Indian Journal of Chemical Technology Vol. 8, November 2001, pp. 473-481

Rheological behaviour of fatty acid methyl esters

A Srivastava & R Prasadt

Department of Chemical Engineering, H B Technological Institute, Kanpur 208 002, India

Received 28 November 2000; revised 18 June 2001; accepted 9 July 2001

Rheology of fatty acid methyl esters of soyabean, used-soyabean, mustard and used-mustard oils has been examined experimentally in the temperature range of-3 to 15°C. Such a low temperature is encountered in the use of these fatty esters as diesel fuels. These fatty esters were prepared in the laboratory by the transesterification of oils with methanol in the pres­ence of sodium hydroxide as a catalyst. Brookfield Synchro-Lectric Viscometer has been used to observe the dependence of shear rate, time, temperature on the apparent viscosity of these fatty esters. Kerosine works satisfactorily as the bath fluid in the Ultra Cryostat for the desired temperature range. The fatty acid methyl esters of soyabean, used-soyabean, mustard and used-mustard oils are found to behave as Newtonian fluids above a temperature of about 5°C. Below this temperature, they are expected to behave as pseudoplastic fluids. These methyl esters also exhibit a thixotropic behaviour. The decrease in the apparent viscosity of these methyl esters with increase in temperature is approximately exponential.

Fatty acid methyl esters can be used as alternatives to fatty acids in the production of many oleochemicals (fatty alcohols, alkanolamides, a-sulphonated methyl esters, sucrose esters and other fatty esters). Com­pared to fatty acids, fatty acid methyl esters are pre­ferred as they yield higher purity finished products and require milder conditions during synthesis. Fur­thermore, fatty acid methyl esters are easier to frac­tionate, are more stable and are less corrosive than the corresponding fatty acid.

There are two methods of producing fatty acid methyl esters. A primary method is the transesterifi­cation of fats and oils with methanol in the presence of an alkaline catalyst, usually sodium methoxide1

•

This method is successful only if the fat is almost neutral and the reaction mixture is substantially anhy­drous. A second method involves the splitting of fats and oils by the energy- and capital-intensive Colgate­Emery process. The resulting fatty acids are then es­terified with methanol.

Rheology plays an important role in the flow be­haviour of fatty acid methyl esters during preparation and processing. The rheological parameters are valu­able for designing or evaluating such chemical proc­ess equipments as heat exchangers, reactors, distilla­tion columns, mixing vessels and process piping. For example, viscosity and its dependence on temperature is an important parameter for estimating distillation

tFor correspondence (Fax: 0512-545312)

column efficiency for separation of fatty acid methyl esters and glycerol as well as designing the piping for oil transport. Viscosity-temperature relationships are of good value in the process control of transesterifi­cation reaction. A factor of particular importance in the transesterification process is the degree of mixing between the alcohol and triglyceride (vegetable oil) phases. Triglyceride and alcohol phases are not misci­ble and form two liquid layers upon their initial intro­duction into the reactor. Mechanical mixing is nor­mally applied to increase the contact between the re­actants, resulting in an increase in mass transfer rate. Therefore, variations in mixing intensity are expected to alter the kinetics of the transesterification reaction. Better understanding of the mixing effects on the ki­netics of the tranesterification process will be a valu­able tool in process scale-up and design. The rheology of liquids plays an important role in governing the hydrodynamics in the mixing vessel. The influence of rheology on the performance of the mixer has been reported in terms of power consumption, circulation capacity and mixing times. The variables like power consumption and circulation capacity not only serve as a useful basis for selection of a mixer for a specific purpose but also help in correlating and scaling up some other physical quantities such as heat- and mass-transfer coefficients. Mixing time, which may be defined as the time necessary to achieve the re­quired uniformity in all the parts of the vessel, is mainly useful for comparing different agitation sys­tems.

474 INDIAN J. CHEM. TECHNOL., NOVEMBER 2001

It is, therefore, proposed to investigate the rheologi­cal behaviour of fatty acid methyl esters of soyabean, used-soyabean, mustard and used-mustard oils.

Various changes which occur in fatty acid methyl esters during preparation and application can be ana­lyzed by studying structural changes with time and temperature. Flow properties are vitally important to successful processing. Rheology plays an important role not only in the flow behaviour, but also in the prediction of the structural characteristics. The rheological data can be used to predict long term ma­terial performance. The rheological classification of fluids alongwith their important characteristics is given in Table 12

.

Viscometric properties of higher fatty acids and their derivatives have been studied by several investi­gators. Teeter and Cowan3 determined the viscosities of the methyl, ethyl, n-propyl and isopropyl esters of the fatty acids from caproic to stearic acids in the temperature range of 20-1 00°C. Crouch and Cam­eron4 studied number of viscosity-temperature equa­tions. It was observed that almost all the standard vis­cosity-temperature laws are based on the solution of a single differential equation of the type5

1 dj..l. 1 ----

J..I. dt f(t) .. . (1)

where f(t) is a polynomial in temperature, t, of the form: f (t)=a + bt + cP + ---- + nt rn_ Most of the stan­dard equations can be derived by retaining different number of terms in the polynomial.

Fischer6 correlated viscosity with temperature and properties such as density, refractivity and surface tension. The viscosities of the methyl esters of hexa­noic, heptanoic, octanoic, decanoic and dodecanoic acids were determined at temperatures ranging from 10 to 80°C by Liew et at.7

. They plotted fluidities (re­ciprocal of viscosity) against the molal volumes of the esters, and obtained smooth curves. Intrinsic volumes were determined by extrapolation to zero fluidity. A following equation relating the fluidity with tem­perature was formulated :

if>=A'e-E'T[ M 1] (k + 1T) V

0 -

.. . (2)

Table !-Rheological characterist;cs of fluids

Fluid type Effect of increasing Time-dependent? shear rate

Pseudo plastic Thins No

Thixl)tropic Thins Yes

Newtonian None No

Dilatent Thickens No

Rheo12ectic Thickens Yes

where V0 is intrinsic volume, ¢> is the Jluidity, E is ac­tivation energy, M is molecular weight, A', k and tare parameters and T is absolute temperature. The maxi­mum error between the experimental fluidities and calculated values was less than 1 percent.

Metzner and Otto8 introduced the concept of the effective shear rate, y0 , which is given by

Yo= ksZ ... (3)

where Z is the speed of agitation, ks is an experimen­tally determined constant and it is a function of the geometry and impeller type. It was originally postu­lated that ks is independent of the liquid rheology. However, recent work suggests that for shear thin­ning fluids its value also depends upon the Power law index. Chavan and Ulbrecht9 have obtained the power consumption data for a number of geometrical ar­rangements of the helical mixers. Generalized power correlations incorporating both the shear-thinning properties of the liquids and the geometry have been proposed by them. Chavan et at. 10 presented the measurements of the circulation, mi xing and blending times for helical screw impellers with the draught tube. The influence of shear-thinning and elastic properties of the liquids on these quantities have been analyzed both experimentally and theoretically. The overall circulation was found to be independent of the shear-thinning character of the liquid. They proposed a relation which incorporates the geometry and rheol­ogy of the liquid. The mixing and blending time re­sults have been analyzed and related to the hydrody­namics using the laminar mixing approach. Patterson et at. 11 used the concept of drag flow about an in­clined blade to predict the power, and the resulting

SRIVASTAVA & PRASAD: RHEOLOGICAL BEHAVIOUR OF FATTY ACID METHYL ESTERS 475

expression was modified to include viscoelastic flu­ids12. The Couette analogy approach has also been used to develop a theoretical framework for the pre­diction of the effective shear rate in the vessel 13

.

Some attempts have been made at elucidating the ef­fect of viscoelasticity on power consumption but con­flicting conclusions have been reported in the litera­ture. For instance, both Chavan and Ulbreche 4 and Yap et al. 12 concluded that the shear-thinning effects completely overshadowed viscoelastic effects for helical ribbon impellers. Nienow et a/.15 reported a slight increase in power consumption for turbine im­pellers in viscoelastic xanthan gum solutions. In most of the aforementioned studies, aqueous polymer solu­tions (exhibiting both shear dependent viscosity as well as varying levels of viscoelasticity) have been used as model test fluids. It is thus not clear whether the observed changes in power consumption are due to the shear-thinning, or due to the viscoelastic be­haviour or due to both. Prud'homme and Shaqfeh16

have used non-shear thinning but highly elastic fluids and reported a large increase in power consumption for turbine impellers. Carreau et a/.17 studied the in­fluence of the shear-thinning and viscoelasticity on the power required for the mixing of viscous liquids (Newtonian as well as non-Newtonian) using different helical ribbon agitators. They proposed simple models to predict the effective shear rate in the tank from the knowledge of the torque or power number. The effec­tive shear rate slightly depenc¥ on the shear-thinning properties. Flu.id's elasticity appreciably increases the power requirement and departures from the general­ized Newtonian power curve in the laminar regime are observed at smaller Reynolds numbers for vis­coelastic fluids. Bottom wall resistance of the mixing vessel makes a negligible contribution to the power consumption.

Smith and Schoen makers 18 studied the effect of the viscosity of the additive on the time required to blend small quantities of fluid into a turbulent low viscosity liquid. They used a conductivity method to compare the time to assimilate various aqueous solutions into water in a stirred vessel. The viscosity of the added fluids ranged up to about 1500 mPa.s. Injecting liquid as an extended pulse was reported to be more efficient than sudden addition. With this provision the viscosity of the additives had little effect on the time to mix except when discrete masses came in contact with and adhered to solid surfaces within the mixing vessel. Nienow and Elson 19 reviewed the literature on the

lollto>lll~ 27. Scm

l ~ ~0 ~ 1"'"' •I

Ul tro Cryostot

Fig. I --Schematic diagram of experimental set-up for rheological behaviour of fatty acid methyl esters.

mixing of rheologically complex non-Newtonian flu­ids in stirred tanks. They described a number of novel experimental techniques; cavern formation in plastic fluids; power consumption; the effect of fluid visco­elasticity on the Weissenberg effect, flow pattern and scale-up; mixing time; the effects of gassing on power and cavity structure, bulk flows, mixing times, mass transfer and hold-up; mixing of shear-thickening, di­latant slurries and on the average shear rate concept in mixing vessels.

The plot of shear stress versus shear rate for oils and 60:40 oil-fat mixture showed a straight line indi­cating Newtonian behaviour in the temperature range of 298-338K. Absolute viscosity of oils decreased as temperature increased, however, the extent and pat­tern of this decrease was dependent on the type of oil20.

Experimental Procedure

A schematic diagram of the experimental set-up designed to investigate the rheological behaviour of fatty acid methyl esters is depicted in Fig. 1. It con­sists of Brookfield Synchro-Lectric Viscometer and Ultra Cryostat. The ultra cryostat equipment is used to maintain required temperature for viscosity measure­ments of fatty acid methyl esters in the temperature range of -3 to l5°C. For this temperature range the bath fluid taken in the Ultra Cryostat reservoir is kerosene. The sample is taken in a mild steel vessel of dimensions (Inside diameter = 73 mm and Height = 137 mm). The vessel filled with fatty acid methyl es­ters is put in the Ultra Cryostat reservoir, where the vessel is surrounded by the circulating bath fluid. The

476 INDIAN J. CHEM. TECHNOL., NOVEMBER 2001

sample is maintained at the constant desired tem­perature by an automatic temperature controller. When the temperature of the sample reaches at de­sired level, Brookfield Viscometer's dial reading is taken at the time intervals of 1, 3, 5, 7, 10, 15 and 20 min for a selected spindle rotating at a fixed speed. After taking one set of readings at a fixed speed (say 3 r.p.m.), the speed is changed to next higher speed (6 r.p.m.). The viscosity of the esters is obtained by mul­tiplying the dial reading by a factor which is specific to speed and spindle used. The spindle numbers 1, 3 and 4 have been used. At higher speed the dial read­ing is taken by stopping the diai and the pointer by proper manipulation of the clutch and motor switch.

The following procedure has been employed to cal­culate the shear rate and shear stress values for each measured value. Shear stress, 't, is directly propor­tional to the spindle speed, N n, raised to the power n, t.e.

't = Constant ( N n ) ... (4)

To translate spindle speed, N, into shear rate, y, vis­cometer scale reading (propo1rtional to shear stress) is plotted against spindle speed on log-log coordinates. The slope of the straight line is taken as n. The shear rate corresponding to any spindle speed is then ob­tained from the expression

4nN y=­

n ... (5)

Shear stress is obtained by multiplying the apparent viscosity with the calculated shear rate.

Experiments were carried out to investigate the rheological behaviour of fatty acid methyl esters of soyabean, used-soyabean, mustard and used-mustard oils in the temperature range of -3 to 15°C. These methyl esters were prepared in the laboratory by the transesterification of soyabean, used-soyabean, mus­tard and used-mustard oils with methanol in the pres­ence of sodium hydroxide as a catalyst. The trans­esterification reaction was carried out at a molar ratio of methanol to oil of 6:1, a sodium hydroxide con­centration of 0.5 wt.%, a temperature of 70°C for 1 hour. Fatty acid methyl esters were separated from the transesterification reaction mlxture by first settling the glycerol content and then distilling the unreacted methanol.

"' II>

20.-----------------------------~

15

SOYABEAN OIL METHYL ESTER

T empeoture •c """""15 ~1 0 ~.Jl..O...QY 5 ttti.tO ·.::.t..±...t;t- -3

(a)

~ 10 "'

5

0 5 10 1 5 20 25 30 35 40 Shear rote (s- 1

)

Fig. 2a-Variation of shear stress with shear rate at different tem­perature for soyabean oil methyl ester.

2~.-------------------------------~ SOYA8EAN Oil. MOH'Il ESTER

(b)

2000

500

35

Fig. 2b--Variation of viscosity of soyabean oil methyl ester with shear rate for different temperature.

To study the rheological behaviour of fatty acid methyl esters the effects of magnitude and duration of shear rate on the apparent viscosity and shear stress were observed in the temperature range of -3 to l5°C. The spindle speed, which is proportional to shear rate, was varied from 6 to 60 rpm. The duration of agita­tion was taken as 20 min as it gives steady values of the apparent viscosity/shear stress. From the observed values of the dial reading and spindle speed, shear

SRIVASTAVA & PRASAD: RHEOLOGICAL BEHAVIOUR OF FA TTY ACID METHYL ESTERS 477

40r-------------------------------~ USED - SOYABEAN OIL METHYL ESTER (a)

0 s "' Ill

30

~ 20 .... "' ... 0 .,

L (/)

Tempeab.lre, •c ~l5 ~10 ~ 5 ~0 ~ -.3

Fig. 3a--Yariation of shear stress with shear rate at different tem­perature for used-soyabean oil methyl ester.

4500 ~-----------------(ihllb)

USED- SOYABEAN OI L METHYL ESTER

~

"'

4000

3500

~ 3000

i .c 2500 ·;;, 0 u

· ~ 2000 ... c: ~ 1500 0 a. Q.

.. 1000 -

500

letr'percrlure,•c

=15 ~~g -0 l±±±!- -3

15 LO 5 30 35 40 45 Shear rate (s-' )

Fig 3b--Yariation of viscosity of used-soyabean oil methyl ester with shear rate fo r different temperature.

stress and shear rate were calculated using the proce­dure given earlier.

Results and Discussion Figs 2-5 are plots of shear stress/apparent viscosity

versus shear rate at five temperatures of 15, 10, 5, 0 and -3 °C for fatty acid me thy I esters of soy abean, used-soyabean, mustard and used-mustard oils. It can be seen from these fi gures that the shear stress-shear

20.------------------------ -------,

"' "' ~TO "' ] Vl

5

.'>I~STARD OIL ~£THY~ ESTER (a)

r~"'P4'ot.!:!!~ <>=1~ ......... ~ 'llll>-' 5 uauo 4_1.U_'"' -)

Fig. 4a--Yariation of shear stress with shear rate at different tem­perature for mustard oil methyl ester.

3000

MUSTARD OIL METHYL ESTER (b )

2500

( ...,.

lcmpt;roture,•c

i.. 2000 an:D15

E ='g ~ -0 £

-t±!±l- - J

~ 1500 u (f)

·;; .... c 1' 1000 0 Q. c. <(

500

~ 00 5 10 15

Shear rate (s- 1) 20 5 30

Fig. 4b--Yariation of viscosity of mustard oi l methyl ester with shear rate for different temperature.

rate curves for the temperatures of 0 and -3 °C pass through origin and are concave downward at low shear rates and become nearly linear at high shear rates. The apparent viscosity of these methyl esters decreases with increase in shear rate at temperatures of 0 and -3°C. These indicate that the fatty acid methyl esters of soyabean, used-soyabean, mustard and used-mustard oils behave as a pseudoplastic fluid

478 INDIAN J. CHEM. TECHNOL. , NOVEMBER 2001

25

20

0

~ 1 5 Vl

"' b "' 0 10 v

.r: V>

5

USED -MUSTARD OIL M ETHYL ESTER (a )

T ernperotu re, "C Q.9.Q.Q.p 15 ~ 10 tlll9 5 <.JUW> 0 ~ -3

Fig Sa--Vari ation o f shear stress with shear rate at different tem­perature for used-mu stard oi l meth yl ester.

350C

3 000

""0"2500 0

n_ E

.0 2000 "iii 0 u Ul

·;; 15CO -» c: ~ 8. 1000 Q.

..:

500

! USED fAUSTARD 01~ METHYL ESTER ( b)

T cmperotun:;, "C

=ts ~tO 0000:¢ 5 ~ 0 -'...l....i±I- -3

Fig Sir-Variati on of viscosit y of used- mustard o il meth yl ester wi th shear rate fo r d ifferent temperature.

or shear-thinning at temperatures of 0 and - 3°C. For these methyl este rs, the shear stress-shear rate curves at temperatures of S, I 0 and IS °C also pass through the ori gin but are approx imate ly linear at low as we ll as hi gh shear rates. Also, the apparent viscosity of these methyl este rs is nearly independent of shear rate at these temperatures . These indicate that the fatty ac id methyl esters of soyabean, used-soyabean, mu s-

4500 r---------------------------------,

4000

.3500 ~ L

~ 3000 E ~

.c 2500 ·,:n 0 u

.\2 2000 >

+' c: 1: 1500 -0 0.. 0.. <( 1000

500

~ Soyabeon cil m~thy 1 es~er CIIID Us~d- t;oyct>e cu: oil m e thyl P.rlcr

0o!----'----,L.o __ ..._ _ ___.,.J2o~--~..--..,J3o~ '---;4"'-o---'--~so·

Shea r rote (s- 1)

Fig. 6-Variati on of apparent viscosity o f fatty ac id methyl esters with shear rate at - 3°C.

tard and used-mustard o il s behave as Newtonian fl u­ids at temperatures of S, I 0 and IS 0 C. Therefore, fatt y ac id methyl este rs of soyabean, used-soyabean, mus­tard and used-mustard oil s are expected to behave like

pseudoplasti c fluid s be low a temperature of about ooc and they behave like Newtonian fl u ids above a tem­perature of about soc.

To study the re lative effect of shear rate on the ap­parent viscosity of fatty ac id meth yl esters of soya­bean and used-soyabean o i Is, a plot of the apparent

vi scosity versus shear rate at a temperature of -3°C is shown in F ig . 6 . It can be seen fro m thi s fi gure that the apparent viscos ity of methyl esters of raw soya­bean oil is lower than the corresponding value for the used-soyabean methyl esters .

Effect of duration of agitation on apparent viscosity Fi gs 7-8 show the variati on of the apparent viscos­

ity of methyl este rs o f soyabean, used-soyabean ,

mustard and used-mustard o il s at -3°C with time at spindle speeds of 6, 12, 30 and 60 rpm. These fi gures indicate that the apparent viscos ity of these methyl

este rs at - 3°C decreases with increase in the duration of ag itati on for spindle speeds of 6, 12, 30 and 60 rpm. Ultimate ly, it reaches a fi xed va lue which is dif­fe rent for diffe rent spindle speed . T herefore, methyl es ters of soyabean, used-soyabean, mu stard and used­

mu stard o il s behave as thi xotropic fluids at - 3°C. A s imilar behaviour has been observed at a temperature

SRIVASTAVA & PRASAD: RH EOLOGICAL BEHAVIOUR OF FATTY ACID METHYL ESTERS 479

3000 l •-----~ OIL M£THYL ESlER (ol

i 20001 \ ~· ~-" ...

~ r \., 3 . --.,._ -~ --- - - --o-----.. 12

-~ ~--------f>.-~ 1000 -~30 g_ a. ...:

0o~~--ts--L-1~o~--'--~15~~-~2~o-~~25 Time ( min )

Fig ?a--Vari ation of apparent vi scosit y of soyabean oi l methyl esters wi th time for different spindle speeds at - 3"C.

5000 USED-SOYABEAN OIL METHYL ESTER

( b)

Spind l~ S :Je'!d , rprn

V)4000 0 a. E

'-'

~3000

~ ~----....,..._ _ _ ___, 12 ·;;

] 2000

0 a. a.

...: ~~~--------c 30 1000 f>-tt--_,.____, ___

·------~60

0o~~--5t-~~-1~o~~-,1~5-J---z~o~~~2s· Tim e (min)

Fig 7b--Variation of apparent viscosity of used-soyabean o il methyl esters with time for different spindle speeds at -3"C.

of 0°C. Therefore, the fatty acid methyl esters of soy­abean, used-soyabean , mustard and used-mustard oil s are expected to behave as thixotropic fluids below a temperature of about 0°C.

Effect of temperature on apparent viscosity The effect of temperature on the apparent viscosity

of methyl esters of soyabean, used-soyabean, mustard

~3000

4000 ·-- - ----

MUSTAAD OIL METHYL ESTER -~

~~ Spindle s peeo, rpm

Ill

ci a. -S ~ -~ 2000 u

"' ·:;; .,.., c ~ 0 a. ;; 1000

- - -- -£16

~~ ~ --- - 12

----+ ·-·-Q----+--~ 30

-----~~--~-----.>-----tr--··--------1¥ 60

5 10 15 20 25 Time ( mi n)

Fig. Sa--Vari ati on of apparent viscosity of mustard oi l methyl esters with time for different spind le speeds at -3"C.

4000,--USED - MUSTARD OI L MET:-!YL ESTER

(b )

1 Spindle •peed, rp"'

~3000 ~~----~r---==86r,-~-"' c a. s ~

'2 2000 u "' ·:;;

1: ~ g_ --,12

;j1 000 -~-~~~Q~~·--------~--~ 30 60

0o!;----'---:,.s- -•-,1?;o--'----o,,.,s--'----o2-,;;o---__,_~2'5

T'm e ( min )

Fig. 8b--Variation of apparent viscosity of used-mustard oil methyl esters with time for different spind le speeds at - 3"C.

and used-mustard oils at various spindle speeds is shown in Figs 9-10. In these figures the ultimate va lue of the apparent viscosity has been plotted. These figures indicate that the apparent viscosity of methyl esters decreases with ri se in temperature at spindle speeds of 6, 12, 30 and 60 rpm. The decrease in the apparent viscosity is approximate ly exponenti al. Also, the apparent viscosity is nearly independent of shear rate at a temperature hi gher than about 5°C.

480 INDIAN J. C HE M. TECHNOL. , NOVEMBER 200 1

2500r---------------------------------~

"' 0 Q

2000

-.S 1500 .c "iii 0 u

"' ·s: 1000 c

~ c c. 0.. <(

500 -

SOYABEAN OIL METHYL ESTER

~ptndle ~d, 1pm

'll!.2.29 6 ~12 ~HJO tiJWo 60

5 10 15 Temperature ('C)

(a)

20

Fig. 9a--Vari ation of apparent viscosity of soyabean oil methyl ester with temperature.

5000.-----------------------------------~ USFD- SOYABEAN OIL MtTHYL ESTER (b)

4000 -~J::!.d !~-~p~~1... -~Q!fl .

'=""' 6 <J1 .c,~·~ 11 c ~3()

Q. tillF 60 f ~.3000

_c. "iii 0 u "' ·;;

2000 c 1:! 0 0. a. <

1000

C?..s 10 15 20 Temperature ("C)

Fig. %--Variation of apparent viscosity of used-soyabean oil methyl ester with temperature.

Conclusions Fatty acid methyl esters of soyabean, used­

soyabean , mustard and used-mustard oils are expected

to behave as Newtonian fluid s at temperatures higher than about soc. These methyl esters behave as pseu­doplastic fluid s at temperatures lower than about soc. These methyl esters also ex hibit thixotropic behav­

IOur.

.5000~ - -1 MUSTARD Oil METHYL eSTER

"' r1. 2000 _§_

;::. ·;;; (, v

.~ >

-;:: ~ 1000 0 0..

~

;,e;...11e ~d, rpl'l ........ . ~l:! ......... .oo ~eo

10 Te mperatuno~ ("c)

\ 5

(a )

20

Fig lOa--V ari ati on of apparent viscosity o f mu stard oi l meth yl ester with temperature.

4000

~3000 <JJ

0 Q.

E

:0 - ~ 2000 u en ., ~

c:

"' 0 0. !t 1000

'2.s

USED-MUSTARD OIL METHYL ESTER

\ 0

~pi•l(l le sp111~~

=• ............. ~ 12

5 10 ,·emp€rot ~~re {'C)

t.~JO a.u .. ,.. to

15

(b)

20

Fi g. I Db-Vari ati on of apparent viscosity of used-mustard oi l methyl ester with temperature.

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Reviews, 4 (2000) I I I .

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SRIVASTAVA & PRASAD: RHEOLOGICAL BEHAVIOUR OF FATTY ACID METHYL ESTERS 481

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