rheological properties of moroccan dairy cattle manure

Bioresource Technology 40 (1992) 149-156

Rheological Properties of Moroccan Dairy Cattle Manure* Abdellatif Achkari-Begdouri Food Engineering Department, 1AV Hassan II, BP 6202 Rabat-Instituts, Morocco

&

Philip R. Goodrich Agricultural Engineering Department, University of Minnesota, St Paul, Minnesota, USA

(Received 9 April 1990; revised version received 8 April 1991; accepted 10 April 1991)

Abstract

The rheological properties such as the consistency coefficient, the flow behavior index and the apparent viscosity of Moroccan dairy cattle manure of various total solids concentrations were studied. In the range o f 2.5-12% total solids and at temperatures between 20 and 60°C, cattle manure behaves as a pseudoplastic suspension fluid. Two equations were established to relate the consistency coefficient and the f low behavior index of the manure to temperature and total solids concentration.

Key words: Dairy cattle manure, animal wastes, physical properties, rheological properties, anaerobic digestion.

INTRODUCTION

The biological degradation of organic animal wastes has been widely studied and extensive data were available, but little data have been reported on the physical properties of organic animal manures. The physical properties of animal manures produced in North Africa were not found in the literature. The objective of this project was to estimate consistency coefficient,

*Published as Paper No. 18 055 of the Scientific Journal Series of the Minnesota Agricultural Experiment Station on research conducted under Minnesota Agricultural Experi- ment Station Project No. 12-080 and was partially supported by USAID - IAV. Hassan II - University of Minnesota project 608-0160.

flow behavior index and apparent viscosity with respect to dilution and temperature of Moroccan dairy cattle manure. These rheological properties were needed in determining the heat transfer coefficients through the surfaces of an aerobic reactor. Knowledge of these coefficients was necessary to properly estimate heat losses from an aerobic reactor to the outside environment and hence to establish the total aerobic reactor energy balance.

The viscosity and more generally the rheological properties of animal waste slurries have been studied by several authors (Kumar et al., 1972; Arai et al., 1976, 1981; Chen & Hashimoto, 1976; Hashimoto & Chen, 1976; Bashford et aL, 1977; Hashimoto et al., 1980; Chen, 1982). Generally liquid animal wastes exhibit non- Newtonian behavior where the relationship between shear stresses and shear rates is non- linear (Kumar et al., 1972).

In most cases the animal slurries were classified as pseudoplastic liquids and the power equation r = K ( d V / d Y ) n could be used to describe their rheological properties (Kumar et al., 1972; Arai et al., 1976; Chen & Hashimoto, 1976; Hashimoto & Chen, 1976; Bashford et aL, 1977; Smith et al., 1980; Chen, 1986). When the shear stress r is plotted against the shear rate (d V/d Y) in a full logarithmic scale, the slope of the straight line rep- resents the rheological behavior index (n) and the rheological consistency coefficient (K) is determined from the intercept value. Non-linear regression techniques may also be used.

149 Bioresource Technology 0960-8524/92/S05.00 © 1992 Elsevier Science Publishers Ltd, England. Printed in Great Britain

150 A. Achkari-Begdouri, P. R. Goodrich

The apparent viscosity is commonly used to express the rheological state of animal slurry (Kumar et al., 1972; Chen & Hashimoto, 1976; Hashimoto &Chen, 1976; Bashford et aL, 1977; Chen, 1986). The apparent viscosity is defined as the viscosity of a non-Newtonian liquid exhibiting the same resistance to flow at the chosen shearing stress or shearing rate.

l~a=K d y ] J (1)

For a pseudoplastic fluid, the apparent viscosity decreases with increasing shear rate (Chen, 1986).

Temperature effect The viscosity or any rheological parameter is con- siderably influenced by temperature. When con- sidering animal wastes, there have been few attempts to explain the influence of temperature on the rheological parameters on a theoretical basis (Heldman & Singh, 1981; Chen, 1986; Ibarz & Pagan, 1987). In rheology, the Arrhenius equation as given in eqn (2) is generally used for expressing temperature dependency. In this study the temperature dependency of the consistency coefficient (K) was used in the determination of activation energy for viscous flow.

K = K,, e x p ( E J R T ) (2)

where K = consistency coefficient, K0 = consistency coefficient at reference temperature, Ea= activation energy for K, T--absolute temperature and R -- gas constant.

The viscosity and consistency coefficient of fresh manure slurry was found to decrease with an increase of temperature (Kumar et al., 1972; Chen, 1986).

Effect of total solids The total solids effect on viscosity has been studied by several authors (Kumar et al., 1972; Arai et al., 1976, 1981; Chen & Hashimoto, 1976; Hashimoto & Chen, 1976; Bashford et al., 1977; Barker & Driggers, 1980; Chen, 1982, 1986). Kumar et aL (1972) found, using a coaxial cylindrical viscometer, that the viscosity of fresh cow manure slurry decreased with an increase in dilution and that the flow was Newtonian below 5% total solids and pseudoplastic above 6%. Samples were from 4-1 to 8"6% solids at temperature from 7"8 to 42°C. Barker & Driggers (1980) studied the relationship between the viscosity of

the swine manure and the dry matter concentration in the range 0-1-3%. The resulting equation was:

= 3.084(1.626) rs (3)

where TS = percentage total solids in the range of 0-3%,/~ = dynamic viscosity in mPa (cP).

Chen (1986) measured the rheological properties of sieved beef-cattle manure slurries having TS concentrations ranging from 2.6 to 19-3% at temperatures of 14.3-59-9°C. Using a single-blob rotational viscometer he found:

kt 0 = 5.24( 10 -6) exp(0-0868 TS) (4)

where kt 0 = limiting viscosity ( T--, oo ),

K o = Z ' 4 2 8 ( l O - 3 ) e x p ( O ' Z 4 9 9 T S ) (5)

where K0 = limiting consistency coefficient (T-.

Bashford et al. (1977) studied the rheological behavior of beef-cattle manure at TS ranging between 5 and 15%, at 25°C, using an eight-speed rotational viscometer and found:

K = 0-0286 exp(0.541 TS); R 2 = 0.94

for whole manure and

(6)

K = 0.023 exp(0"2499TS); R 2 = 0-99 (7)

when particles larger than 50 ktm were removed.

METHODS

A coaxial-cylinder rotational viscometer (Rheo- mat 15, Outraves AG, Zurich) was used to measure the rheological properties of the cattle manure having total solids contents ranging from 2.5 to 12.1% (wet basis) and at temperatures ranging from 20 to 60°(2. The coaxial-cylinder viscometer was judged to be more suitable for animal manure slurries than a capillary viscometer, especially for total solids concentrations higher than 2% (Kumar et al., 1972; Bashford et al., 1977; Chen, 1986). The viscometer used had two concentric cylinders with cattle manure in the annular space, a speed-generator with 15 speeds (1 = 5"59 rpm, 15 = 352"0 rpm) to rotate the inner cylinder (spindle) and a measuring device to indi- cate the torque on this inner cylinder. The viscometer was also equipped with a thermostatic bath surrounding the outer cylinder (cup) to con- trol the working temperature.

Rheological properties of Moroccan dairy cattle manure 151

Test procedure Experiments were conducted at 2.5, 5.4, 7.5, 9.1 and 12.1% TS and for each total solids concentration tests were performed at 20, 30, 35, 40, 45, 50, 55 and 60°(2. The total solids range was chosen to fit within the range reported by Chen (1982). The low temperature was determined by the attainable room temperature and the upper temperature has been used successfully in digester heat exchangers. Test procedures outlined by the viscometer manufacturer were followed. The two largest spindles A and B (Fig. 1) were used for most of the tests. In each test and for each total solids concentration the outer cylinder (cup) was filled with the recommended amount of sample, 120 ml when using spindle A and 80 ml when using spindle B. The sample was heated using a thermostatic bath. At 20°C, the spindle was rotated at 15 speeds starting at graduation 1 (5"6 rpm) and ending at graduation 15 (352 rpm). At each speed, after a 1 min stabilization period, the reading indicated by the measuring device was recorded. The same sample was then heated to 30°(2. At 30°(2, readings for the same rotational speeds were recorded. The same procedure was followed until a temperature of 60°C was reached. After the last reading, the outer cylinder (cup) was emptied, cleaned and filled with fresh manure having the same total solids concentration. The test was performed three times and readings at each temperature and each rotational speed were averaged and the standard deviation was com- puted. It took 7 h to perform the three replicates of one total solids concentration.

e -

l

" !

0 hi

I

I

h2

Fig. 1. Details of coaxial cylinders of viscometer. Inner cylinder (rotor): radius, R l (22.8 mm); height, h 0 (56 mm); h I (99 mm). Outer cylinder (cup): radius, R2 (24 mm); height, h2 (148 mm). Sample volume: measurement system A, V= 120 ml; measurement system B, V= 80 ml.

The shear stress was calculated from the readings (% full scale) by applying a factor of 0.1962 Pa/(unit of reading scale) for spindle A or 42.29 Pa/unit of reading scale for spindle B.

For each rotational speed graduation of the spindle (rotor), a corresponding value of the shear rate was taken from the instrument manufacturer's tabulated data. The rheograms were constructed by plotting shear stress against shear rate. An example of the calculations for rheograms is:

For graduation speed 3 and at temperature 20°C:

- - T h e three readings collected in the three runs performed were averaged; their average was 7.6. This value multiplied by r%--- 0.1962 is equal to the shear stress. r= 0"1962 x 7.6 = 1.49112 Pa.

- - T h e value of the corresponding shear rate was taken from table 2301 in the instructions.

dV D = = 19.72

dY

- - Then by plotting the log of r versus the log of D and solving the regression equation, K and n are obtained.

Experimental errors The instructions for the Rheomat 15 did not dis- cuss possible moisture loss. The instructions indicated only the quantity of sample to use for each spindle, 120 ml for spindle A and 80 ml for B. It was assumed that the moisture loss effect was negligible.

It was known from a preliminary unpublished study (Achkafi-Begdouri, 1989) that the settling velocity of the particles in the dairy cattle manure in the range of total solids concentrations studied was extremely low. No clarification zone was observed after 3 h settling of the samples in a 1 liter graduated cylinder. Therefore we assumed no significant settling occurred in the viscometer during the measurement.

All experiments in this study were performed with sufficient care to minimize possible sources of error. Prior to starting each trial, the viscometer was heated, the thermostatic bath was carefully regulated and all the readings were made after the pointer became stable. The high solids content of the material limited the evaporation loss to the upper layers of the samples assuring that the manure in the annular space was unaffected.


Settling was insignificant even when the rotation speed was zero as shown by previous tests.

Manure The manure used in this investigation was scraped from the concrete surface at the So.De.A (Societe de developpement agricole) in Sidi Yahia de Zaer, 25 km from the Hassan II Institute. An effort was made to collect fresh droppings on the floor with approximately the same characteristics and to prevent any contamination of the collected manure in the dust. The total solids of the fresh and diluted manure were determined according to Standard Methods for Examination of Water and Wastewater (APHA, 1980). The collected raw manure TS ranged from 15 to 18%. After collec- tion and transport to the laboratory, the manure was diluted with tap water to approximately 12%TS and mixed with an electric stirrer. Long straw pieces were separated by sieving with a 1 cm screen. The slurry was then stored at 4°C until needed. Samples from the individual con- tainers were analyzed to determine the dilution needed to attain the total solids concentration for each experiment. The slurries used for tests were stored from 2 to 6 days before dilution and use. The basal ration of the animals during the major part of the experiment period is shown in Table 1. Knowing that the dairy cattle were fed with a constant ration, we could expect a manure with almost the same characteristics. The particle size and particle size distribution were not determined because total solids was used to compare our results to other studies.

Regression analyses were performed for each set of data using the STATISTIX Program (Heisey & Nimis, 1985a,b). The plots show that the rela- tionships between log(z) and log(dV/dY) were linear which indicated that the power law

=

e-

Fig. 2.

S 1 J 100 1000

Shear Rate (l/s)

Shear stress versus shear rate curves for TS = 2.5%.

(Q 0

a $

10

1 1 0 100 1000

RESULTS AND DISCUSSION Shear Rate (l/s)

Fig. 3. Shear stress versus shear rate curves for TS = 5.4%.

The data in Figs 2-6 show the experimental results of shear stress (r) versus shear rate (dV/dY) displayed on log-log scales for the different total solids concentrations and temperatures.

Table 1. Composition of basal ration for dairy cattle

Ingredient Amount (kg)

Bersim 40 FVA (oat hay) 2 Straw 3 Molasses 1 Beet pulp 2 Barley 0-5 CMV (mineral and vitamin concentrate) 0"15

100":

.=

i

1 0

Fig. 4.

T= 20=C\ T=30~ \

T=40=C

100 1000

Shear RaW (l/s)

Shear stress versus shear rate curves for TS = 7-5%.


100.

10

¢/I

1 10

Fig. 5.

T = 2 0 " C \

*f = 30'=C~ \

T . 40 '~

1 O0 1000

Shear Rate (1/$)

Shear stress versus shear rate curves for TS= 9-1%.

lOO,

1 . . . . . . lO lOO lOOO

Shear Rate ( l / s )

Fig. 6. Shear stress versus shear rate curves for TS= 12.1%.

r = K ( d V / d Y ) n can be applied. The resulting regression equations were used to compute consistency coefficient (K) and behavior index (n) for the different samples. These values of K and n are summarized in Table 2.

It was observed from Table 2 that the consistency coefficient (K) increased with the increase in total solids concentration whereas n decreased. This agreed with reported data on cattle manure slurries (Kumar et aL, 1972; Bash- ford et aL, 1977; Hashimoto et al., 1980; Chen, 1982, 1986). As the total solids increase, the solids volume increases (Hashimoto & C h e n , 1976) which increases K because there is an increase in the cohesive forces between the manure particles. There is less water to provide the slippage between particles of manure. As the total solids increase, the flow behavior becomes less Newtonian and the behavior index (n) decreases, moving away from unity.

It was observed from the data in Table 2 that K decreased as the temperature increased. This ~agrees with the results reported by Kumar et al. (1972) and Chen (1986), but does not agree with C h e n & Hashimoto (1976). This latter study reported that the results were inconclusive when they determined the effect of temperature on K for an aerated poultry slurry. This could be due to the three-phase (air, water, solids) slurry and the confounding effect of the treatments. The viscosity of a liquid decreases when the temperature increases while the gas viscosity increases with increasing temperature (White, 1979). In our study with a two-phase mixture of water and solids, the temperature effect would only influence the suspending medium (water) where the viscosity decreases when the temperature increases.

In this study we found that the behavior index n increased with an increase in temperature and became more Newtonian. This agreed with the data reported by Chen (1986) for sieved cattle manure slurries with TS < 4%. For TS > 4.5%, the data reported by Chen (1986) were not clearly conclusive. Data presented by Kumar et al. (1972) showed that for fresh cow manure at 7.03% TS, n at 42°C was higher than the n at 8Y~, however at 8.6%TS, the opposite was observed. C h e n & Hashimoto (1976) found that in general n decreased as the temperature increased for aerated poultry slurries with TS concentrations between 2.71 and 6.63% in the temperature range of 9-5-26°C. The shear stress, the consistency coefficient and the behavior index are primarily dependent on the magnitude of the cohesive forces that tend to keep adjacent molecules in the sample in a fixed position relative to each other and to resist relative motion. Because these forces decrease with increase of temperature, the sample consistency coefficient decreases as the temperature rises. As these forces decrease the molecules initially tangle up, start to fall into lines and to slide easily on each other. The fluidity of the sample increases which makes it closer to a New- tonian fluid and therefore its behavior index increases and becomes closer to unity.

As the total solids increases, the intramolecular cohesion increases, which increases the consistency coefficient. The flow behavior becomes less Newtonian and the behavior index decreases moving away from unity. In general, the lower the total solids concentration, and the higher the temperature, the more Newtonian the behavior of the cattle manure slurries.


Table 2. Consistency coefficient (K) and behavior index (n) of the dairy cattle manure as a function of total solids concentration and temperature

% TS T (~C) Consistency coeff. Behavior index Correlation Shear rate coefficient range

K + n + (l/s) (Pa s") t S(K) t S(n)

12.1 20 9.952 0.258 0.320 0.009 0-999 3-63 30 6.783 0.307 0-362 0.016 0-997 3-63 35 5.885 0.163 0.367 0-008 0.999 3-149 40 5.184 0.135 0.370 0.008 0.999 3-149 45 4.622 0.143 0.376 0-009 0.999 3-149 50 4.129 0-105 0.372 0.007 0.999 3-149 55 3.495 0-130 0.373 0.011 0-998 3-149 60 2.208 0-065 0.443 0.009 0-999 3-149

9.1 20 2.005 0.074 0.416 0.010 0.999 11-156 30 1.242 0.073 0.448 0.014 0-998 11-399 35 1.052 0.061 0.467 0.013 0-998 11-156 40 0.925 0.043 0.476 0.010 0-999 11-532 45 0.752 0.021 0-490 0.006 1.000 11-702 50 0-568 0-023 0-517 0.009 0.999 11-702 55 0.463 0.012 0.528 0.006 1.000 11-702 60 0.430 0-017 0.520 0.009 0.999 11-702

7-5 20 0.859 0.004 0-479 0-001 0.999 11-156 30 0-591 0-003 0-501 0-001 1-000 11-399 35 0.525 0-001 0.533 0-000 1-000 11-399 40 0.342 0-001 0-558 0-001 1.000 11-532 45 0.278 0.002 0.576 0-001 0.999 11-702 50 0.233 0.001 0.586 0.001 0.999 15-702 55 0.163 0-001 0.648 0.002 0.999 20-702 60 0-122 0-001 0.674 0.002 0.999 26-702

5.4 20 0.281 0.014 0.556 0-011 0.999 15-532 30 0.202 0.009 0.572 0.009 1.000 15-532 35 0.192 0.029 0.562 0.028 0.996 50-702 40 0.096 0.009 0-652 0.017 0-999 50-702 45 0.070 0.012 0.694 0-033 0.997 50-532 50 0.065 0-004 0.685 0-011 1.000 50-532 55 0-041 0.005 0.755 0.022 0.999 88-532 60 0-032 0-002 0.774 0.011 1.000 88-532

2.5 20 0.060 0-003 0.655 0.008 1.000 226-702 30 0.043 0-002 0.668 0.008 1.000 226-702 35 0.042 0.002 0.710 0-009 1-000 226-702 40 0-018 0.002 0.761 0.016 0.999 226-702 45 0-014 0.001 0.784 0-008 1.000 226-702 50 0.011 0.001 0.813 0.015 1.000 303-702 55 0.006 0.001 0.909 0-020 0-999 303-702 60 0.005 0.000 0-929 0-012 1-000 303-702

Temperature effect At each total solids concen t ra t ion , a re la t ionship be tween the consis tency coeff icient (K) and the t empe ra tu r e was deve loped using the Ar rhen ius - type equa t ion (2) which can be wri t ten in the fol- lowing form:

ln (K) = ln(K,,) + E a / R T (8)

By plot t ing K versus l I T on semilogar i thmic coord ina tes , as i l lustrated in Fig. 7, straight l i n e s were obta ined. T h e slope of the curves are values of Ea/R. It appea red that the act ivat ion energy

dec rea sed as the total solids concen t r a t i on increased. At a high total solids concen t r a t i on (high K) even a high shearing stress may cause a small de fo rma t ion o f the dai ry catt le manu re and the re fo re a small act ivat ion energy.

Total solids concentration effect For each value o f the t empera tu re , a regress ion analysis was p e r f o r m e d using the 'STATISTIX' p r o g r a m to relate the cons i s tency coeff ic ient to the total solids concen t r a t i on o f the catt le manure . T h e plots o f K v e r s u s % T S i l lustrated in Fig. 8


A %

¢_ v .5 =

:t 2

. • "[5=5"4%

4 • •

0.0030 0.0031 0.0032 0.0033 0.0034 0.0035

1/Temperature O/degrees K)

Fig. 7. In(K) versus the reciprocal of the absolute temperature of dairy manure.

A

i ~I ¸

. 0 0 1 . . . . . . . .

1 0 1 0 0 1 0 0 0

Shear Rate (l/s)

Fig. 9. Apparent viscosity of the dairy cattle manure as a function of the shear rate.

0 / =

g v

- C 6 "

o &" .¢-,

C 2 '

8

0 m , . , . - , . , ,

4 6 8 10 12

Total Solids (%)

Fig. 8. Effect of total solids concentration on the consistency coefficient K.

show that K can be expressed as an exponential function of the total solids.

Temperature and total solids combined effect A single equation relating the consistency coefficient, K, to both temperature and total solids concentration was established using linear multiple regression analysis in the 'STATISTIX' program. Equation (10) shows that K can be expressed as an exponential function of the total solids concentration and the reciprocal absolute temperature of the manure.

ln(K)=20.86+4830(1/T)+O'58319(TS) (9)

where R 2 = 0-99 and overall F--- 1764, D F = 38, K in Pa.s", T in Kelvin and TS in percent, or

K = [8"722 exp(4830(1 / T ) + 0.583 19( TS))] 10- ,,,

( l O )

Equation (11) relating the flow behavior index n to both temperature and total solids concentrations was also established. It shows that n can be expressed as a linear function of the total solids concentration and absolute temperature.

n = 0-689 4 + 0.004 683 1 ( T - 273)

- 0"042 813(TS) (11)

where R~=0.96 and overall F = 4 2 1 , D F = 3 8 , T in Kelvin and TS in percent.

The above equations can be used to compute the consistency coefficients and behavior indexes of any temperature and total solids concentration within the range of the experimental data. Figure 9 illustrates some examples of the relationship between the apparent viscosity and the shear rate. Figure 9 shows, as was stated in the literature (Chen, 1986), that the apparent viscosity decreases as the shear rate increases for a pseudoplastic type of fluid.

CONCLUSIONS

In the range of 2.5-12%TS and temperatures between 20 and 60°C, Moroccan dairy cattle manure behaved as a pseudoplastic fluid. Under these conditions, the consistency coefficient and the behavior index can be predicted by eqns ( 11 ) and (12), respectively. It was observed that n increased as the temperature increased, while K decreased as the temperature increased, and at a given temperature, K increased with increase in total solids concentration whereas n decreased. The lower the total solids concentration, and the higher the temperature, the more Newtonian the behavior of the cattle manure slurries.


R E F E R E N C E S

Achkari-Begdouri, A. (1989). Anaerobic digestion of dairy cattle manure autoheated by aerobic pretreatment. PhD thesis, University of Minnesota, St Paul, MN 55108, 231 pp.

APHA (1980). Standard Methods for Examination of Water and Wastewater. American Public Health Association, Inc., New York.

Arai, S., Shioya, T. & Imaizumi, S. (1976). Studies on treat- ment and utilization of animal waste by means of machin- ery. I -- Investigation of physical properties (consistency, fluidity and other characters) of dairy waste and its classi- fication. Bulletin National Grassland Research Institute, Japan, 9, 90-102.

Arai, S., Tamaki, T. & Imaizumi, S. (1981 ). Studies on treat- ment and utilization of animal waste by means of machin- ery. IV -- Physical properties of animal waste. Bulletin National Grassland Research Institute, Japan, 19, 66-75.

Barker, J. C. & Driggers, L. B. (1980). Design criteria for alternative swine waste flushing systems. In Proceedings of the 4th International Symposium on Livestock Wastes. Livestock Waste: A Renewable Resource. ASAE, St Joseph, Michigan, pp. 367-70.

Bashford, L. L., Gilbertson, C. B., Nienaber, J. A. & Tietz, D. (1977). Effects of ration roughage content on viscosity and theoretical head losses in pipe flow for beef-cattle slurry. Transactions oftheASAE, 20 (6), 1106-9.

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ture and solids concentration. Agricultural Wastes, 15, 17-33.

Chen, Y. R. & Hasimoto, A. G. (1976). Rheology properties of aerated poultry wastes slurries. Transactions of the ASAE, 19 (1), 128-33.

Hashimoto, A. G. &Chen, Y. R. (1976). Rheology of livestock waste slurries. Transactions of the ASAE, 19 (5), 930-4.

Hashimoto, A. G., Chen, Y. R., Vare, V. H. & Prior, R. L. (1980). Anaerobic fermentation of agricultural residue. In Utilization of Agricultural Wastes and Residues, ed. Michael L. Shuler. CRC Press, Boca Raton, Florida, pp. 135-96.

Heisey, D. & Nimis, G. (1985a). STATISTIX. An interactive statistical program for microcomputers. NH Analytical Software, 801 W Iowa Ave., St. Paul, MN 55117.

Heisey, D. & Nimis, G. (1985b). Users Manual for STATIS- TIX. An interactive statistical program for microcomputers. NH Analytical Software, 801 W Iowa Ave., St Paul, MN 55117.

Heldman, D. R. & Singh, R. Paul (1981). Food Process Engineering. AVI, Westport, CT.

lbarz, A. & Pagan, J. (1987). Rheology of raspberry juices. Journal of Food Engineering, 6, 269-89.

Kumar, M., Bartlett, H. D. & Mohsenin, N. N. (1972). Flow properties of animal waste slurries. Transactions of the ASAE, 15 (4), 718-22.

Smith, D. R., Greiner, T. H., Smith, R. T. & Marley, S. J. (1980). Characteristics of heat exchangers used on digest- ing beef-cattle manure. In Proceedings of the 4th Inter- national Symposium on Livestock Wastes. Livestock Waste: A Renewable Resource. ASAE, St Joseph, Michigan, pp. 101-4.

White, F. M. (1979). Fluid Mechanics. International Student Edition. McGraw-Hill-Kugoakuska, Ltd, Tokyo.

rheological properties of moroccan dairy cattle manure

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