Rheological measurements on artifical muds

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"tj~ ~~fT.~'$.r

T

U

Delft

DelftUniversity of Technology

Department of Civil Engineering

Hydraulicand Geotechnical Engineering Division Hydromechanics Section

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Rheological measurements on

artiflcial muds

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P.J. de Wit report no. 9-92

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November 1992

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H

y

d rom

e

chanies Section

Hydraulic and Geotechnical Engineering Division

Department of Civil Engineering

Delft University of Technology

Delft, The Netherlands

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Abstract

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The rheological behaviour of three artificial muds was determined using a rotational viscometer. First some characteristics of the viscometer used were rneasured. For want of an appropriate calibration tluid, the viscosity of demineralized water was determined. The result agreed very well with what

could be expected from literature.

Then the rheological behaviour under simple shear tlow was determined of suspensions of three kinds of artificial muds, namely Bali, China and Westwalder clay. All of these clays are commercially available. It was found that these clays had a shear-thinning viscoplastic behaviour. The intluence of NaCI, salinity

5%0,

on the behaviour was also studied. The measurements showed that the yield stress was maximal for suspensions of Westwalder cJay (suspended sediment concentrations ~ 200kg-m"). BaU clay showed the lowest yield stress and the yield stress of China cJay was intermediate. Any intluence of the addition of NaCI was not detectable.

However, the behaviour ofhighly concentrated suspensions of China clay with concentrations ranging from 300 to600kg-m? was clearly affected by the addition of salt. When salt was added, an increase in the yield and the Bingham stresses was observed.

Finally, sorneoscillatory shear tlow measurements were made in order to determine some viscoelastic properties of saline China clay suspensions. The frequency selected in the experiments was 0.66 Hz and the strain ranged from 1 to 7. The results showed a decrease in the amplitude of the complex modulus of elasticity and the phase shift for increasing strain.

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Abstract 1.

Introduetion

2. Constitutive models used for mud . . . .. 1

2.1 Newtonian fluid model 2 2.2 Elastic model 2 2.3 Viscoelastic models 3 2.3.1 Periodic response of a linearly viscoelastic material to periodic loading 4 2.4 Viscoplastic models 6 3. Experimental procedure . . . .. 8

3.1 The Haake viscometer . . . .. 8

3.2 Sensor systems used . . . .. 11

3.2.1 Sensor system DA 45 11 3.2.2 Sensor system PK 45 . . . .. 13

3 .

2.3 Sensor system

Q

30

14

3.3 Preparation of the sample. . . .. 14

4. Results . . . .. 16

4.1 The viscosity of demineralized water. . . 16

4.2 The intluence of the sensor type on a measurement . . . 17

4.3 Flow curves of Bali and Westwalder clay suspensions at low sediment concentrations 18 4.4 Flow curves for highly concentrated suspensions of China Clay 21 4.5 Oscillatory measurements on saline China Clay suspensions 22 5. Conclusions 26 6. Acknowledgements... 26

7. List of symbols . . . 27

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1. Introduction

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During the last decades an interest has arisen for the complex behaviour of cohesive sediments. The

environment, for instance, is increasingly suffering from these sediments; they adsorb large amounts

of pesticides and other dissolved pollutants, on deposition resulting in a heavily polluted bottom layer.

Furthermore, large amounts of mud may be transported by waves and/or current into a harbour or

navigation channel, wh ere it may settle due to a lack of current. As a consequence the navigation may

be hindered by the accumulated mud. The costs of maintenance dredging and in particular the costs

of the disposal and the c1eaning of the polluted mud are very high.

Until about thirty years ago hardly any knowledge was present on the behaviour of mud.

Therefore many research projects have been started to study the behaviour of mud. Among other

things, the influence of waves or/and current on the eros ion of a muddy bed has been studied by

many researchers. The rheological behaviour of the sediment was found to be one of the most

important aspects. The term "rheology" is coined from the Greek words oe» and ÀO'Yoç meaning flow

and science, respectively. The science of rheology studies the deformation and the flow of matter

induced by an external loading. Within this science the reaction of almost every material to applied

loads can be characterized by the so-called constitutive equations, since these equations describe the

macroscopie mechanical behaviour of the material resulting from the intern al constitution of the

materia!. In literature various constitutive equations have been used to characterize mud. Also several

laboratory-based rheometrical techniques have been used to determine rheological properties of mud,

see for instanee James et al. (1988) and Williams & Williams (1989).

This report deals with the rheological properties of mud. In section 2 an overview will be given

of the constitutive equations used to characterize mud. In the framework of the Netherlands Centre

for Coastal Research a Haake viscometer was made available by Delft Hydraulics. Rheological

propertjes of the mud used in the experiments of De Wit (1992) and two other artificial muds were

determined with this instrument. An outline of the apparatus and the experimental procedure used are

given in section 3. The results of the experiments are presented and discussed in section 4. Finally,

some conclusions will be drawn in section 5.

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2. Constitutive models used for mud

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The rheological behaviour of mud is very complex and it is not completely understood at present. As

a consequence several rheological models have been proposed to approximate physical observations

of the mechanical behaviour of mud. Low-concentrated, water-based suspensions of mud can be

regarded as Newtonian fluids with viscosities larger than the viscosity of water. If the suspended

sediment concentration is increased, a non-Newtonian behaviour may be observed such as viscoelastic

or viscoplastic behaviour. At very high concentrations the mud may even show elastic properties. In

the following sections several of the current rheological models will be discussed. Collyer & Clegg

(1988) and Ferguson & Kernblowski (1991), tor instance, give more information about rheology in

genera!. Every model can be constructed from the mechanies of a continuous medium. For further

inforrnation see Malvern (1969), tor instance.

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2.1 Newtonian f1uid model

The constitutive equation for a Newtonian or viscous fluid relates the rate of deformation D to the applied stress and is generalized in the form

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T'ij = 2p.D'ij (2.1.1)

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where - 1

[OU

j

OU

j] D..- - _ +_ IJ 2

ëx

.

àx

.

} I (2.1.2)

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Here. T and D are the stress - and rate of deformation tensors, respectively. i,j, are indices,

u

j is the velocity in the

x

j direction and p. the dynamic viscosity. The prime indicates the

deviatoric part of the tensor. Under the assumption of incompressibility it is found that D~ = Dij .

For a stationary flow of an ideal Newtonian fluid past a flat boundary equation 2.1.1 can be simplified to the form T = P. dv / dy =

Wy

where T is the shear stress, y is the coordinate perpendicular to the direction of the flow at speedv(y) and

'Y

is the shear rate. The behaviour of a Newtonian fluid is shown in figure 2.4.1. The slope of this line is the viscosity.

Mud has often been modelled as a Newtonian fluid, especially in models simulating the wave damping over a muddy bed; e.g. Dalrymple & Liu (1978) and Jiang& Zhao (1989). However, it is found that the viscosity of mud depends on the shear rate and the oscillatory frequency (Maa, 1986; Toorman, 1992) which is inconsistent with the Newtonian tluid model.

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2.2 Elastic model

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equation for an incompressible material is represented byFor an isotropie and homogeneous linear elastic body, a so-called Hookean solid, the constitutive

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Tl. = 2GEl. I) IJ (2.2.1) where

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E..=

.!.

[oçj

+

Oçj]

I) 2 àx. àx. ) I (2.2.2)

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Here E is the strain tensor, G the shear modulus and çj the displacement in the

x

j direction.

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Equation 2.2.1 can be written tor pure shear flow as

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T = G"( (2.2.3)

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where "( is the imposed strain.

This model was used for muddy seabeds under wave motions by Mallard and Dalrymple (1978), for instance. They used this model to study the stress and displacement of a soil bed. They predicted that the wave length of a wave travelling over a soft muddy bottom, i.e. a smaller shear modulus, would be smaller than the wave length of wave travelling over a more rigid bottom. However, the flume experiments of Yamamoto et al. (1986) showed that the wave length of waves propagating over soft muds is greater than the value that would be expected assuming a rigid bed. Another serious drawback of this model is that no wave damping occurs, because no dissipating terms are involved in this model. However, significant wave damping was observed in many coastal regions where the bottom consists of soft mud and in various laboratory experiments described by Sakakiyama and Bijker (1989) and De Wit and Kranenburg (1992). Therefore, the conclusion can be drawn that a purely elastic model is not suitable to model a soft mud (Chou, 1989).

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2.3

Viscoelastic models

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Insectioris 2.1 and 2.2 it was pointed out that simple elastic or Newtonian models alone are not weIl suitable to model mud. A combination of elastic and viscous properties seems more favourable to model mud. It is obvious that several researchers, e.g. MacPherson (1980) and Hsiao &

Shemdin (1980), tried to use a viscoelastic model to describe the behaviour of mud.

Several viscoelastic models are described in literature (Kuiken and Merk, 1978) and they generally describe behaviour between the extremes of a viscous fluid and an elastic solid. Two of the most basic models will be described in this section, namely the Kelvin - or Voigt model and the Maxwell model. These models are based on the analogy with aspring-dashpot system and are described as follows:

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/ •I Tij = 2GE/ij + 2JLE ij É' =

_I_t

l

+ _I_Tl.

'

/

2 G

IJ 2JL IJ

For a simple shear with shear stress T andstrain

v

.

these equations can be expressed in the form:

Maxwell model: (2.3.2)

Kelvin model: (2.3.1)

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Kelvin model: T=GY+JL'Y (2.3.3)

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Maxwell model: T =

!J.

'Y

-

.!!:..t

G (2.3.4)

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The Kelvin model is represented in tigure 2.3.1 as a parallel combination of a spring and a dashpot. In this configuration the strain is equal for both elements. However, the total stress is the sum of the stresses of the spring and the dashpot. The stress depends on the strain according to equation 2.3.3, therefore this model illustrates a viscoelastic solid-Iike behaviour. At a constant strain equation 2.3.3 reduces to T

=

Gv, i.e. to the relationship of a Hookean solid.

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The Maxwell model is aserial combination of a spring and a dashpot and consequently the elements undergo the same shear stress, see figure 2.3.1. However, the total strain is a summation of the strains of both elements. Equation 2.3.4 shows that the stress depends on the rate of strain. Consequently, the Maxwell model describes the behaviour of a viscoelastic fluid. At constant stress equation 2.3.4 reduces to the relationship for a Newtonian fluid T=

Wy.

Using these basic mechanical elements it is very easy to built more complex modeis, such as the multi element generalized Kelvin-Voigt or Maxwell model or the four element Burgers model. However, none of these models can describe the complete behaviour of a viscoelastic medium. For reasons of brevity, these models will not be described in this report. For more information about these models see Kuiken and Merk (1978), for instance.

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G

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a

b

Figure 2.3.1

Mechanical representation of the Maxwell model (a) and the Kelvin

model (b).

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Three rheological tests are commonly used to determine the response of a viscoelastic material, namely creep tests, stress relaxation tests or dynamic response to loads varying sinusoidally in time. The dynamic test will be described in the next section.

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2.3.1 Periodic response of a Iinearly viscoelasticmaterial to periodic loading

Cohesive sediments may be subjected to oscillatory shear stresses by water waves, in particular during storm conditions. In order to model the behaviour of mud under these conditions, it is necessary to use a rheological model that is calibrated under almost the same conditions. Although, the rheological properties of mud are usually determined under steady rotational shearing, therefore it is favourable to determine the rheological properties under oscillatory shearing as weil.

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Consider a linearly viscoelastic material exposed to a periodic oscillation of the strain )'(t) with strain amplitude )'0 and angular frequency w according to the formula:

)' = )'0sinwt (2.3.5)

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Under these conditions the response will be an oscillating stress at the same frequency, but out of phase:

'T = 'Tosin(wt +ó) (2.3.6)

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where 'Tois the stress amplitude and ó is the phase shift. The phase shift is equaJ to zero in the case of an ideaJ elastic materiaJ, for which 'T

=

G)'. The response of an ideaJ viscous material, for

which T

=

J.L

'Y,

will be 7r /2 out of phase with the imposed strain.

Equations 2.3.5 and 2.3.6 can also be represented in a complex way as,

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(2.3.7)

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T

=

T e-i(wI+6) o (2.3.8)

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Introducing the complex modulus of elasticity or often caJled the complex shear modulus G· as

G·

T

=

,G., e-i6

=

G1 - iG"

)'

(2.3.9)

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where G

1 isthe storage modulus and Gil is the loss modulus. Consequent!y,

G1 =

IGï

cosê

(2.3.10)

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Gil =

IGï

sinê

(2.3.11)

and

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Gil =

tanê

.

G

1 (2.3.12)

The ratio Gil / G1 is caJled the loss tangent (MaJvern, 1969).

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Calculating the storage modulus and the loss modulus for the Voigt model, it is found(Chou, 1989)

th at G' = G (2.3.13)

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Gil = JlW (2.3.14)

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and for the Maxwell model (Ferguson and Kernblowski. 1991):

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G' = W2Jl2G G2 +W2Jl2 Gil

=

WJlG2 G2 +W2Jl2 (2.3.15) (2.3.16)

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Equations 2.3.13 and 2.3.14 show that tor the Voigt model the storage modulus G' is independent

of the frequency and the loss modulus Gil is proportional to the frequency. Equations 2.3.15 and

2.3.16 show that for the Maxwell model both the loss and storage modulus depend on the frequency.

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2.4 Viscoplastic models

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The viscoplastic behaviour of mud has been simulated by several authors

.

In this section some of

the proposed viscoplastic models will be discussed.

The so-called Bingham model is the most commonly used model to describe the properties of mud;

see Migniot (1968) and Mei & Liu (1987), for instance. The constitutive equation of this model can

be expressed as

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(2.4.1)

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where TB is the Bingham yield stress and Jlp is the so-called plastic or Bingham viscosity, see also

figure 2.4.1.

In rheology the so-called Herschel-Bulkley model (Ferguson and Kemblowski, 1991) is often used

to describe the mechanical behaviour of aviscoplastic material. This model in fact is a generalization

of the Bingham model:

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T

=

T_y +

K-y"

(2.4.2)

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where K and n are material constants and Ty is the (apparent) yield stress. This model can be used

both for pseudoplastic or shear-thinning materials (n

<

1)and dilatant or shear-thickening materials

(n

>

1). The behaviours of these shear-thinning and shear-thickening materials are also plotted in

figure 2.4.1.

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Figure 2.4

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'"'"

o

..

...

'"

..

~ o ..c: en Newtonian Bingham plastic Shear rate

Example

s

offlow

c

urves ofmaterials witn different rheologi

c

al b

e

haviour.

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_3.

_{Experimental procedure}

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Rheological properties of three artificial muds were determined under both steady rotational shearing and oscillatory motion using a Haake Viscometer, made available by Delft Hydraulies. A detailed description of the Haake viscometer will be given in section 3.1. In section 3.2 some of the sensor systems used will be described. The composition and the preparation of the artificial muds used will be given in section 3.3.

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3.1 The Haake viscometer

The Haake viscometer is a rotational viscometer and it comprises two separate units namely, the Rotovisco RV 100, the Measuring System CV 100.

1 9 2

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3

4

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Figure 3.1.1 Sketch of {he HC111ke Rotovisco RV ]()O.

(For an explanation

of

(he numbers see text)

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The material is sheared, for instanee in the gap between to plates. The lower plate rotates at aThe Rotovisco RV 100 is the controller uf the CV 100, where the actual measurement is made. constant rate and the resulting torque on the axis of the upper plate is measured. An outline of the Measuring System CV 100 is shown in figure 3.1.1. The measuring head 1, which contains the torque piek-up system and the preamplifier. is rnoveable in the vertical direction. An air bearing 3 is fixed to the measuring head. Prior to a rneasurernent the head and the air bearing are placed in the most upward position by pushing button 5 on the front panel of the device. The shaft of the inner sensor element is secured to the measuring head by a knurled screw 4. The outer sensor element is fixed in

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the temperature controlled beaker housing 8. Several sensor systems are available. A description of the sensor systems used will be given in section 3.2. The temperature is controlled by circulating water of a constant temperature through the beaker housing. The water temperature is controlled by an external thermostatic heat controller. When a sample has been brought into the outer sensor

element, the measuring head is lowered by pushing button 6. The measuring head stops automatically when the preselected distance between the inner and outer sensor elements is reached. This distance depends on the sensor system used and it is set with a micrometer knob 2 on top of the device prior to measurement in the following way. When the preferred sensor system has been instalied and no

sample is present inside the sensor, the micrometer knob is turned in clockwise direction, looking from above, as far as possible (some 15 revolutions). Then the head is lowered. The micrometer knob is carefully turned in anticlockwise direction until the inner sensor element touches the outer element,

which is visible at the recorder pen of the Rotovisco RV 100. Then the knob isturned in clockwise direction until the sensor dependent distance is set, an interval of 10 scale divisions corresponds with 0.5 mm height adjustment. A full description of the height adjustment is given in the instruction manual.

To proteet the sensor system from air drafts and dust a perspex air shield 9 is placed between the measuring head and the beaker housing. A warning control lamp 7 is mounted at the front panel of the device. This lamp flashes if the pressure of the air supply for the air bearing is less than 1 bar.

In that case the program is locked automatically in order to prevent permanent damage to the very sensitive bearing and torque piek-up system. At Delft Hydraulics the air supply is withdrawn from

a ring main.

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The Rotovisco RV 100 is the operating control unit of the measuring system CV 100. It also contains a simple recorder. The panel of the Rotovisco RV 100 can be divided into four sections;the

measuring operations - (A)

,

the recorder operations -

(B),

the programrner operations - (C) and the

recorder section (0), see figure 3.1.2. The function of the most important buttons and switches on the panel will be described next.

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Figure 3.1.2

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A

---__

"\

i

_.

»> t~% »> 2 [1]4 ₀ l...--

r-1B3

₌₌

---ltl El

lèw

.r:

2 [UJ]% • D r--~3 Dl-3 t~

.

_~

-

»>: 4 S 6 7 8 9 10

c

D B

Top view of the Haake Rotovisco RV 100.

(For an explanation of the numbers see text.)

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The mains switch Al is mounted in the measuring operations section A, see figure 3.1.2. Using

this switch will start or stop the RV 100.The maximum shear stress in % is set by digital switch A2.

The maximum value is 100% and refers to the maximum measurable torque. The zero-potentiometer A3 is used to place the recorder pen in the zero position before a measurement is made.

Several push buttons are placed in the recorder operations section

B.

These buttons control the

functions of the integrated recorder. When push button

BI

is pressed, the chart paper is held in place

electrostatically and the recorder is ready for a measurement. If the button is released the recorder

is in stand-by mode; the viscometer is fully active but the recorder is switched off. The operation

mode of the recorder is set by push buttons B2 and B3. If push button B2 is pressed the shear stress

will be recorded as a function of the shear rate, i.e. a flow curve is measured. A record of the shear

stress versus time will be made if push button B3 is pressed. If both buttons are pressed simultaneously the system is switched to the oscillation mode.

For a proper operation in oscillation mode the following settings have to be checked: the damping A4 must be equal to zero, just as the hold time ti and switch C3 must be set to 'X 1'. For normal dynamie measurements, switch C2 may be set to '000'. The duration of a measurement is set with

switch C5. On the front panel of the Haake RV 100, not shown in figure 3.1.2, two switches are

instalied for adjusting the frequency of oscillation (ranging from 0.01 to 9.99 Hz) and the amplitude (ranging from 1° to 39°). Furthermore, the analogue signals during an experiment are available by

a 5 pins socket, which is also installed on the front panel.

Push button Cl, in the programmer operations section C, starts a pre-selected program. The digital switch C2 presets the maximum shear rate in % of the maximum shear rate that may be generated

by the used sensor system. The slide switch C3 can be used to reduce the shear rate by a factor 10.

However, this applies when only button B3 is depressed. The digital switches B4, B5 and B6 select

the hold period ti at shear rate 0=0, the program time ~ and the hold period 1, at the selected

maximum shear rate, respectively. The units of time of these switches are hours or minutes,

depending on push button B7. The push buttons B8, B9 and BlO can be used to run a program with

an automatic reversal, with an automatic reset to zero speed once the hold period t3has ended and

with an unlimited repetitions of the program, respectively. The recorder section 0, which is also shown in figure 3.1.2, contains a simple pen recorder. For a more detailed description of the Haake

viscometer see the instruction manual or Brownsey (1988).

Ouring an experiment the data were recorded using the pen recorder. Additionally a personal

computer was used to store the available analogue signals.

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3.2 Sensor systems used

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Several

s

en

s

or systems were available at Delft Hydraulics

.

Each sensor system is designed to

pr

o

vide a specific range of shear rate, shear stress and viscosity. To determine the actual

s

hear rate

and

s

hear stress values from the recorded curves

,

the calculation factors A and M of the sensor

system applied have to be u

s

ed. A and M are the so-called shear

s

tress and shear rate factors

,

respectively

.

The

s

hear rate and the shear stress are calculated in the following way.

shear rate:

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s

hear

s

tress

:

T

=

A· %T' ST [Pa]

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where

So

and

ST

are the scale values taken from the recorded flow curve. %D and

%T

are the preset

s

hear rate and

s

hear stress values

.

The strain during an oscillatory measurement is calculated by

,

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s

train

:

"y

=

-'M'r,&'1

12

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where

Some chara

cp

is the value set at the front panel of the Haake RV 100

c

teristics of the sensor systems used to determine rheological properties

.

o

f mud will be

described next.

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3.2.1 Sensor system DA 45

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Figure 3.2.1 Outline of the sensor system DA 45.

1 An outline of the sensor system DA 45 is shown in figure 3.2.1

.

The centre cylinder is placed in

the beaker. Two annular gaps are formed when the inner cylinder is placed into the beaker. In this

way the sensor is a combination of a Couette (outer gap) and a Searle (inner gap) sensor system

.

Non-I

aminar, instabie flow patterns may be generated in the gap for high values of the rotational speed

when low viscous samples are tested with this system. The transition from laminar to turbulent flow

is characterize by a sudden increase in the viscosity when measuring the flow curve of a substance

.

A

cco

rding t

o

the manufacturer

,

the small end face error has been determined following the German

DIN 53 018 and the shear stress calculation value has been adjusted accordingly. Some properties of

this sensor system are listed in table 3.2.1.

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Figur

e

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2.2 I

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Table 3.2.1 Specifications of the sensor system DA 45.

INNER CYLINDER diameter D2 38.0

rnrn

diameter D3 41.74

mm

length L 39.4

mm

BEAKER diameter DI 35.25

mm

diameter D4 45.0

rnrn

h 1.6

rnrn

sample volume 16 cm'

CALCULA TION FACTORS

A 0.051 Pa/scale div.

M 3 s-I/scale div.

RANGE

shear rate 0.5 - 500 S-I

shear stress 10-2- 8 Pa

viscosity 10-2- 104ml'a-s

h

Outfine of the sensor system PK 45.

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3.2.2 Sensor system PK 4S

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Sensor system PK 45 is a plate-cone sensor (figure 3.2.2) and it requires only small sample

volumes. The cone angle is 40• Using this system minimizes the effect of preshear when a sample is

placed in the sensor system, because the volume elements are just slightly squeezed sideways when

the cone is lowered. Prior to a measurement the distance h between the cone and the plate has to be

adjusted very carefully. The cone has been truncated to eliminate a direct frictional torque which

would result from a direct contact of the cone and the plate. For further specifications of the sensor

system see table 3.2.2.

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Table 3.2.2

Spectfications of the sensor system PK 45

.

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CONE diameter D2 41.7 mm diameter 03 5.0 mm cone angle a 6.98.10-2 rad PLATE diameter DI 45 mrn h 0.175 mrn SAMPLE VOLUME 1.4

cm

"

CALCULATION FACTORS A 0.515 Pa/scale div.

M 3 s-I/scale div.

RANGE

shear rate

0.5 -

500

S-I shear stress 10-1- 80 Pa viscosity 10-2- 105mf'a-s

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g

ur

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3.2.3 Outline of the sensorsystem Q30.

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_3.2.3 _{Sensor system Q 30}

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The plate-plate sensor

Q

30 is shown in figure 3.2.3. The distance h between the two plates may

be varied depending on the preferred operating range. The shear rate range is adjusted by changing

the distance h,because the shear rate is inversely proportional to the distance between the plates:

wR

'Y -

h

(3.2.1)

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1

where w is the angular frequency and R is the radius of the plates. More specifications of this senor

are listed in table 3.2.3.

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Table 3.2.3

Specifications of the sensor system Q 30

.

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UPPER PLATE diameter O2 27.83 mm LOWER PLATE diameter DI 45 mm h variabIe

SAMPLE VOLUME variabIe

CALCULATION FACTORS A 2.3 Pa/scale div. M 2.91h s+/scale div. RANGE

(h

=

1 mm)

shear rate 0.5 - 500 S-I shear stress 0.5 - 500 Pa viscosity

1 - Hf mêa-s

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3.3 Preparation of the sample

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The properties of three kinds of clay were determined at several suspended sediment

concentrations. These clays were purchased from Johnson Matthey, Colour and Paint Division B.V.,

Maastricht, the Netherlands and are provided as a dry powder. Some properties of these clays, as

supplied by the manufacturer, are listed in table 3.3.1.

The samples were prepared in the following way. The maximum suspended sediment concentration

(about 600 kg-m") was prepared in a beaker. The water used for the suspension was demineralized.

In some tests NaCI was added to the water, in that case the salinity was 5%0. The suspension was

mechanically mixed for at least half an hour, then it was ultrasonically mixed for about 10 minutes

and finally it was mechanically mixed again for about 15 minutes. A sample with a certain volume

was taken from the suspension in the beaker by a pipet and was then put into the sensor system of

the Haake viscometer and it was allowed to adjust to the temperature ofthe beaker (20°C). The initial

1

14

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(19)

1

Table 3.3.1 Properties of the artificial clays used.

1

Product code RM.225 RM.239 RM.I44

Description Kaolin GTY Powder "Westwalder Clay" "BalI Clay"

"China Clay" Chemical Analysis (percent by weight) Si02 46.9 57.4 54.4 AI2O) 37.7 26.9 30.3 Ti02 0.1 2.2 1.8 Fe203 0.9 1.9 1.2 K20 1.6 1.5 2.5 CaO 0.0 0.4 0.3 MgO 0.1 0.2 0.5 N~O 0.2 0.1 0.4 Loss on ignition 12.5 9.4 8.1

I

suspension in the beaker was diluted until a concentration of 500 kgrn? was madewas not taken before this suspension had been mixed for at least half an hour. In this way several. The next sample suspensions with different concentrations were prepared, from which samples were taken which were analyzed.

I

1

1 I

I

1

1 I

.

15

(20)

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I

4. Results

I

Several types of experiments were carried out with the Haake viscometer. As the writer had hardly

anyexperience with this viscometer, the first experiment made was acalibration of the instrument. Demineralized water was used since a proper calibration tluid was not available. The results of this test are presented in section 4.1. Several sensor types were available at Delft Hydraulics. The operation ranges for several sensor types were almost identical. To check the intluence of a sensor type on the resultsof an experiment, two sensor types were used on several low concentrated China Clay suspensions. In section 4.2 the results of these measurements will be presented. In section 4.3 the tlow curves of concentrated mud suspensions are shown. The intluence of the addition of NaCI

on the tlow curves will also be discussed in this section. Also high concentrated mud suspensions were examined, again incombination with the addition of salt (seesection 4.4). Finally, the results of the oscillatory experiments are presented in section 4.5. Only China Clay suspensions were

examined in these tests and three sensor types were used.

I

4.1 The viscosityof demineralized water

I

Prior to a rheological measurement the instrument and the sensor types used should becalibrated.

Several very expensive calibration tluids are commercially available. Due to a lack of such a tluid,

demineralized water was used as the calibration fluid. As the viscosity of this calibration fluid isquite low tor the purpose, only sensor type DA 45 was "calibrated".

The sensor type was properly installedin the Haake CV 100. The temperature ofthe recirculating

water in the beaker housing was 20

.

SoC

.

A sample of demineralized water was put into the beaker

and the inner cylinder was lowered. A possible sample surplus was removed and the test was started as soon as the sample temperature had adjusted to the beaker temperature. The measured tlow curve isshown in figure 4.1.1.

Regression analysis shows that the measured viscosity is equal to 1.030

±

0.007 mPa·s. The absolute viscosity of water at 20°C for calibration purposes is 1.002 ml'a-s according to Weast

I

.--. 0.08 0.07 ti:! p.. ... 0.06 0.05 til til Q.) _0.04 M

-

til 0.03 M ti:! Q.) 0.02

..c:

CZl 0.01

I

10 20

Shear rate

30 40 50

[S

60

-

l]

70 80

Figure

4 .

1 .

1. Measuredflow curvefor demineralized water

(20.5°e).

I

16

(21)

I

₍₁₉₈₈₎

_.

_{Consequently, the result corresponds very well with what may be expected, although the}

measurement was made only just within the operating ranges of the sensor type. The stepwise

variation of the flow curve is a consequence of the operation of this sensor in the lower operating

range.

In this experiment and also in the experiments discussed next, the shear rate continuously

increased in three minutes from zero to a maximum preselected value (about 150

s''),

When the

maximum shear rate was reached, the shear rate decreased to zero in the same time interval

,

see

figure 4

.

1.2. This time interval was chosen, because it was found (Various authors, 1992) that the

.

acceleration time does not affect the rheological quantities when a time interval of four minutes or

less is chosen and a maximum shear rate of 150 s

:

is reached.

I

max

s

_os

_..

..

os U ..d V) / 0 0 2 3 4 S 6 Tune [minutes]

I

Figure 4.1.2 The shear rate as a function of the time.

I

4.2 The influence of the sensor type on a measurement

I

Two sensor types, PK 45 and DA 45, were used to measure flow curves of two suspensions of

China Clay and saline water. The saline water was prepared by dissolving

5%0

NaCI in demineralized

water. The PK 45 sensor requires only a very smalI sample volume, which may be an advantage in

some situations

.

However, in general the PK 45 sensor is not easy to use. First of all this sensor

requires a very careful adjustment of the distance between the plate and the cone. Furthermore, only

small sample volumes are needed, which makes it more difficult to put the exact sample volume on

the plate. When the cone is lowered

,

the sample must completely fill the gap and, ideally, form a

convex profile at the free surface. The preparation of a sample for this sensor type requires a lot of

experience

.

Sensor type DA 45 is easier to use, because it requires a larger sample volume and the

influence

of an inaccurate sample volume on the results of an experiment is only moderate. However,

when using this sensor on suspensions attention should be paid to the settling behaviour of the

suspension. An initially well-mixed suspension, for instance, may start to settle before the

measurement has started, resulting in an erroneous interpretation of the measurement.

The suspended sediment concentrations of the suspension were 50 and lOOkg-m". Due to a lack

of time the accuracy of suspended sediment concentrations in all of these tests was about

±

7

%.

The

I

17

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(22)

I

1.4 ,... ~ _1.2 P-4

...

1 ~ _0.8 ~ ~

....

...

0.6 ~

....

~ ~ _0.4 ..r::: Cl) 0.2 0 0 50 kg·m·'

I

₅₀ ₁₀₀ ₁₅₀

I

_Figur_e _4.2.1

Shear rate

[S·l]

Flow curves of two China

Clay

suspensions measured

witn two sensor types (PK

45

and DA 45)

.

I

results of these measurements are shown in figure 4.2.1.

The measured yieldstresses measured with both sensor types are of thesame order of magnitude.The

yield stress is defined here as the residual stress after the application of shear; the stress value

measured when the shear rate during the decelerating flow has decreased to 0

s'

.

However, in both

measurements the value of the plastic viscosity measured with the PK 45 sensor is about 15% greater than the plastic viscosity measured with the DA 45 sensor. Further research is necessary to explain this difference in the measured plastic viscosity.

In figure 4.2.1 and following figures most of the flow curves have been truncated beyond a certain

shear rate.

I

4.3 Flow curves of Bali and Westwalder clay suspensions at low sediment concentrations

I

The rheological behaviours at low concentrations(:s; 200kg-m") of the Westwalder and Bali clays

were determined with the DA 45 sensor under simple shear flow. Measurements were made on

suspensions with and without dissolved NaCI. If salt was added, the salinity was 5%0.

Due to the addition of salt, the clay particles may flocculate (e.g., Van Olphen 1977). The

rheological behaviour of a suspension with a certain concentration in a flocculated state differs from

that of the same suspension in a dispersed state. It was tried by adding small quantities of salt to

measure any kindof change in the rheological behaviour of a clay suspension, resulting from achange

in thestateofflocculation. The influence ut" dissolved NaCI on the Newtonian viscosity of water was

not detectable.

The tlow curves obtained from the rneasurements on the non-saline suspensions of BalI and

Westwalder clays are shown in figure 4.3.1 and figure 4.3.2, respectively.

The flow curves for saline suspensionsof Bali and Westwalder clays are presented in the figures

4.3.4 and 4.3.5, respectively.

I

- 18

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I

(23)

I

3 ,..., 200kg'm-3 Cl:! ~ 2.5

...

I

2 ril ril ~ _1.5

....

I

....

ril

....

_134kg'm-₃ Cl:! ~ ..r:=

I

Cf.) 0.5 100kg'm-3 0

I

0

Shear ra te

50 100

[S-l]

150

I

Fi

g

ur

e

4.3.1

Fl

o

w

c

urv

es

f

o

r

s

uspensions of Bali clay

.

I

2.5 ,..., Cl:! _150kg-m? ~ 2

I

...

<Il 1.5 <Il

I

_....

~

....

100kg·m·3 <Il 1

;

~

I

..r:=Cf.) ₀_.₅ 50 kg-m?

I

50 100 150

Shear rate

[s']

I

Fi

g

ur

e

4.3.2

Flow

c

urves for Westwalder clay

.

I

19

-I

I

(24)

The measurements show that the addition of 5%0

NaCI has no significant effect on the rheological

behaviour of low concentrated suspensions of Bali and Westwalder clay

.

Furthermore,

the yield

stresses of suspensions of Westwalder clay are higher than the yield stresses of Ball clay suspensions

or China clay suspensions,

at the same concentration. For example, the yield stress of a Westwalder

clay suspension with a concentration of 100kg-m?

is

about 0.35 Pa, see figure 4.3.2.

Figure 4.3.1

shows that a BalI clay suspension with the same concentration has a yield stress of about 0.15 Pa. The

yield stress of a China clay suspension with a concentration of 100 kg-m?

is about 0.2 Pa, see figure

4 .

2.1. I

1

1 Figure 4.3.3

1 I

I

1 Figure 4.3.4

1 I

I

1

1 I

I

.

3 ,..., ~ 2.5 ~

...

2 lil lil 11.) 1.5

...

lil

...

~ 1 11.) .d

en

0.5 50 kg·m·3 0 0 50 100 150

Shear rate

[S-l]

Flow

curvesjor suspensions oj Bali clay.

(salinity

5%0) 2.5 ,..., ~ ~ 2 Herschel-Bulkley approximation lil 1.5 lil 11.)

...

_lil 1

...

~ 11.) .d

en

0.5 50 kg- m-3 0'---'---'---'

o

50

Shear rate

150

Flow curvesjor Westwalder clay.

(salinuy

5%0)

(25)

20-1

1

1 I

1

1 I

.

Furthermore, these measurements show that the clay suspensions show a shear-thinning

viscoplastic behaviour under simple shear flow, which can be described by the Herschel-Bulkley

equation, see eq. 2.4.2. As an example the constants Ty' K and nare determined for a Westwalder

clay suspension (concentration: 150 kg-m", salinity: 5%0) using a least squares approximation. It was

found that Ty = 0.67 Pa,

K

= 0.12 Pa·sO.45and

n

= 0.45. The Herschel-Bulkley approximation

calculated using these constants is also shown in figure 4.3.4. The agreement with the measurement is very good.

4.4 Flow curves for highly concentrated sus pensions of China Clay

Several China clay suspensions with sediment concentrations ranging from 100 to 600 kg-m? were

examined using the Q 30 sensor. The influence of salt on these concentrations was also determined.

The flow curves for the non-saline suspensions and the saline suspensions (salinity 5 %0) are shown

in figures 4.4.1 and 4.4.2, respectively.

Comparing these figures shows that the yield stress increased when salt was added to the China

clay suspensions. The Bingham yield stress, defined as the intersection of the line with slope/Lp

through the almost linear portion of the flow curve and the vertical axis, showed a significant increase

when salt was added. However, the plastic viscosity of the suspensions was not influenced by the

additionof salt. 25 600kg·m·3

~-500 kg-m? ~ 400 kg·m·' po 300kg·m·' <I'l 15 <I'l ~

...

....

<I'l 10

...

~ o ..c: ti) 5

o

20 40 60 80 100 120 Figure 4.4.1

Shear rate

[S·l]

Flow curves for suspensions of China clay

,

(26)

-I

I

25 600 kg·m·'

==

500 kg'm"

v--=-

400 kg-nr

v-300 kg'm"

I

,...,CI$

e:.

20

I

ril 15 ril u

....

Vl 10

....

CI$ u ..c: Cf) 5

I

o

20 40 60 80 100 120

Figur

e

4.4.2

Shear rate

[S·l]

Flow curves for suspensions of China clay.

(salinity

5%0)

I

4.5 Oscillatory measurements on saline China c1ay sus pensions

I

When the Haake viseometer isset to oscillation mode, a preseleeted maximum strain is foreed on the sample at a preseleeted frequeney. The oscillating frequeney of alloscillatory measurements was

set at 0.66 Hz, corresponding with the wave period used (1.5 s) in the flume experiments of De

Wit (1992)

.

Due to the viscoelastic property of a mud sample

,

the measured shear stress will be out

of phase with the strain. An example of sueh a measurement is shown in figure 4.5.1.

I

,..., 3 6 /strain

'"

2 4 ~ 2 <I>

=

<I>

ë;

<I.) 0 0

...

--

<I> Cl)

...

_·₁ ·2

'"

<I.)

-=

Cl) ·2 ·4 shear stress ·3 ·6 0 2 3 4 5 Tune [sj

I

Figure 4.5.1

An example of an oscillatory experiment made on a saline suspension

of China clay. (

c

oncentration

300

kg-m", salinuy

5%0)

I

The measurements were made with the sensors DA 45 and Q 30 and repeated with the PK 45

sensor on identical saline suspensions of China clay with concentrations ranging from 100 to 600 kg-m". In this way the influence of the sensor type on the oscillatory measurements was determined. The relation between the amplitude of the complex modulus of elasticity G· and the

strain amplitude 'Y is shown in figure 4.5.2.

I

22

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I

(27)

I

6 6 5

..

5 ~4 ~4 ... 3 ~ 3

b

-2 -2

:::::--:---_

0 0 0 2 3 4 5 6 7 0 Stram amplitude

I

2 3 4 5 6 7 Strain amplitude

I

~600 k,.ni'+soo k,.ni'+4OQ kl·m" -300 11.,,";]-200,,&.mJ~100k,..n' - 600 kl,m-3-+-soak,_m"" 400 ".-'" - 3lMl kl·m·' ...200

k,

.

"'

· l ...

IOO "1-"']

I

a) b)

Figure 4.5.2 The amplitude of complex modulus of elasticity versus the imposed strain amplitude.

a) sensor types: DA 45 & Q 30 b) sensor type: PK 45

I

The rneasured phase shiftsas a functionof the strain amplitude for both series are shown in figure 4.5.3.

I

1.5 1.5 1.4 1.4 ,..., "'0 :0-as

.=..

0:1 .!:!. 1.3 1.3 4:: ~ ~ ~

:a

~ 1.2 ~ 1.2 ~ as "

.

..0:: ..Q

""

~ 1.1 1.1

I

1~~~~~~~ --02345 h Strain amplitude 1 1~~~~~~~~~~ 023 4 5 6 Strain amplitude 7

I

... r.ookl·niJ-t- 500 kl.m·l....wokC '"I,

- 3(X)k•.""'- 200 kc·"""-- HlO kam ':

~6Ilf) k&,ni'+500 kl·ni'....400 kJ.m"

-300 kl·",··'-2Ilfl q.ni'-IOO kl·ni"

I

a) b)

I

Figure 4.5.3 The phase shift versus the strain amplitude. a) sensor types:DA 45 & Q 30

b) sensor type: PK 45

I

- 23

-I

I

(28)

I

1

Figure 4.5.2 shows that the measurements made with the various sensor types show the same

tendency. However, the measurements made with the sensors DA 45 and

Q

30 show larger values

of the complex modulus of elasticity for the same strain amplitude than the measurements made using

sensor PK 45.

I

1

104,.---,

1 I

.

_..

. .

I

1

10+-~~~~r_~~~~-~~~ 0.001 0.01 0.1 strain amplitude

The amplitude of the complex modulus of elasticity GO =

I

G·

I

versus the strain amplitude (Chou, 1989). (1

dyne-cm

?

=0.1 Pa)

Figure 4.5.4

I

1

The modulus of elasticity of a China clay suspension seems to decrease with increasing strain

amplitude. This phenomenon has also been observed by Chou (1989). Chou made oscillatory

experiments on kaolinite, the main clay mineral present in China clay. He used a Weissenberg Rheogoniometer in combination with a plate-cone sample holder. In figure 4.5.4 one of his results is shown. The sample used was a saline kaolinite suspension, salinity 35%0, with asolid concentration

by weight of 41 %. This corresponds to a concentration of about 600 kg-m", The oscillating angular

frequency used was 1.5 rad-sol which corresponds to a frequency of 0.24 Hz. For comparison, the

frequency used in these experiments was 0.66 Hz. Figure 4_5.4 shows that the amplitude of the modulus of elasticity is approximately 6 Pa for a strain amplitude of about 1, which is of the same order of magnitude as determined from the present results, although the oscillating frequencies differ signiticantly. This observation agrees with another result of Chou's work. He found that, for oscillation periods varying from 1 to 10 s, the amplitude of the modulus of elasticity is almost independent of the oscillation period.

The order of magnitude of the phase shift at a strain amplitude of 1, as shown in figure 4.5.3,

agrees with a similar measurement of Chou (1989), see figure 4.5.5. He observed that the phase shift was almost proportional to the logarithm of the strain amplitude in the range of 0.01 to approximately 0.2. For strain amplitudes in the range of 0.2 to 1, the phase shift is not proportional to the strain amplitude any more. The present results show that the phase shift tends to decrease very little with increasing strain amplitude in the range of 1 to 7. Furthermore, figure 4.5.3 shows that there is no clear relation between the suspension concentration and the phase shift.

I

1

1 I

I

1

24

-I

I

.

(29)

I

Figure 4.5.5

I

1 I

1

I. ,

-

C lil "0 ~ 1.0 '-'

.;

I

·1

.

/

.

/',

0.0 0.001 0.01 0.1 strain amplitude

The phase shift versus the strain amplitude (Chou, 1989). (Kaolinite, solid concentration 41%, salinity 35%0,

angular frequency 1.5 raa-s')

(30)

-I

I

5. Conclusions

Summarizing the following conclusions may be drawn from the results of this preliminary research

on the rheological properties of three artificial muds, namely Bali, China and Westwalder c1ay. First of all, the measurements showed that the clays used have an shear-thinning viscoplastic

behaviour under simple shear flow. Furthermore, Westwalder clay may be the most cohesive sediment, because the yield stress is largest for these suspensions, see figure 4.3.2 for instance.

Secondly, any influence oflow concentrations of NaCl, salinity 5%0, on the rheological behaviour of low concentrated suspensions of Bali and Westwalder c1ay was not detectable. However, the rheological behaviour of suspensions of China clay with concentrations ranging from 100 to 600 kg-rn ? was influenced by the salt. Due to the salinity of 5%0 the yield stress and the Bingham stress increased significantly, see figures 4.4.1 and 4.4.2.

The results of the oscillatory tests showed that the clay suspensions seem to behave Iike an viscoelastic material under oscillatory motions. However, further research is necessary to validate which viscoelastic model can be used to model the mechanical behaviour of these muds. Furthermore,

the amplitude of the complex modulus of elasticity as a function of the strain amplitude agrees very weil with the measurements made by Chou (1989). The order of magnitude of the measured phase

shift also agrees with the measurements made by Chou. However, the trend of the phase shift as a function of the strain amplitude does not correspond at all. Chou reports a phase shift that increases

almost proportionally with the strain amplitude (0.01 ~)' ~0.3). However, the present results show

anopposite trend, the phase shift tending to decrease with an increasing strain amplitude (1 ~)' ~ 7}.

Finally, a1though the Haake viscometer is not an extremely sophisticated rheological measuring device, relatively good measurements can be made with this instrument. Furthermore, this instrument has several options to make oscillatory, relaxation or steady experiments in an easy way.

Nevertheless

,

a lot of experience has to be gained before each measuring option of this device can

be used.

6. Acknowled2ements

This work was partly funded by the Commission of the European Communities, Directorate General for Science, Research and Development under MAST2 (G8 Morphodynamics research programme).

Special thanks go to Miss Manon Moot for her assistance in the experiments and to Delft Hydraulics for making available their Haake viscometer.

(31)

26-I

I

_7.

_{List of syrnbols}

I

Latin symbols

I

D_IJ

s'

rate of deformation tensor

E.. strain tensor

I

G

I) Pa shear modulus

G'

Pa storage modulus

I

Gil _Pa _{loss modulus}

G·

_Pa _co_{mplex shear modulus}

h m distance between plates

I

K

n

Pa's" material constantmaterial constant

R m radius of plate

I

t S time Tij Pa stress tensor u m-s' velocity

I

x

m direction

I

Greek symbols

I

s

'Y

rad phase shift

strain

1'0 strain amplitude

I

T Pa shear stress

TB Pa Bingham yield stress

Ty Pa apparent yield stress

I

To Pa stress amplitude

i'

s'

shear rate

I

J.Lç mPa's displacementdynamic viscosity

J1.p Pa's plastic viscosity

I

w rads' angular frequency

I

Superscripts

I

deviatoric part

I

1

-27

-I

I.

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I

8. References

Brownsey, G.J., 1988, "Commercial rotational instruments", Rheologicai Measurement, edited by

Collyer, A.A. and Clegg, O.W., Elsevier Applied Science, ISBN 1-85166-196-4.

I

Chou, Hsien-Ter, 1989,

"Rheological

response of

cohesive sediments

to water waves", dissertation,

University of California, Berkeley, U.S.A.

Collyer, A.A. and Clegg, O.W., 1988, "Rheological measurement", Elsevier Applied

Science, ISBN 1-85166-196-4.

I

Oalrymple, Robert A. and Liu, Philip L., 1978, "Wavesover soft muds: a two-layer fluid model",

Journal ofPhysical Oceanography, Vol. 8, pp. 1121- 113l.

Ferguson, J. and Kernblowski, Z., 1991, "Appliedfluid rheology", Elsevier Applied Science,

ISBN 1-85166-588-9.

I

Hsiao, S.V. and Shemdin, O.H., 1980, "Interaction of ocean waves with a soft bottom", Journalof

Physical Oceanography, Vol. 10,pp. 605 - 610.

James, A.E., Williams, OJ.A. and Williams, P.R., 1988, "Small strain, low shear rate rheometry

of cohesive sediments"

,

Physical proce

s

ses in estuaries

,

ed.

Job Dronkers and

Wim

van Leussen,

Springer Verlag, pp. 488 - 500.

I

Jiang, L. and Zhao, Z., 1989, "Viscous damping of solitary waves over fluid-mud seabeds", Journal

of Waterway. Pon. Coastal and Ocean Engineering, Vol. 115, No. 3, pp. 345 - 362.

I

_Kuiken_, _{G.D.C. and Merk}_, _HJ., ₁₉₇₈_,

_"

_Rhe

_o

_logie

_der

_fluïde",

_{parts A}_, _{B and C}_, _{in Dutch}_,

Delft University of Technology, The Netherlands.

I

Olphen, H. van, 1977, "An introduetion (11claycolloid chemistry"; Second edition,

John Wiley& Sons, Inc., ISBN 0-471-01-+63-X.

Maa, P.-Y., 1986, "Erosion of soft muds by waves", dissertation, University of Florida,

Gainesville, U.S.A.

I

Macpherson, H.Mechanics, Vol. 97, part. 4, pp, 1980, "The attenuation. 721o-f w742.ater waves over a non-rigid bed", Journalof Fluid

I

Malvern, Lawrence E., 1969, "Introduction to the mechanics of a continuous medium",

Prentice-Hall, Inc.

-28

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I

SakakiyamaJournalof Waterway, Port, Coastal and Ocean Engineering, Vol. 115, No. 5, pp. 614 - 633.,S. and Bijker, E.W., "Mass transport velocity in mud layer due to progressive waves",

I

Toorman, Erik A., 1992, "Modelling of fluid mudflow and cansolidation", dissertation, Katholieke Universiteit Leuven, Belgium.

I

Various authors, 1992, "On the methodology and accuracy of measuring physico-chemical properties

to characterize cohesive sediments", Draft, Version: May 7 1992, Prepared as part of the EC

MAST-I research program.

I

_{Walters, K., 1980, "Rheometry: industrial applications" , Research Studies Press,} ISBN 0-471-27878-5.

I

Weast, Robert C., 1988, "Handbook of chemistry andphysics", CRC Press, Inc., ISBN 0-8493-0740-6.

I

Williams, P.R. and Williams, DJ.A., 1989, "Rheometry for concentrated cohesive suspensions",

Journal of Coastal Research, Special Issue No. 5, ed. AJ. Mehta and EJ. Hayter, CERF, pp.

151 - 164.

I

Wit, PJ. de, 1992, "Experiments on China Clay", Report no. 9-92, Delft University of Technology, The Netherlands.

I

Wit, P.1. de

,

and Kranenburg

,

C

.,

1992, "Liquefaction and erosion of China Clay due to waves and

current",proceedings of the

zs:

International Conference on Coastal Engineering, held in Venice,

Italy, to be published.

I

Yamamoto, T. et al., 1986, "Experiments on wave-soil interaction and wave-driven soil transport in clay beds" ,

Continemal

ShelfResearch, Vol. 5, No. 4, pp. 521 - 540.

I

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