biodiesel was produced from soybean oil by transesterification of the oil with methanol using potassium hy-
droxide as a catalyst at a temperature of 60˚C in a batch reactor. Binary and ternary blends of the soy-biodiesel were
prepared with soy bean oil and petroleum diesel fuel, respectively. Viscosities and densities of the binary and ternary
blends were measured at different temperatures of 20˚C to 90˚C as to determine the effect of temperature on viscosities
and densities of the blends. The properties of the soy-biodiesel produced were compared with ASTM standard and
found to be within the limits. The results show that the viscosities and densities of both the binary and ternary blends
are temperature dependent. The viscosities of binary and ternary blends decreased nonlinearly with temperature, while
their densities decreased linearly with temperature. Th e variation of temperature with viscosity and density of the blends
was correlated and the polynomial equation offered th e best correlation between temperature and viscosity, while lin ear
equation gave the best correlation between temperature and density. In conclusion, the efficiency of binary and ternary
blends of biodiesel in combustion engines is dependent on the viscosity and density of the blends which are invariably
temperature dependent.
Keywords: Densities; Viscosities; Batch Reactor; Diesel Fuel; Soy-Biodiesel; Vegetable Oil
1. Introduction
The depletion of world petroleum reserves and the in-
creased environmental concerns have stimulated the
search for alternative sources for petroleum based fuel,
including diesel fuels. With increasing demand on the
use of fossil fuels, stronger threat to clean environment is
being posed as burning of fossil fuels is associated with
emissions like CO2, CO, SO2, NO2 and particulate matter
which are currently the dominant global source of emis-
sions. The harmful exhaust emissions from the engines,
rapid increase in the prices of petroleum products, the
increasing fuel prices and uncertainties of their supply
have jointly created renewed interest among researchers
to search for suitable alternative fuels. There is therefore
a growing substitution of fossil fuels with fuel derived
from renewable resources. This substitution requires in-
creased efforts in the research and development of pro-
ducing these fuels from different renewable resources.
This is the case for biodiesel (alkyl esters) production
from vegetable oils [1]. The use of vegetable oil as an
alternative fuel had been under study as far back as 1979
[2]. Vegetable oil based fuels are sustainable sources of
fuel because as long as they are produced in an ecologi-
cally sustainable way, they will not run out. Depending
upon the climate and soil conditions, different countries
are looking for different types of vegetable oils as sub-
stitutes for diesel fuels. For example, soybean oil in the
US, rapeseed and sunflower oils in Europe and palm oil
in Southeast Asia are being con sidered [3]. The possibil-
ity of using vegetable oils as fuel has been recognized
since the beginning of diesel engines.
In 1911, Rudolph Diesel presented an engine based on
compression ignition; the diesel engine. At that time,
there was no specific fuel to feed this engine and
*Corresponding a uthor.
C
opyright © 2012 SciRes. ACES

O. A. AWORANTI ET AL. 445
groundnut oil was used [4]. There have been many prob-
lems associated with using vegetable oils directly in die-
sel engines; coking and trumpet formation on the injec-
tors to such an extent that fuel atomization does not oc-
cur properly or is even prevented, decrease in power
output and thermal efficiency of the engines, carbon de-
posits, oil ring sticking; thickening or gelling of the lu-
bricating oil as a result of contamination by vegetable
oils [2,5]. Vegetable oils also have high viscosity (11 -
17 times higher than diesel fuel) and lower volatility that
results in carbon deposits in engines due to incomplete
combustion. However, the high viscosities and low vola-
tilities of this oil have been reported to make them ineffi-
cient for most combustion engines [6] and thus the need
to get them chemically altered or transesterified to obtain
alkyl esters of the oil (biodiesel). Besides all the above,
vegetable oils con tain polyunsaturated compounds.
Transesterification has been tested to be one of the
chemical modifications to overcome these problems
caused by the use of vegetable oils. The transesterifica-
tion reduces the molecular weight of vegetable oils and
also reduces the viscosity and improves the volatility.
The product of the reaction is biodiesel, glycerol, alcohol
and catalyst. Biodiesel is produced through a transesteri-
fication reaction [7]. In this reaction, with the presence of
a catalyst, triglycerides react with an alcohol producing a
mixture of fatty acid alkyl esters (FAAE) and glycerol
[8]. The stoichiometric reaction requires 1 mole of tri-
glycerides and 3 mole of alcohol. However, excess alco-
hol is required to drive the reaction close to completion
[9,10]. Biodiesel extracted from vegetable oil is one of
such renewable alternative under consideration, and be-
cause of its closer properties to diesel fuel, biodiesel fuel
(fatty acid methyl ester) from vegetable oil is considered
as the best candidate for diesel fuel substitute in diesel
engine [11]. Biodiesel can therefore be technically de-
fined as the alkyl ester of fatty acids, made by the trans-
esterification of oils or fats, from plants or animals, with
short ch ain alcohols such a s methanol and ethanol.
The catalysts used for transesterification could be
classified as homogeneous and heterogeneous catalysts
Homogeneous catalysts are alkalis such as hydroxides
(NaOH, KOH, carbonates and corresponding sodium and
potassium alkoxides) [12] and acids like sulphuric acid
and hydrochloric acid; while heterogeneous catalysts
include among others tungsten oxides, resins and sul-
phonated saccharides [7,13]. However, in the last few
years, the studies of the enzymatic catalyzed production
of biodiesel have shown significant progress [14-16].
The main problem of the enzyme catalyzed process is the
high cost of the lipases (enzyme) used as catalyst [16]. At
industrial scale, alkaline catalysis is usually used in bio-
diesel production from edible oil.
The properties of biodiesel are close to conventional
diesel and hence become a strong candidate to replace
the diesel fuel [11]. Its advantages over conventional
diesel fuels are its lower toxicity, high biodegradability,
substantial reduction in SOx emissions, considerable re-
duction in carbon monoxide (CO), polyaromatic hydro-
carbons, smoke and particulate matter [12]. In addition,
biodiesel has a high heat value, high oxygen content (10% -
11%) [17] and does not contribute to global warming due
to its carbon closed cycle [1]. Biodiesel has substantially
different properties than vegetable oils and result in bet-
ter engine performance. However, there are some draw-
backs of biodiesel like higher cost and cold flow proper-
ties. Among the possible raw materials for the production
of biodiesel, the use of rapeseed oil, canola oil, soybean
oil, palm kernel oil, coconut oil, cotton seed oil and citrus
seeds oil has been investigated [5,18-22]. Several studies
on binary blends of biodiesel and diesel fuel or vegetable
oils have been investigated, but not much has been done
on ternary blends of biodiesel, diesel fuels and vegetable
oils.
Viscosity is one of the most important physical prop-
erties of a fluid system [23]. Viscosity changes with
shear rate, temperature, pressure, moisture, and concen-
tration; all these changes can be modelled by equations
[24,25]. Studies on viscosity have been performed on
pineapple juice, vegetable oil, etc. [26]. However, there
is a dearth of information on the effect of temperature
on the viscosity and density of binary and ternary
blends of biodiesel oil. Modelling of the temperature
effect on the dynamic viscosity of oils is important and
has been investigated by some researchers [25,27-29].
However, modelling of the effect of temperature on vis-
cosity and density of biodiesel is rarely reported. There-
fore, the main objective of this study was to produce
soy-biodiesel from soybeans oil and the effect of tem-
perature on the viscosities and densities of binary and
ternary blends of this biodiesel. Furthermore, polynomial
and/or linear dependence of dynamic viscosity and den-
sity of soy biodiesel and its blends on temperature was
determined.
2. Materials and Methods
2.1. Materials
Refined soybeans oil (being a product of UAC Foods,
Nigeria) was purchased from a local market in Lagos,
Nigeria. Methanol (99% purity) and potassium hydroxide
being products of Merck Dam were purchased from a
chemical store in Lagos, Nigeria. The equipments used
for the experiments are: VT 550 rotating viscometer,
flash point analyzer, 50ml density bottle, mass balance,
mechanical stirrer (overhead stirrer fixed with a stainless
steel propeller) and electromagnetic stirrer, water bath,
thermometer, 1000 ml jacketed glass, electric burner,

O. A. AWORANTI ET AL.
446
reflux condenser and oven.
2.2. Methods
2.2.1. Methanol y si s o f Soybean Oil : Productio n
of Biodiesel
The production of biodiesel was carried out in a batch
reactor. The reactor consisted of a 1 L jacketed glass,
electrical stirrer fitted with a stainless steel propeller(for
thorough mixing/agitation), thermometer and a reflux
condenser(for preventing the methanol from escaping out
of the reactor) since methanol boils at 65˚C in a hot water
bath to control the reaction temperature. Transesterifica-
tion reaction of soybean oil was carried out with potas-
sium hydroxide (1%). Potassium hydroxide (mass frac-
tion 1%) was dissolved in 46 ml of methanol using the
magnetic stirrer to make a homogenous mixture. Soy-
beans oil was measured (167.04 g), pre-heated to a tem-
perature of 60˚C and poured into the reactor. The ho-
mogenous mixture of methanol and potassium hydroxide
was then poured into the reactor containing the soybean
oil. The electrical stirrer was set into motion and the re-
action was carried out at a temperature of 60˚C fo r 1 hour.
The mixing mole ratio of methanol to oil used was 4:1.
At the end of 1 hour, the oil has been effectively trans-
esterified; two layers were formed, an upper layer of
amber yellow colour [0.5 ASTM] was suspected to be
biodiesel while the lower layer of a wine//oxbow lake
colour [2.5 ASTM] was suspected to be glycerol. The
dark colour of the glycerol was due to the presence of
excess catalyst in the lower layer. The suspected bio-
diesel was separated, washed with warm water and then
heated above 65˚C (boiling point of methanol) to remove
any excess methanol in it. The suspected biodiesel was
then analysed for its fuel properties.
2.2.2. Binary and Ternary Blending of Soy Biodiesel
The biodiesel produced from soybean oil was blended
with petroleum diesel oil and soybean oil, respectively,
using direct blending method. The blends were prepared
according to the stated measured percentages (Table 1)
using a beaker, electrical stirrer with a stainless steel
propeller and mixed at room temperature for 1 hour. For
example, the blend with a mixture of 30% biodiesel and
70% petroleum diesel is referred to as B30 blend.
2.2.3. Anal y ses
The suspected biodiesel was then analysed for some
properties such as dynamic viscosity, density, cloud point,
pour point, flash point and colour, respectively. Density
and viscosity measurements were made according to
ASTM standard D1298 and D445, respectively. Dynamic
viscosity 14˚C was measured using a Bookfield vis-
cometer. Flash point was measured using the flash point
analyzer, colour was measured using the colour meter,
and pour point and cloud point were measured using ice
packs, test tubes and transparent cooling chamber. The
pour and flash points were determined following ASTM
standard D297, D25100-8 and D56, respectively.
1) Determination of Viscosity
The viscosities of the blends were measured using VT
550 rotating viscometer by putting the blend in a beaker
while the beaker was put in a water bath (to control the
temperature of the mixture) on an electric burner. Tem-
peratures were increased at 10˚C interval from 20˚C to
90˚C and readings of viscosities were recorded. Ther-
mometer was placed in both the water bath and blend
mixture to ensure accuracy in temperature readings. The
readings of viscosities were done in triplicates and the
average value s were used.
2) Determination of Density
The densities of the blends were taken from a tem-
perature range of 20˚C to 90˚C. The blends were put in a
50 ml density bottle and weighed on a mass balance. Th e
densities were then obtained as given in Equation (1).
The densities were measured in triplicates and the aver-
age values were used.


B
LB
L
MM
DV

 (1)
where D is density of liquid (g/cm3);
B
L
M
, the mass of
bottle and liquid (g);
B
M
, the mass of bottle only and
L
V is the volume of the liquid (cm3).
3. Results and Discussion
3.1. Properties of the Soy-Biodiesel
The physical properties of the suspected biodiesel (vis-
cosity, density, cloud point, pour point, flash point and
colour) was determined and compared with the interna-
tional standard for biodiesel as shown in Table 2. It
could be seen from Table 2 that the fuel properties of the
soy-biodiesel are within the value range limits specified
by international standard for biodiesel.
3.2. Dynamic Viscosities and Densities of Blends
Viscosity is a measure of the internal flow resistance of a
liquid (i.e. the thickness of the oil) and this constitutes an
intrinsic property of vegetab le oils. This is determined by
measuring the amount of time taken for a given measure
of oil to pass through an orifice of a specific size. Vis-
cosity affects injection lubrication and fuel atomization
[30]. The higher is the viscosity, the greater is the ten-
dency for the fuel to form engine deposits [31].
The variations in viscosity of different binary blends
of soybean oil and petroleum diesel with temperature are
shown in Figure 1. The result shows that for each of the

O. A. AWORANTI ET AL.
447
Table 1. Preparation of binary and ternary blends of soy biodiesel.
Run Composition of Blends Volume of Mixtu res
1 P100 100 ml petroleum diesel (PD)
2 95% PD + 5% SO 95 ml petroleum diesel + 5 ml soy bean oil (SO)
3 90% PD + 10% SO 90 ml petroleum diesel + 10 ml soy bean oil
4 80% PD + 20% SO 80 ml petroleum diesel + 20 ml soy bean oil
5 70% PD + 30% SO 70 ml petroleum diesel + 30 ml soy bean oil
6 B100 100 ml soy biodiesel (SBD)
7 B5 95 ml petroleum diesel + 5 ml soy biodiesel
8 B10 90 ml petrole um diesel + 10 ml soy biodiesel
9 B20 80 ml petrole um diesel + 20 ml soy biodiesel
10 B30 70 ml petroleum diesel + 30 ml soy biodiesel
11 95% PD + 3.5% SBD + 1.5% SO 95 ml PD + 3.5 ml SBD + 1.5 ml SO (Ternary)
12 90% PD + 7% SBD + 3% SO 90 ml PD + 7 ml SBD + 3 ml SO
13 80% PD + 14% SBD + 6% SO 80 ml PD + 14 ml SBD + 6 ml SO
14 70% PD + 21% SBD + 9% SO 70 ml PD + 21 ml SBD + 9 ml SO
Table 2. Measured properties of soy bean oil, soy biodiesel and petroleum diesel as against ASTM standard.
Properties Soy bean oil Soy bean biodiesel Petroleum dieselStandard for
petroleum diesel Standard for biodiesel (EN 14214)
Dynamic viscosity at 28˚C 33.33 6.809 4.024 1.3 - 4.1 at 40˚C 3.08 - 4.4 at 40˚C
Density (g/cm3) 0.9068 0.8712 0.8354 0.82 - 0.86 0.86 - 0.90
Water content (%) 0.03 0.00 - - -
Flash point 170 102 69 60 - 80 >101
Cloud point - –1 –5 - –2 to 12
Pour point –0.4 –6 –9 –35 to –15 –15 to 10
Colour 0.5 0.5 2 2 -
0
1
2
3
4
5
6
7
8
9
290 300310 320330 340350 360370
Viscosity(mpa‐s)
Temperature(K)
380 390400
100%PD95%PD+5%SO
90%PD+10%SO 80%PD+2 0%SO
70%PD+30%SO Th i rdorderpolynomial
Figure 1. Effect of temperature on viscosities of binary blends of soybean oil with petroleum diesel oil at different volume
fraction.

O. A. AWORANTI ET AL.
448
binary blends with differen t percent mixture compos ition,
the viscosity decreased non-linearly with temperature.
Also at a fixed temperature, there was a decrease in vis-
cosities of the soybean oil and petroleum diesel blend as
the percent volume of petroleum diesel in the mixture
increases (i.e. the blend with 70% petroleum diesel and
30% soybean oil has the least viscosity). The viscosity
for this blend is moderately high at low temperature
(varying from 7.843 at 20˚C to 1.845 at 90˚C) and de-
creased at high temperature. Nevertheless, manufacturers
of diesel engines will not accept blends with viscosities
that fall below the range limit of viscosity for diesel fuel.
The viscosities of each binary blend of soy-biodiesel
and petroleum diesel of different percent mixture com-
position decreased non-linearly with temperature as
shown in Figure 2. The viscosity for each of the different
blend was very high at low temperature and decreased as
the temperature increased. Also at a fixed temperature,
there was a decrease in viscosities of soy-biodiesel and
petroleum diesel blend as percent volume of petroleum
diesel in the mixture increased. The viscosity for this
blend falls within the limit of tested viscosity of blends
for diesel engines used across the globe (varying from
5.226 at 20˚C to 1.845 at 90˚C).
Figure 3 shows the variation in viscosity of ternary
blends of soybean oil, soy-biodiesel and petroleum diesel,
of different percent volume mixture composition with
temperature. From the figure, it could be seen that viscos-
ity was high at low temperature, however, decreased as the
temperature increased. That is, viscosity decreases non-
linearly with temperature. Also at a fixed temperature,
there was a decrease in viscosities of the ternary blend as
the percent volume of petroleum diesel in the mixture in-
creases. The viscosity for this ternary blend falls within
reasonable limit of tested viscosity of blends that can be
used for diesel engines used across the globe (varying
from 5.508 at 20˚C to 2.264 at 90˚C). This was not far
from the viscosity variation for the binary blend of bio-
diesel and petroleum diesel. Further investigation by prac-
tical testing of this blend on diesel engines shall be carried
out in our next research work to ascertain if it will possible
to use it on diesel engines wit hout much m odifi cations.
Figures 4 and 5 show the variations in densities of bi-
nary blends of soybean oil and soy-biodiesel; soybean oil
and petroleum diesel fuel; and soy-biodiesel and petro-
leum diesel fuel, respectively, (all of different percent
volume mixture composition) with temperature. Density
or specific gravity has been described as one of the most
basic or important parameters of fuel as certain perform-
ance indicators such as heating value and cetane number
are correlated with it [5,30,32]. Compression ignition
engines are designed to inject fuel into the combustion
chamber by volume rather than mass and it is desirable to
maintain diesel density with in a tigh t tolerance to ach iev e
optimal air to fuel ratios. The results from each of Fig-
ures 4 and 5 revealed that for each of the binary blends,
densities were high at low temperature and decreases as
the temperature increased. That is, densities decrease
non-linearly with temperature. Also at a fixed tempera-
ture, there was decrease in densities of soybean oil and
soy-biodiesel blends as the percent volume of soy-bio-
diesel in the mixtures increased. This decrease in densi-
ties was also observed for the soybean oil and petroleu m
diesel blend, and soy-biodiesel and petroleum diesel blend
as the volume fraction of petroleum diesel increased in
the mixtures.
Figure 6 also shows the temperature and composition
dependent behavior of the densities of ternary blends of
soy-biodiesel, soybean oil and petroleum diesel fuel. The
results as revealed in the figure were similar to those
obtained for the binary blends. However, the densities of
binary blend of biodiesel and petro diesel falls within
range limits for international standard of biodiesel and
the ternary blends show density closely related to that of
biodiesel. Further investigation will ascertain its suitab il-
ity for use.
0
1
2
3
4
5
6
7
8
290 300 310320 330 340 350 360 370 380 390 400
Viscosity(mpa‐s)
Tempe rature(K)
B100 B5B10 B20 B30 Thirdorder polynomial
Figure 2. Effect of temperature on viscosities of binary blends of soy biodiesel with petroleum diesel oil at different volume
fractions.

O. A. AWORANTI ET AL. 449
0
1
2
3
4
5
6
290 300 310 320 330 340 350 360 370 380
Viscosity(mpa‐s)
Tem perature(K)
390 400
3.5%SBD+1.5%SO+95%PD 7%SBD+3%SO+90%PD
14%SBD+6%SO+80%PD21%SBD+9%SO+7 0%PD
Thi rdorderpolynomial
Figure 3. Effect of temperature on viscosities of ternary blends of soy biodiesel With soybean oil and petroleum diesel oil at
different volume fractions.
0.79
0.8
0.81
0.82
0.83
0.84
0.85
0.86
0.87
290 310 330 350
Den sit y(g/cm
3
)
Tem perature(K)
370
100%PD95%PD+5%SO 90%PD+10%SO
80%PD+20%SO 70%PD+30%SO Third‐order polynomial
Figure 4. Effect of temperature on densities of binary blends of soybean oil with petroleum diesel oil at different volume frac-
tions.
0.79
0.8
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
290 300 310 320 330 340 350
Density(g/cm
3
)
Tem perature(K)
360 370
B100 B5 B10 B20 B30 Third ‐orderpolynomial
Figure 5. Effect of temperature on the densities of binary blends of soy biodiesel with petroleum diesel oil at different volume
fractions.

O. A. AWORANTI ET AL.
450
23
CT DT 
3.3. Prediction of the Viscosities and Densities of
Blends Determined by Correlation where N is either viscosity or density, A, B, C and D are constants and T is temperature (K).
To predict the viscosities and densities of binary and ter-
nary blends of soybeans oil, soy biodiesel and petroleum
diesel at different temperature the correlation between
viscosity and temperature and density and temperature
were determined as shown in Figures 1 to 6 and the cor-
responding equations are presented in Tables 3 and 4,
respectively. The best correlation between viscosity and
temperature as well as between density and temperature
for each of the binary an d ternary b lends wa s obtained by
a third-order polynomial equations; respectively. The
equation can generally be written as:
4. Conclusion
It can be concluded from the result of the present study
that, the binary and ternary blends show temperature de-
pendent behaviors. The densities and viscosities of bi-
nary and ternary blends decreased non-linearly with
temperature, respectively. Accurate evaluation of the
variations in viscosities and densities of the blends with
respect to temperature, done by correlation showed that
the polynomial equation correlates very well the varia-
tion of density and viscosity with temperature. The den-
sities and viscosities of ternary blends and the binary
lends of soy-biodiesel and petroleum diesel fall within
NABT (2) b
0.8
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
0.9
290 300 310 320 330 340 350 360 370
Density(g/cm
3
)
Temperature(K)
3.5%SBD+1.5%SO+95%PD 7%SBD+3%SO+90%PD
14%SBD+6%SO+ 80%PD21%SBD+9%SO+70%PD
Third‐ord erpolynomial
Figure 6. Effect of temperature on densities of ternary blends of soy biodiesel with soybean oil and petroleum diesel oil at
different volume fractions.
Table 3. Correlation equation to predict the viscosity of binary and ternary blends at different temperature for different per-
centage volume of mixtures.
% Volume of Mixture Third-Order Polynomial Equation (R2)
P100 Y1 = 1E10–6x3 – 0.001x2 + 0.144x + 10.56 0.996
95% PD + 5% SO Y1 = –1E10–5x3 + 0.0 1 0 x2 – 3.619x + 425.4 0.986
90% PD + 10% SO Y1 = –8E10–6x3 + 0.0 0 8 x2 – 2.808x + 332.3 0.990
80% PD + 20% SO Y1 = –8E10–6x3 + 0.0 0 9 x2 – 3.339x + 414.8 0.996
70% PD + 30% SO Y1 = 7E10–6x3 – 0.006x2 – 2.065x + 198. 8 0.996
B100 Y1 = 1E10–5x3 – 0.010x2 + 3.160x – 3 03.6 0.985
B5 Y1 = 6E10–6x3 – 0.005x2 + 1.410x – 1 22.3 0.997
B10 Y1 = 7E10–6x3 – 0.006x2 + 1.873x – 17 7.5 0.999
B20 Y1 = 6E10–6x3 – 0.006x2 + 1.797x – 17 0.4 0.996
B30 Y1 = 1E10–5x3 – 0.012x2 + 3.847x – 39 3.0 0.997
95% PD + 3.5% SBD + 1.5% SO Y1 = 9E10–7x3 – 0.000x2 + 0.053x + 18.30 0.9 95
90% PD + 7% SBD + 3% SO Y1 = 8E10–8x3 + 0.000x2 – 0. 201x + 44.90 0.994
80% PD + 14% SBD + 6% SO Y1 = 1E10–6x3 – 0.000x2 – 0.127x + 9.387 0.995
70% PD + 21% SBD + 9% SO Y1 = 6E10–7x3 – 0.000x2 – 0.055x + 30.15 0.992
Where Y1 = Dynamic viscosity (mpa .s) and x = Tem perature (K).

O. A. AWORANTI ET AL. 451
Table 4. Correlation equation to predict the density of binary and ternary blends at different temperature for different per-
centage volume of mixtures.
% Volume of Mixture Third-Order Polynomial Equation (R2)
P100 Y2 = 1E10–8x3 – 1E10–5x2 + 0.003x + 0.645 0.999
95% PD + 5% SO Y2 = 6E10–8x3 – 6E10–5x2 + 0.017x – 0.786 0.997
90% PD + 10% SO Y2 = 0.000x3 + 2E10–6x2 – 0.002x + 1.268 0.998
80% PD + 20% SO Y2 = 5E10–8x3 – 5E10–5x2 + 0.014x – 0.534 0.997
70% PD + 30% SO Y2 = 1E10–8x3 – 1E10–5x2 + 0.001x + 0.870 0.992
B100 Y2 = –2E10–8x3 + 2E10–5x2 – 0.007x + 1.942 0.998
B5 Y2 = –3E10–8x3 + 2E10–5x2 – 0.008x + 1 .925 1.000
B10 Y2 = –1E10–8x3 + 1E10–5x2 – 0.005x + 1.621 0.999
B20 Y2 = –2E10–8x3 + 2E10–5x2 – 0.006x + 1.771 0.994
B30 Y2 = –4E10–8x3 + 4E10–5x2 – 0.015x +2.741 0.998
95% PD + 3.5% SBD + 1.5% SO Y2 = –3E10–8x3 + 3E10–5x2 – 0.012x + 2.426 0 .998
90% PD + 7% SBD + 3% SO Y2 = 5E10–8x3 – 5E10–5x2 + 0.014x – 0. 4 47 0.999
80% PD + 14% SBD + 6% SO Y2= 1E10–8x3 – 1E10–5x2 + 0.003x + 0.669 0.999
70% PD + 21% SBD + 9% SO Y2= –6E10–8x3 + 6E10–5x2 + 0. 019x + 3.102 0.999
Where Y2 = Density (g/cm3) and x = T emperature (K)
the range limit of international standard for petroleum
diesel and biodiesel. This means that ternary blends of
vegetable oils, diesel fuels and biodiesel can be used in
diesel engines when the right proportion are blended to
give the density and viscosity at which the diesel engine
can function effectively. Further investigation to practi-
cally test ternary blends on diesel engines is presently
being carried out in our laboratory to ascertain its use-
fulness and acceptability in the world market.
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