Dielectric behaviour of flowing thixotropic suspensions

Colloids and Surfaces, 22 (1987) 271-289 Elsevier Science Publishers B.V., Amsterdam

271 -

Printed

in The Netherlands

Dielectric behaviour of Flowing Thixotropic Suspensions* J. MEWIS’,

L.M. DE GROOT’ and J.A. HELSEN’

‘Instituut voor Chemie-Zngenieurstechniek, K. U. Leuven, Leuven (Belgium) *Dept. Metaalkunde en Toegepaste Materiaalkunde, K. U. Leuven, Leuven (Belgium) (Received 21 February

1986; accepted 31July 1986)

ABSTRACT The dielectric properties of sheared suspensions of carbon black in mineral oil are analyzed. These systems are known to be thixotropic, i.e. their viscosity changes with shear rate and with time. The shear history also affects the dielectric properties as well as other properties which are determined by the interparticulate structure. Here, the dielectric response is used to probe the shear-induced structural changes. We describe an improved version of an apparatus with which the variable dielectric spectrum of flowing systems can be screened rapidly. In this manner the equilibrium behaviour during shear as well as shear-induced transients can be measured. At present, attention is focused on the dielectric equilibrium properties during shear flow. The effects of shear rate, concentration and temperature are investigated systematically. The results are discussed in terms of the variable microstructure and are compared with rheological data.

INTRODUCTION

Adding particles to a medium will alter the dielectric properties of the system. The most prominent change is the appearance of an additional relaxation owing to the polarization of the charge carriers at the particle-medium interface. This usually occurs in a frequency range well below that of molecular and atomic relaxations. The Maxwell-Wagner theory describes the effect of interfacial polarization in dilute suspensions of spherical particles [ 1,2]. It predicts a dielectric increment which changes linearly with concentration and a relaxation frequency which is independent of concentration. An extension of the full analysis into the non-linear concentration range is hardly possible at this stage [ 3,4]. With non-spherical particles shape and orientation have to be taken into account [ 51. These geometrical parameters often have to be represented by a distribution rather than by a single value. As a result the dielectric relaxation *Dedicated

to the memory of Professor

0166-6622/87/$03.50

E. Wolfram.

0 1987 Elsevier Science Publishers

B.V.

272

will show a corresponding distribution [ 61. In principle, dielectric measurements could be used to determine particle shape and orientation. In practice this method is not commonly used. Application of shear flow could affect the dielectric response in several ways. In a colloidal dispersion of non-spherical particles the orientational distribution function will now be determined by the relative effects of shear-induced orientation and rotational diffusion. Consequently the dielectric properties should be expressed as a function of a Peclet number, in the same way as the rheological properties [ 71. In weakly flocculated systems the floe size depends on the shear history. As far as the dielectric properties would change with floe size, this would provide an extremely suitable technique to study floes. The earliest experimental attempts failed [ 81 but later workers were more successful [ 9-12], The measured effects have been attributed to shape and orientation of the floes [ 13-151. It seems unlikely that sheared floes should be highly anisotropic and that they should orient perpendicular to the flow direction. Yet this is actually assumed in the common explanation of floe size effects. Most published data are fragmentary and do not provide any insight into the underlying mechanisms, the work by Kuo et al. [ 121 being an exception. Therefore an experimental programme was set up to generate systematic data which could be used to develop a more detailed description of the dielectric behaviour of flocculated dispersions. RELAXATION MECHANISMS

The basic Maxwell-Wagner theory does not predict a size effect whereas the Sillars analysis [ 5,161 shows the pronounced effect of particle geometry with non-spherical particles. Applying this theory to floes requires them to grow in a non-spherical manner with the long axis making a sufficient angle with the flow direction. The formation of long slender floes during flow seems unlikely because of the intrinsic fragility of such structures. Furthermore, long floes should tend to orient themselves mainly in the flow direction thus reducing the dielectric effect. Comparison of the changes in dielectric increment with the corresponding shift in relaxation frequency could provide decisive evidence, but it seems that no suitable experiments have yet been reported in the literature, probably because they are so extremely difficult to perform. The simple interfacial polarization of the Maxwell-Wagner-Sillars theories is not the only possible mechanism which should be considered. The presence of a surface conductivity should be sufficient to generate a size effect [ 15,173. The fact that shear effects have been obtained on non-conductive particles like glass, fumed silica or bentonite [ ll-13,181 might be explained on such a basis, even in non-aqueous media. At any rate it might be unwarranted to treat floe size effects solely as particle size effects. This procedure tacitly assumes that

273

dielectric interactions between elementary particles in a floe can be ignored. However, even the conductivity of a floe iself might be determined by the resistivity of the contact zones in between particles of the floe. Solving the governing field equations for possible floe structures is very complicated, so the effect of dielectric interactions on the response of flocculated systems cannot be easily estimated. Interactions have been used in a very simple approach which assumes the dielectric effects to be concentrated solely in the liquid layer between the particles [ 191. This corresponds to a case in which the particles are ideal conductors. If the particles are then organized in chainlike structures the resulting behaviour can be calculated. Although such a model predicts a structure-dependent conductivity, the relaxation frequencies would hardly change at all with the degree of structure. There is only a limited amount of experimental information of this nature and it is not conclusive. Therefore there is a clear need for some systematic experiments to be carried out which could guide further modelling. EXPERIMENTAL

In order to follow structural changes with time and shear rate a suitable dielectric device was developed in this laboratory [ 20,211. It is designed to rapidly screen the dielectric spectrum in flowing systems. Fast measurements are necessary if one wants to follow the change of structure in time. It seems that time-dependent spectra of flowing suspensions are not available in the literature. In the present instrument the time-consuming bridge technique is replaced by a fast network analyzer which determines the complex impedance of the sample. Guard electrodes are used to avoid fringing fields and surface conduction effects. This requires a three-terminal measurement, which is achieved by interfacing the cell containing the sample and the analyzer with an operational amplifier in the inverting feedback configuration [ 22 1. The sample itself fills the annular gap between two coaxial cylinders. This geometry is suitable for calculating the impedance. Besides, it guarantees a constant shear rate throughout the sample if the gap width is small compared with the radii of the cylinders [ 231. The ratio of outer to inner radius is 1.02 in the present set-up. Cells have been constructed in stainless steel and in platinized titanium. The latter is used to reduce electrode polarization. The insulation between measuring and guard electrodes in the titanium cell consists of a ceramic, the thermal expansion of which matches that of titanium. Thus the temperature can be varied over a wide range. A frequency range of 10-l to lo4 Hz is covered by this instrument. The sample is sheared by means of a tachogenerator controlled DC-motor on the inner cylinder. The whole experiment is computer controlled, and any desirable shear history and measuring sequence can be generated. The materials under investigation consist of carbon black particles (Neo

274

Spectra Mark II from Cities Services) dispersed in an unrefined naphthenate distillate (S6141 from Shell Co). The carbon black is a HCC-3 type [ 241. The elementary particles are roughly spherical and have a diameter of 13 nm, some being possibly sintered together. Flocculation is very pronounced in the system used. Furthermore, the floe structure changes with shear rate and time. The suspending medium is Newtonian and has a viscosity of 1.2 Pa s at 298 K. Sample preparation is important as the dispersion process is never complete. In order to avoid variations due to the degree of dispersion, all samples are prepared from the same mother batch. The latter is obtained by dispersing a 0.075 volume fraction on a three-roller mill. This process results in a pastelike slurry of high consistency. The desired concentrations are obtained by diluting the mother batch and mildly homogenizing the samples on a laboratory roller mill. The material is subject to ageing, which is counteracted by redispersing the samples 1 to 2 weeks prior to measurement. The rheology of this sytem has been studied in detail [ 25,261. The shear-induced changes in structure are known to affect the dielectric properties of carbon black or coal suspensions [ 13,14,27]. DC-CONDUCTIVITY

The DC-conductivity ( bnc) measures global features of the structure in the sample. As such it provides only limited information about the microstructure but it is highly sensitive to small changes in it. Furthermore, comparison between DC- and AC-data can be helpful when studying the effect of various parameters. Finally, CJnc will be more readily tractable in theoretical modelling than the dielectric spectrum, especially with the present developments in percolation and fractal theories [ 28,291. The data reported in this section refer to the equilibrium behaviour under shear. Behaviour at rest and during the various possible types of transients are not considered for the time being. The conductivity was measured at shear rates ranging from 0.5 to 50 s-’ and for volume fractions between 0.01 and 0.05 (Fig. 1). The DC-conductiviy decreases with shear rate over the whole shear rate range covered here. In a stable dispersion, where the number of flow units, i.e. the individual particles, does not change, the conductivity should either remain constant or increase with shear rate. The increase occurs if the flow-induced particle collisions contribute noticeably to the charge transfer. The decrease which is experienced here, indicates that the flow-induced breakdown of floes more than compensates the contribution of the collisions. From Fig. 1 a general pattern can be deduced for the one-concentration curves. If the sample is structurized enough, a limiting slope of - l/2 seems to appear at low shear rates: lim(aDc)p_o =IzjW112

(1)

275

o 327

NO_

3 E

b : -I

1

2 -*-@Y._ *-.a

0

1 -*-.-*-_

._O_

1

Fig. 1. Effect of concentration

2

(vol. 5%)and shear rate on the specific DC-conductivity.

Under similar limiting conditions lim(?j)i_o=It’j-l

the rheological

behaviour

is plastic-like: (2)

An increase in shear rate will enhance the hydrodynamic forces between the floes. These forces will cause the floes to break. A reduction of the floe size corresponds electrically to smaller conductive paths. A smaller floe will reduce both the stresses and the conductivity. This effect is not compensated by the increase in number of floes. In the present case the viscosity changes as the square of the conductivity. There is no obvious scaling law which leads to such result. A reduction of the attractive forces between particles can be expected to shift the balance between the effects of path length and collision frequency. Consequently, the shape of the conductivity-shear rate curve will change correspondingly. The floe strength can be reduced-in the carbon black, dispersions by adding a wetting agent. Gilsonite, a naphthenic hydrocarbon (molecular weight of approximately 1500) is known to be suitable for this purpose [ 301. Its addition leads to a drastic decrease in both the viscosity and the conductivity. Both are related to a reduction in floe size. The magnitude of the conductivity will be further reduced by the presence of an electrically insulating

276

0

A

-t \

0

0 \

6 c

\

b ul 2 -’

Fig. 2. Reduction in conductivity owing to the addition of Gilsonite, open symbols: without Gilsonite; filled symbols: with Gilsonite (parameter: cont.; T 300 K) .

Gilsonite layer on the surface of the particles. This will hamper the charge transfer by tunnelling between particles. The overall effect of the addition of Gilsonite on the DC-conductivity of flowing carbon black dispersions is shown in Fig. 2. The conductivities are up to 2 orders of magnitude lower than for the non-treated samples. Furthermore, the shape of the curves has changed, especially for the lowest temperatures and

277

the highest concentrations. The latter conditions correspond to the case with the strongest hydrodynamic particle interactions. In these cases a shallow minimum can be seen as shear rates of the order of 10 s-l. The altered shape suggests that not only the intrinsic conductivity mechanism is affected but that the floe strength is changed as well. This conclusion is corroborated by the drop in viscosity when Gilsonite is added. Because of the reduced floe strength the collision effect begins to dominate at lower shear rates in the samples with Gilsonite. A positive slope in the conductivity-shear rate function has been observed earlier in stable carbon black dispersions [ 311. The data provide some insight into the relative importance of various parameters. Except for shear rate, particle concentration and temperature are relevant parameters affecting DC-conductivity. Although the concentration levels are always low, their effect is strongly non-linear. Again this reflects a relatively high degree of structurization, which therefore will also change with concentration. At the lowest shear rates, i.e. at the highest degrees of structure, the concentration has the strongest effect. In the steepest part of the curve bnc becomes proportional to c5. At the highest volume fraction (0.05) the curves seem to level off, but this is not the case for the samples containing Gilsonite. At higher concentrations the floe size is bound to become smaller because of larger hydrodynamic interactions, which might explain the levelling off. When the floes are larger the latter effect will appear at lower concentrations. A more quantitative description of the results does not seem possible at this stage. The DC-conductivity of the flowing suspensions is found to be extremely sensitive to temperature. Figure 3 shows that a change of less than 10% in absolute temperature can entail a more than twenty-fold change in bnc. Contrary to the viscosity, the conductivity increases with temperature although both phenomena should be explained by the same change in microstructure. The forces exerted on the floes, and consequently the floe size, are determined by the hydrodynamic interactions between floes. These forces should scale with the medium viscosity. The latter decreases with temperature according to an Arrhenius relation: qrn= rm,Oexp( 7200/T) The suspension viscosity itself is a much weaker function of temperature, resulting in an increase of the relative viscosity Q with temperature (Fig. 4). At the low concentration levels used here the contribution of Brownian motion to viscosity is expected to be minor [ 71. Therefore a change in Peclet number with temperature cannot explain the increase. However, if the temperature rises, the lower medium viscosity will cause a reduction in hydrodynamic forces. Considering that the attractive forces will not change dramatically, or might even increase, the net result could be a growth of the floes. From the known effect of structure on the DC-conductivity for the present conditions (Fig. 1) , one then expects an increase of this characteristic with

278

280

300

T

(K)

320

Fig. 3. Sensitivity of DC-conductivity to temperature at c = 4% (parameter: shear rate) G

temperature. The experimental results of Fig. 3 confirm this idea. Additional evidence for the given interpretation is found in the shape of the conductivity-shear rate curves. When a minimum occurs, the corresponding critical shear rate increases with temperature. This reflects the fact that at higher temperatures larger shear rates are required for the hydrodynamic forces to balance the attraction forces. The previous argument does not mean that no other phenomena interfere with the conductivity. As the intrinsic conductivity is thought to be governed by tunnelling [ 321, it could be expected to increase with temperature as well. The contributions of the two effects can be combined in a global activation energy E,. It is obtained by comparing conductivities at equal values of shear rate (Figs 3 and 5 ) . Hence it should be considered as an apparent activation energy. The values of E, change with shear rate. At low shear rates a limiting value

279

I

3.0

I

I

I

I

3.2 103/T

( K-’

I

3.4 )

Fig. 4. Effect of temperature on the relative viscosity (c = 4% ) .

is reached which hardly changes with concentration. A reduction in the degree of structure, by increasing the shear rate or decreasing the temperature, results in lower activation energies. The contribution of shear-induced collisions as well as structural changes might be responsible for the decrease. The limiting behaviour at low shear rates (high structural levels) can be approximated by the relation: one = 0nc.Oexp (11000/T)

(3)

This relation can be compared with the much smaller effect of temperature on the suspension viscosity: rj( T) =q(O)exp(

-1100/T)

(4)

The decrease in conductivity upon addition of a wetting agent shifts the

3.4

3.2

3.0 103/

T

(K-l)

Fig. 5. Activation energy for DC-conductivity,

effect of concentration.

conductivity to lower values. The decrease can be related to the lower structural levels existing here. Yet the temperature dependence is hardly affected at all by Gilsonite (Fig. 2). In this respect the wetting agent seems to cause a change which is similar to that induced by a reduction in concentration rather than by an increase in shear rate (Fig. 5 ) . Dielectric properties Although they are less sensitive to structure than the DC-conductivities, the dielectric spectra provide much more detailed information about the microstructure. This is true in general for spectral information as compared with stationary results. The latter, in this case the DC-conductivity, measures the integral of the frequency distribution given in the spectrum. In the case of the dispersions of carbon black in mineral oil, the experimental values of the complex dielectric constant can be represented by a symmetrical spectrum. Hence the dynamic data can be characterized by means of 4 parameters: the dielectric

281 TABLE 1 Dielectric properties of a flowing carbon black dispersion ( 4% )

T

i

(K)

(s-‘)

300

0.5 1 2 5 10 50

40 28 21 13 8 3.8

310

0.5 5 50

327

0.5 5 50

AC

9, Gnax

f max (Hz)

ODC (nS

8.0 5.5 4.3 2.7 1.8 0.7

2 6 10 21 40 130

22 16 12 9 8 6

58 19 6

11.5 4.2 1.2

10 50 180

97 33 17

120 32 12

25 7.5 2.7

60 100 250

912 278 83

m-‘)

increment de’ ( =~‘~-e,‘), the maximum dielectric loss E”,, and the frequency at the maximum loss fm,,. Table 1 shows the parameters for the dielectric data at 0.04 volume fraction. The data can be described by the Cole-Cole equation:

In Table 1 it can be seen that the ratio between maximum loss and dielectric increment does not change with shear rate. This means that the spectral dispersion parameter (x in Eqn (5) does not depend on shear rate. As a result the data can be normalized as illustrated in Fig. 6. The parameter (Yis quite large (0.5), which indictes a rather wide distribution of relaxation times. The distribution is independent of shear rate or temperature but is a weak function of concentration. The angle of which (Y is the tangent changes from 47” at 2% to 43” at 4%. If the Sillars model is used to describe the data, extreme values of the shape factor (of the order of several hundred) have to be used. This requires the presence of long slender floes perpendicularly oriented on the flow direction, which seems unlikely. From the strong effect of shear rate on the dielectric constant and on the mean value of the relaxation time it can be concluded that these parameters are determined by the microstructure, i.e. the floe size. In that case the distribution of relaxation times could reflect the distribution of floe sizes. The latter should then remain constant in the present experiments when changing shear rate or temperature. The behaviour suggests the possible existence of a constant fractal

1

m

pQ m

0

I

fr 0

Fig. 6. Normalized plot of the dielectric constants (c = 4% ) .

dimension. Small angle neutron diffraction measurements on the same samples seem to confirm this [ 331. Two parameters of the spectrum seem likely candidates to characterize the degree of structure: de andf,,,. Data from the literature on flocculated systems often show a nearly linear dependency of dielectric increment on concentration [ 131.The result is somewhat surprising as the structure must change with concentration if the shear rate is kept constant. In practice the various contributions seem to balance each other, which constitutes an important result with respect to eventual modelling. The linearity in concentration also shows up in the present data. Furthermore, de seems to be linked in a simple manner to temperature and shear rate, as illustrated in Fig. 7. The dielectric increment changes in a manner inversely proportional to the square root of the shear rate. This relation holds for all temperatures and concentrations investigated here. In all cases the limiting value at infinite shear rate equals zero. Hence the relaxation mechanism responsible for the measured dc disappears at high shear rates when the floes can be assumed to be broken down. The temperature dependence can be represented by an Arrhenius equation. Combination of the effects of the various parameters leads to a global empirical relation for de: de = 4.106~j-~/~ exp ( -4000/T)

(6)

283

1

0

I

1

Oa5

4

(s-l)

1

1

’

1.5

Fig. 7. Linear relation between dielectric increment and the square root of shear rate for various concentration/temperature combinations.

The dielectric results described by Eqn (6) can now be compared with the data on DC-conductivity. Qualitatively some similarities can be noticed. Both characteristics decrease with increasing shear rates, which can be understood on the basis of decreasing floe size. A square root dependence on shear rate is also a feature which both parameters have in common. For bnc the relation is only reached in the limit of highly developed structures, for dr it holds throughout the whole measuring range. Possibly interactions between floes and particles contribute increasingly to the conductivity whenever the structure breaks down. Therefore, de might reflect the floe size more directly than enc. Indeed the proportionality with the square root of the shear rate compares well with earlier data and earlier estimates of the relation between shear rate and floe size [ 14,341. This is also roughly comparable to the reported proportionality between the level of the mechanical spectrum during flow and 9. The dielectric increment increases with temperature but to a lesser extent than the DC-conductivity. It can be argued that the former is mainly determined by the microstructure and by the values of the dielectric constants of

3.0

3.1

3.3

3.2 103/T

( K -’

)

Fig. 8. Temperature effect on specific DC-conductivity, electric increment.

compared at constant values of the di-

the components. This can be verified in the various expressions for de in the interfacial polarization models. The dielectric properties of the components do not change noticeably with temperature. On the other hand the determining step for conductivity might be charge transfer through the gap between adjacent particles. Tunnelling constitutes the basic mechanism for this process, which consequently should change clearly with temperature. Therefore the one temperature dependence of 0 nc can be divided into two contributions: related to structural changes and one related to the intrinsic conductivity mechanism. If the dielectric increment is a reasonable measure for structure, conductivities should not be compared at constant shear rate but at constant de. The result is shown in Fig. 8. At low structural levels a rather anomalous temperature dependence is encountered. Under these conditions collision effects might interfere, as could be seen from the shear rate dependence. At the opposite extreme, i.e. at a high structural level, an Arrhenius-type behaviour is found which can be expressed as: ( oDC)Ac = k”exp ( -8000/T)

(7)

Equation ( 7) should more closely describe the temperature dependence of the intrinsic conductivity. The activation energy is similar to that for the medium viscosity. Taking into account the effect of temperature on intrinsic conductivity, the dielectric data still show a net increase with temperature. Again this suggests an increase of floe size with temperature, thus confirming the data on relative viscosity and on DC-conductivity. The correspondence between rela-

285 TABLE 2 Effect of temperature, comparing dielectric properties at constant relative viscosities

T W)

?i (s-l)

At

300 310 327

1.0 1.5 4.0

28 30 28

fm. (Hz)

ODC

5 20 100

17 66 333

( qr= 200)

(nS m-l)

tive viscosity and dielectric increment can be illustrated by comparing dielectric parameters at different temperatures at constant relative viscosities. The results for Q = 200 are given in Table 2. In such a comparison the dielectric constants become independent of temperature but fmaxand one do not. The relation between the latter two characteristics will be discussed later. Again Table 2 suggests that relative viscosity and dielectric constant might be suitable measures for the microstructure. Finally, the relaxation frequency should be considered. As mentioned above, the simple theories for interfacial polarization do not predict any effect on particle size. A similar result could then be expected, at least as a first approximation, for floe sizes. Only in the case of dominating surface conductivity can a clear size effect be predicted. The carbon blacks which have been used here are conductive in the bulk. Nevertheless, fmaxchanges drastically with shear rate, a change which can be attributed to variations in floe structure. The few results which are available in the literature are not conclusive. Whereas some show a more or less constant relaxation frequency, others indicate a shear rate dependency [ 11,12,18,19]. The measured variations of fmaxdo not obey a simple law. Contrary to the results for the dielectric increment a strong interaction is observed between shear rate and temperature effects. At high temperatures the values become shear independent whereas at 300 K a linear relation with shear rate can be detected. This means that f,, becomes proportional to the square of the dielectric increment, for which again no theoretical basis is available. Considering the global effect of temperature, one finds that the activation energy for fmaXdecreases strongly with increasing shear rate. This point will be considered again later. The concentration effect also differs from the theoretical predictions of the linear Maxwell-Wagner theory. Instead of being constant, the relaxation frequency increases with the concentration to the power 1.5-2for volume fractions of 0.02-0.04. This parameter does not seem to interfere as much with the other parameters as shear rate and temperature do. If the changes in the various dielectric characteristics with shear rate, temperature and concentration are considered, an apparent inconsistency can be

286

Fig. 9. Relation between relaxation frequency and DC-conductivity

at constant values of Ac.

noticed. Above, it has been concluded that the floes grow with decreasing shear rate and increasing temperature. Consequently the relaxation frequency is expected to decrease in both cases. However, it increases with temperature. The following argument can be developed to rationalize the experimental results. All basic theories for interfacial polarization predict the relaxation frequencies to be proportional to the intrinsic conductivity. The values for bnc at high structural levels, compared at equal values of de, should approximately scale with the intrinsic conductivity (Fig. 8). Hence the relationf_+nc should become linear under these conditions. The corresponding plot is shown in Fig. 9. A linear region appears at high degrees of structure as expected from the previous argument. This is the region where the activation energies for relaxation time and DC-conductivity are indeed comparable to each other, providing further evidence for a possible interconnection. At lower degrees of structure the curves are steeper because the conductivity increases owing to particle collisions, a mechanism which does not affect the relaxation frequency in the same manner. Figure 9 includes data from different concentrations. Somewhat surprisingly the curves seem to be nearly independent of this parameter.

287

Fig. 10. Double relaxations (c=2%,

)‘=5 s-l, T=300 K).

Whether this result is specific for the carbon blacks or whether eral is not known at this moment.

it is more gen-

DOUBLE RELAXATIONS

Reported values for the dielectric relaxation frequency in the literature are much higher than the ones measured here. The data in the literature have most often been obtained on less structurized systems and therefore are not necessarily incompatible with the present results. However, the discrepancy is a reason to investigate in more detail the high frequency region. Moreover, the dielectric constants measured at the highest frequencies are much higher [ 5-71 than would be expected above the interfacial polarization region [ 3,4]. A small relaxation buried in a much larger one is extremely difficult to detect. The high frequency experiments were therefore performed at low structural levels. The absolute accuracy of these measurements is lower than for the low frequency ones but the main interest is in relative values. Low levels of structure can be realized by using low concentrations, high shear rates and/or by adding Gilsonite. The resulting dielectric spectrum is shown in Fig. 10. The presence of two relaxation mechanisms is clearly visible. Multiple relaxations as such are not uncommon in suspensions [ 11,35,36]. Often aqueous sytems are involved and/or the frequency range is higher than in the present case. A noticeable difference from the published data is the fact that both relaxations change with shear rate. The effect is not identical for the two mechanisms, hence they seem to be related to different aspects of the structure. The high frequency relaxation, which occurs above 10 kHz, is systematically less sensitive to shear than the low frequency one discussed above. Therefore the former becomes more visible at higher shear rates. The corresponding dielectric increment does not change in a manner inversely proportional to the square root of the shear rate but rather with the power 0.15. At all concentrations the high frequency fmax is proportional to the 3rd power of shear rate for the samples containing Gilsonite. The dispersion factor is similar for all sam-

288

ples, treated and untreated, in the second relaxation. Its value (52’ ) is slightly larger than that for the low frequency relaxation. There is no obvious structural explanation for the high frequency relaxation. It could reflect a different aspect of the same structural elements that cause the low frequency relaxation. Alternatively, it could be associated with different structural elements. Possible candidates of the second kind are the elementary particles and the strong small aggregates which exist either in the floes or as separate entities. CONCLUSIONS

Dielectric spectra of flowing thixotropic dispersions were measured. Shear rate, temperature and particle concentration were varied systematically. The concentration levels were always low (14% ) , but nevertheless these nonaqueous samples were highly structurized. They showed a shear rate dependent relaxation at low frequencies (between 1 and 1000 Hz). A Maxwell-Wagner effect seems an unlikely explanation. It would require extremely high shape factors which seems unrealistic for flowing suspensions. The various dielectric parameters (dielectric increment, relaxation frequency and DC-conductivity) do not correlate in any simple manner. The most striking feature of the spectra is a distribution which does not change with shear rate. As far as it reflects a distribution in structural sizes this result could suggest a constant fractal dimension. The data for the dielectric increment are the only ones which can be reduced to a single equation for all the variables. They seem to follow floe size more closely than the other parameters. The proportionality with the inverse of the square root of shear rate fits in with earlier estimates for floe size. The increase with temperature corresponds to an increase in relative viscosity. The relaxation frequency and the DC-conductivity show a more complex pattern. Two interfering factors can be identified. Firstly, collision effects affect conductivity at low levels of structure. Secondly, the intrinsic conductivity increases with temperature thus affecting selectively some features of the dielectric spectra. At the highest degrees of structure all dielectric properties evolve in a parallel fashion. In less structurized samples a second relaxation mechanism can be detected in the kHz range. It also changes with shear rate and consequently seems to probe an aspect of the particulate structure, possibly smaller floes or a substructure of the floes. The high frequency relaxation is less sensitive to shear than the low frequency one.

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