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Consolidation of depletion flocculated concentrated suspensions Influence of nonadsorbing polymer concentration on consolidation rate constants
Colloids and Surfaces, 54 (1991) 125-134 Elsevier Science Publishers B.V., Amsterdam
125
Consolidation of depletion flocculated concentrated suspensions Influence of nonadsorbing polymer concentration on consolidation rate constants D.J. Wedlock, A. Moman and J. Grimsey Shell Research Ltd, Sittingbourne Research Centre, Sittingbourne, Kent ME9 8AG (United Kingdom) (Received 16 March 1990; accepted 25 June 1990)
Abstract
Observations have been made on the effect of varying the concentration of a nonadsorbing polymer in sterically stabilised concentrated suspensions of organic crystals (a herbicide) using an ultrasound velocity scanning technique. The rate of sediment or floe consolidation is satisfactorily quantitatively interpreted using a first-order rate equation and the variation in that rate constant with polymer concentration is described by a single power law for observations at all added polymer concentrations. Qualitative interpretation of ultrasound velocity scans of the consolidating sediment suggests that the process of depletion flocculation of the dispersed particles occur at free-polymer concentrations at least an order of magnitude less than the dilute/semidilute transition regime, the socalled coil overlap concentration in these polydisperse suspensions.
INTRODUCTION
The gravitational consolidation or compression of stable or flocculated concentrated suspensions has received theoretical consideration [l-5] but relatively little detailed experimental data have been published, because of the lack of readily available techniques for following such processes in any great detail. The use of high-energy radiations to derive concentration profiles for concentrated suspensions has received some attention [ 31, but is obviously not a technique that can be used as a matter of routine. The approach of observing boundary movement in gravitational fields has provided much useful information on floe consolidation [4,5] but does not give detailed information on the concentration profiles in the region of perhaps most interest, at the base of the column of particles, where the floe is most extensively compressed. Uniform compression cannot be assumed [ 61. The advent of ultrasound velocity scanning [6-81 has allowed the use of a
0166-6622/91/$03.50
0 1991-
Elsevier Science Publishers
B.V.
126
noninvasive, low-energy technique for the investigation of the sedimentation and consolidation processes in opaque colloidal and noncolloidal dispersions, over a range of volume fractions from little more than zero to the close-packed limit. In this report, we describe the application of the ultrasound technique to investigate the case of consolidation of a water-continuous, polydisperse colloidal suspension of organic particles made into an initially stable state with a nonionic block copolymer, and subsequently flocculated by adding a nonadsorbing high molecular weight water-soluble polymer in order to moderate sedimentation. This is typical of the approach that may be followed in an industrial formulation process. In a previous report [9] the flocculation of a similar concentrated suspension by the same water-soluble polymer (a cellulose ether, hydroxyethylcellulose) was shown to be due to bridging flocculation of the particles. By changing the dispersant type from an anionic polyelectrolyte/block copolymer that essentially charge stabilises, to a nonionic dispersant that confers colloidal stability by a steric mechanism, the cellulose ether can be changed from an adsorbing polymer to a nonadsorbing polymer. The nonadsorbing polymer has the capability to cause flocculation of the particles by depletion forces [lo] and this floe can be a sufficiently self-hindering, connected assembly that close packing of the particles by gravitational sedimentation can be resisted. The dilatant properties of close-packed colloidally stable particles has been well documented [ 111, and prevention or retardation of such sediments is of industrial relevance, enabling control of the flow properties of concentrated suspensions. A full understanding of the consolidation process is important, both theoretically and experimentally. We show that it is possible to define a rate of consolidation of a floe in the region of importance, i.e., at the base of the column, the position where dilatant particulate assemblies are likely to be initially formed, and relate this rate to polymer concentration. The kinetics of particle accumulation are analysed by a first-order rate equation, where we consider the approach of the volume fraction of the dispersed phase, at a fixed level in the suspension, to the ultimately achievable packing fraction. This packing fraction is shown to have a value between random packing and close packing of spheres. The first-order rate constant is a continuous function of polymer concentration, for a range of polymer concentrations covering the dilute to semidilute regime. Previous reports [ 10,12,13] suggest that there is a molecular weight dependent propensity of a nonadsorbing polymer to induce depletion flocculation and that, furthermore, there is a critical free-polymer concentration dependence of the onset of flocculation for a given molecular weight of free polymer. There is also said to be a particle volume fraction dependence of the critical polymer concentration for the onset of depletion flocculation, although this
127
last effect is weak for particle volume fractions below 30%, according to Sperry
[131.
There have been reports [ 121 of discontinuities in the rheological behaviour of suspensions at a critical polymer (continuous phase) concentration. This has been supported by microscopic observations of the onset of flocculation above this concentration. We have different, but not inconsistent findings. MATERIALS AND METHODS
Nonadsorbing
polymer
Hydroxyethylcellulose (HEC ) was supplied by Hercules Ltd. It had a degree of substitution of 2.5 hydroxyethyl groups per glucose residue and a molecular weight of 1.01*105 determined from intrinsic viscosity measurements. It was added to the suspensions in the form of a predissolved concentrate. A spin-labelled version of the same polymer was prepared as described previously [ 91 using 2,2,6,6-tetramethyl-l-piperidino-oxyl (TEMPO ), a nitroxyl spin label, covalently linked after cyanogen bromide activation of the polymer in water. Suspensions
The preparation and milling of these suspensions of technical cyanazine, 2(4-chloro-6-(ethylamino)-1,3,5-triazin-2-yl)amino-2-methylpropanenitrile, has been described previously [ 91, except that only samples dispersed with the poly (ethylene oxide) /poly (propylene oxide) block copolymer were investigated. Samples of the milled dispersions with a volume mean diameter of 2.4 pm were prepared at various added HEC levels. The HEC was added as a predissolved concentrate. Concentrations of HEC were calculated as concentrations in the continuous phase. Ultrasound velocity scanning
The essential instrumental details have been reported previously [ 6-91. Ultrasound scans of various samples of a 40% v/v water-continuous suspension of the particles (described under Suspensions) were logged for up to N 150 days at 20’ C in undisturbed cells of horizontal cross section 32 x 32 mm. Electron spin resonance
The spectrometer was a Brucker Model ER 200. The absence of adsorbed HEC on the surface of the particles was established by equilibrating the colloidally stable particles with various levels of spin-labelled HEC, centrifuging
128
the suspensions, discarding the supernatant and resuspending and washing the particles with water presaturated with cyanazine. When the supernatant was established to be free of nonadsorbed spin-labelled polymer, a concentrated slurry of suspended particles was examined in the spectrometer, using a shortpathlength, aqueous-type ESR cell [ 91 in order to minimise dielectric losses. RESULTS
AND DISCUSSIONS
Nonadsorption of added polymer The ESR spectra of washed particles that had previously been equilibrated with spin-labelled HEC showed no evidence of any adsorbing polymer [ 91. It is therefore considered that flocculation of the particles, due to added polymer, would not be by a bridging mechanism in this particular instance but more likely by the depletion mechanism associated with nonadsorbing polymers [ 1316]. Sedimentation of suspensions and compression of floes Figure 1 shows sedimentation in progress for a 40% v/v particulate suspension in water with no added polymer. In the form of ultrasound scans, we can 07-
0.6 -
0.5
-
8 c‘ 0.4 .g x 2 f
0.3
-
0.2
-
3
0.1 -
/
0
20
40
60
80
100
120 Height
140
160
160
200
220
240
260
bmn,
Fig. 1. Sedimentation of a 40% v/v suspension of sterically stabilised cyanazine particles. Volume fraction, @,versus height of column (mm). No polymer added.
129
see the process of sedimentation of colloidally stable particles to form a dilatant sediment. A maximum packing fraction of 0.68 is obtained for these particles. This is slightly larger than the characteristic random packing limit of 0.62 for spheres but is explicable in terms of the size and shape polydispersity of the particles, allowing some interstitial packing. The overlapping plateau regions in the centre of the column scans, we feel, demonstrate the colloidally stable nature of the suspension. Influx and efflux of individual sedimenting particles will be balanced and lead to no net change in particle volume fraction in the region of the column centre. This is consistent with no long-range particle connectivity in this system, as indicated by the sedimentation profiles. Figure 2, on the other hand, shows no such overlapping plateau regions, with compression of the total mass of underlying particles occurring from relatively early times. The concentration of added polymer is 1.9 g ml-’ and hence well within the dilute region of polymer solution behaviour. Interestingly, Fig. 2 also shows particle packing at the base of the cell, to the same packing limit as the system containing no added polymer. In fact, for the lowest concentrations of added polymer, the same overall effect was observed as seen in Fig. 2. We might interpret this either as coexistence of flocculated and deflocculated phases within the suspension, or alternatively as formation of a very weak homogenous floe phase with a sufficiently weak network struc0.7-
A 0.6
-
0.5
-
0.4
-
8 g
“I:::,, 0 day
i;;,,-_
-ADda”
_
‘G D 2
I 4::
1
40 Height
Imm,
160
:::: I
180
I
1
I
I
200
220
240
260
Fig. 2. Sedimentation of a 40% v/v suspension of flocculated cyanazine particles containing 1.9 g I-’ hydroxyethylcellulose. Volume fraction, @,versus height of column (mm).
130 0.8 -
07-
0.6 -
8 E‘ 0.5 .g
-
8 .e $
0.4 -
>”
0
I
I
20
1 40
1 60
1
SO
1 100
1 120
1 140
180
180
1
1
1
1
200
220
240
260
Height/mm
Fig. 3. Consolidation of a 40% v/v column of flocculated suspension of cyanazine containing 21 g 1-l hydroxyethylcellulose. No dilatant sediment at cell base. Volume fraction, 9, as a function of height of column (mm).
ture (small uniaxial compression modulus), to permit compression of the floe to the packing limit of the particles. Figure 3 shows consolidation of a flocculated suspension containing 21 g 1-l HEC, a polymer concentration well into the semidilute regime. The rate of consolidation is attenuated, but the final packing fraction is expected to approach the close-packed limit given sufficient time. Floe consolidation rates Taking the maximum packing fraction &,, as that obtained at the base of the cell containing the stable suspension with no added polymer, we have expressed the rate of accumulation and consolidation of particles in terms of changes in volume fraction #, at a fixed low level above the cell base. We did not choose the very base of the cell to avoid difficulty in experimental determination of volume fraction values, but we selected a region where the volume fraction undergoes a high rate of change, i.e., 10 mm above the base. The empirical rate equation is expressed as kt= -log(@,,,-@)
(1)
131
where k is an assumed first-order rate for the consolidation of particles. We refer to k as a consolidation rate constant. Figure 4 shows some typical plots of log (g,,, - $) versus time for different polymer concentrations and the fit (linear least squares) is reasonable over quite long time periods, in excess of 100 days. Figure 5 shows a plot of the resultant first-order rate constants as a function of polymer concentration. It can be seen that for concentrations from 1.9 to 26.5 mg ml-’ there is a single power law, determined by geometric regression analysis, describing the relationship between consolidation rate constant and polymer concentration, which goes in inverse proportions to the polymer concentration to the power 3/2. Discontinuities in this power-law relationship are only apparent at polymer concentrations below - 1.9 mg ml-‘, where the consolidation rates become constant. Polymer concentrations below 1.9 g 1-l were not used in the fitting procedure, but are shown in Fig. 5 for completeness. The reason that concentrations of polymer below 1.9 mg ml-’ were not used in the fitting procedure was that observations of the sedimentation velocity of the boundary with the supernatant (tangents to the height/time plot) showed that there was an initial increase in the sedimentation velocity with increasing polymer concentration which maximised and then decreased at concentrations of free polymer - 1.9 mg ml-’ upwards. The sedimentation velocity was measured as the tangent to the boundary movement line after 5 days, and the resultant sedimentation velocities as a function of free polymer concentration
1.0
1
0
I
1
1
25
50
75
I
100 Time
Fig. 4. Determination
of consolidation
1
125
I
150
I
175
I 200
Idays)
rate constants for two levels of added hydroxyethylcellulose.
132
Fig. 5. Consolidation rate constant versus hydroxyethylcellulose 40% v/v cyanazine suspensions.
concentration.
Suspensions were
are shown in Fig. 6. The effect is ascribed to the formation of floes, at low polymer concentration, with no significant self-hindering connectivity, such that the overall effect is to increase the sedimentation velocity in a Stokesian manner for the initial increments in polymer concentration. At higher polymer concentrations the greater degree of flocculation reduces the sedimentation velocity as expected, suggesting that the polymer concentration giving the maximum sedimentation velocity might correspond to a balance between two opposing effects, namely increasing floe size assisting sedimentation and increasing suspension viscosity causing retardation of sedimentation. Our results do not show any obvious critical discontinuities in the consolidation rate constant at any free-polymer concentration, rather a continuous increase in the degree of flocculation from the lowest polymer additions upwards, but we feel that this is not necessarily inconsistent with previous reports [ 121, the time scale of our experiments being very long term compared to the time scale of the microscopic observations. Since the degree of depletion flocculation is a polymer concentration dependent phenomenon [ 171, the consolidation rate constants reflecting the attractive force between the particles, then at low polymer concentrations the rate of assembly and the extent of the connectivity of the floes that result is sufficiently limited that it requires longer time scales to become manifest. Our longer time scales of observation can appreciate this.
0.0
1
0
I
I
I
I
I
I
5
10
15
20
25
30
Polymer
concentration
mglml
Fig. 6. Sedimentation velocity of a 40% v/v cyanazine suspension ethylcellulose. Rate determined after 5 days.
as a function of added hydroxy-
CONCLUSION
We have demonstrated that it is possible to quantify a rate of sediment formation or floe consolidation for polydisperse industrial suspensions by direct observations on the sediment using ultrasound velocity measurements. Observations on the boundary between the suspension and the supernatant continuous phase give only limited insight into the most significant changes. The first-order rate constant that we determined for floe consolidation is in inverse proportion to the added nonadsorbing polymer concentration to the power 3/2. The rate of boundary subsidence goes approximately with the inverse of the square root of polymer concentration in the same free-polymer concentration range. The functions describing both processes do not appear to have critical discontinuities at any polymer concentration. The above findings mean that it should be possible to predict the likely rate and extent of dilatant sediment formation in long term stored polydisperse suspensions from ultrasound scanning experiments. Direct observation of freeliquid formation in concentrated suspensions is probably a poor guide to dilatant sediment formation.
134 REFERENCES
2 3 4 5 6
8 9 10 11 12 13 14 15 16 17
G.A. Ratcliffe, J. Colloid Interface Sci., 25 (1967) 587. R.S. Crandall and R. Williams, Science, 198 (1977) 293. A.S. Micheals and J.C. Bolger, Ind. Eng. Chem. Fundam., 1 (1962) 24. R. Buscall, J.W. Goodwin, R.H. Ottewill and Th.F. Tadros, J. Colloid Interface Sci., 85 (1982) 78. R. Buscall and I.J. McGowan, Faraday Discuss. Chem. Sot., 76 (1983) 277. D.J. Wedlock, I.J. Fabris and J. Grimsey, Colloids Surfaces, 43 (1990) 67. P.A. Gunning, D.J. Hibberd, A.M. Howe and M.M. Robbins, Food Hydrocolloids, 2 (1988) 119. S.D. Lubetkin, D.J. Wedlock and C.F. Edser, Colloids Surfaces, 44 (1990) 139. D.J. Wedlock, ACS Symp. Ser., 371 (1988) 190. B. Vincent, P.F. Luckham and C.F. Waite, J. Colloid Interface Sci., 73 (1980) 508. Th.F. Tadros, in Th.F. Tadros (Ed.), Solid/Liquid Dispersions, Academic Press, New York, 1987, p. 225. Th.F. Tadros and A. Zsednai, Colloids Surfaces, 43 (1990) 95,105. P.R. Sperry, J. Colloid Interface Sci., 99 (1984) 97. S. Asakura and F. Oosawa, J. Chem. Phys., 22 (1954) 1255. A. Vrij, Pure Appl. Chem., 48 (1976) 471. D. Heath and Th.F. Tadros, Faraday Discuss. Chem. Sot., 76 (1983) 203. E. Dickinson, J. Colloid Interface Sci., 132 (1989) 274.
125
Consolidation of depletion flocculated concentrated suspensions Influence of nonadsorbing polymer concentration on consolidation rate constants D.J. Wedlock, A. Moman and J. Grimsey Shell Research Ltd, Sittingbourne Research Centre, Sittingbourne, Kent ME9 8AG (United Kingdom) (Received 16 March 1990; accepted 25 June 1990)
Abstract
Observations have been made on the effect of varying the concentration of a nonadsorbing polymer in sterically stabilised concentrated suspensions of organic crystals (a herbicide) using an ultrasound velocity scanning technique. The rate of sediment or floe consolidation is satisfactorily quantitatively interpreted using a first-order rate equation and the variation in that rate constant with polymer concentration is described by a single power law for observations at all added polymer concentrations. Qualitative interpretation of ultrasound velocity scans of the consolidating sediment suggests that the process of depletion flocculation of the dispersed particles occur at free-polymer concentrations at least an order of magnitude less than the dilute/semidilute transition regime, the socalled coil overlap concentration in these polydisperse suspensions.
INTRODUCTION
The gravitational consolidation or compression of stable or flocculated concentrated suspensions has received theoretical consideration [l-5] but relatively little detailed experimental data have been published, because of the lack of readily available techniques for following such processes in any great detail. The use of high-energy radiations to derive concentration profiles for concentrated suspensions has received some attention [ 31, but is obviously not a technique that can be used as a matter of routine. The approach of observing boundary movement in gravitational fields has provided much useful information on floe consolidation [4,5] but does not give detailed information on the concentration profiles in the region of perhaps most interest, at the base of the column of particles, where the floe is most extensively compressed. Uniform compression cannot be assumed [ 61. The advent of ultrasound velocity scanning [6-81 has allowed the use of a
0166-6622/91/$03.50
0 1991-
Elsevier Science Publishers
B.V.
126
noninvasive, low-energy technique for the investigation of the sedimentation and consolidation processes in opaque colloidal and noncolloidal dispersions, over a range of volume fractions from little more than zero to the close-packed limit. In this report, we describe the application of the ultrasound technique to investigate the case of consolidation of a water-continuous, polydisperse colloidal suspension of organic particles made into an initially stable state with a nonionic block copolymer, and subsequently flocculated by adding a nonadsorbing high molecular weight water-soluble polymer in order to moderate sedimentation. This is typical of the approach that may be followed in an industrial formulation process. In a previous report [9] the flocculation of a similar concentrated suspension by the same water-soluble polymer (a cellulose ether, hydroxyethylcellulose) was shown to be due to bridging flocculation of the particles. By changing the dispersant type from an anionic polyelectrolyte/block copolymer that essentially charge stabilises, to a nonionic dispersant that confers colloidal stability by a steric mechanism, the cellulose ether can be changed from an adsorbing polymer to a nonadsorbing polymer. The nonadsorbing polymer has the capability to cause flocculation of the particles by depletion forces [lo] and this floe can be a sufficiently self-hindering, connected assembly that close packing of the particles by gravitational sedimentation can be resisted. The dilatant properties of close-packed colloidally stable particles has been well documented [ 111, and prevention or retardation of such sediments is of industrial relevance, enabling control of the flow properties of concentrated suspensions. A full understanding of the consolidation process is important, both theoretically and experimentally. We show that it is possible to define a rate of consolidation of a floe in the region of importance, i.e., at the base of the column, the position where dilatant particulate assemblies are likely to be initially formed, and relate this rate to polymer concentration. The kinetics of particle accumulation are analysed by a first-order rate equation, where we consider the approach of the volume fraction of the dispersed phase, at a fixed level in the suspension, to the ultimately achievable packing fraction. This packing fraction is shown to have a value between random packing and close packing of spheres. The first-order rate constant is a continuous function of polymer concentration, for a range of polymer concentrations covering the dilute to semidilute regime. Previous reports [ 10,12,13] suggest that there is a molecular weight dependent propensity of a nonadsorbing polymer to induce depletion flocculation and that, furthermore, there is a critical free-polymer concentration dependence of the onset of flocculation for a given molecular weight of free polymer. There is also said to be a particle volume fraction dependence of the critical polymer concentration for the onset of depletion flocculation, although this
127
last effect is weak for particle volume fractions below 30%, according to Sperry
[131.
There have been reports [ 121 of discontinuities in the rheological behaviour of suspensions at a critical polymer (continuous phase) concentration. This has been supported by microscopic observations of the onset of flocculation above this concentration. We have different, but not inconsistent findings. MATERIALS AND METHODS
Nonadsorbing
polymer
Hydroxyethylcellulose (HEC ) was supplied by Hercules Ltd. It had a degree of substitution of 2.5 hydroxyethyl groups per glucose residue and a molecular weight of 1.01*105 determined from intrinsic viscosity measurements. It was added to the suspensions in the form of a predissolved concentrate. A spin-labelled version of the same polymer was prepared as described previously [ 91 using 2,2,6,6-tetramethyl-l-piperidino-oxyl (TEMPO ), a nitroxyl spin label, covalently linked after cyanogen bromide activation of the polymer in water. Suspensions
The preparation and milling of these suspensions of technical cyanazine, 2(4-chloro-6-(ethylamino)-1,3,5-triazin-2-yl)amino-2-methylpropanenitrile, has been described previously [ 91, except that only samples dispersed with the poly (ethylene oxide) /poly (propylene oxide) block copolymer were investigated. Samples of the milled dispersions with a volume mean diameter of 2.4 pm were prepared at various added HEC levels. The HEC was added as a predissolved concentrate. Concentrations of HEC were calculated as concentrations in the continuous phase. Ultrasound velocity scanning
The essential instrumental details have been reported previously [ 6-91. Ultrasound scans of various samples of a 40% v/v water-continuous suspension of the particles (described under Suspensions) were logged for up to N 150 days at 20’ C in undisturbed cells of horizontal cross section 32 x 32 mm. Electron spin resonance
The spectrometer was a Brucker Model ER 200. The absence of adsorbed HEC on the surface of the particles was established by equilibrating the colloidally stable particles with various levels of spin-labelled HEC, centrifuging
128
the suspensions, discarding the supernatant and resuspending and washing the particles with water presaturated with cyanazine. When the supernatant was established to be free of nonadsorbed spin-labelled polymer, a concentrated slurry of suspended particles was examined in the spectrometer, using a shortpathlength, aqueous-type ESR cell [ 91 in order to minimise dielectric losses. RESULTS
AND DISCUSSIONS
Nonadsorption of added polymer The ESR spectra of washed particles that had previously been equilibrated with spin-labelled HEC showed no evidence of any adsorbing polymer [ 91. It is therefore considered that flocculation of the particles, due to added polymer, would not be by a bridging mechanism in this particular instance but more likely by the depletion mechanism associated with nonadsorbing polymers [ 1316]. Sedimentation of suspensions and compression of floes Figure 1 shows sedimentation in progress for a 40% v/v particulate suspension in water with no added polymer. In the form of ultrasound scans, we can 07-
0.6 -
0.5
-
8 c‘ 0.4 .g x 2 f
0.3
-
0.2
-
3
0.1 -
/
0
20
40
60
80
100
120 Height
140
160
160
200
220
240
260
bmn,
Fig. 1. Sedimentation of a 40% v/v suspension of sterically stabilised cyanazine particles. Volume fraction, @,versus height of column (mm). No polymer added.
129
see the process of sedimentation of colloidally stable particles to form a dilatant sediment. A maximum packing fraction of 0.68 is obtained for these particles. This is slightly larger than the characteristic random packing limit of 0.62 for spheres but is explicable in terms of the size and shape polydispersity of the particles, allowing some interstitial packing. The overlapping plateau regions in the centre of the column scans, we feel, demonstrate the colloidally stable nature of the suspension. Influx and efflux of individual sedimenting particles will be balanced and lead to no net change in particle volume fraction in the region of the column centre. This is consistent with no long-range particle connectivity in this system, as indicated by the sedimentation profiles. Figure 2, on the other hand, shows no such overlapping plateau regions, with compression of the total mass of underlying particles occurring from relatively early times. The concentration of added polymer is 1.9 g ml-’ and hence well within the dilute region of polymer solution behaviour. Interestingly, Fig. 2 also shows particle packing at the base of the cell, to the same packing limit as the system containing no added polymer. In fact, for the lowest concentrations of added polymer, the same overall effect was observed as seen in Fig. 2. We might interpret this either as coexistence of flocculated and deflocculated phases within the suspension, or alternatively as formation of a very weak homogenous floe phase with a sufficiently weak network struc0.7-
A 0.6
-
0.5
-
0.4
-
8 g
“I:::,, 0 day
i;;,,-_
-ADda”
_
‘G D 2
I 4::
1
40 Height
Imm,
160
:::: I
180
I
1
I
I
200
220
240
260
Fig. 2. Sedimentation of a 40% v/v suspension of flocculated cyanazine particles containing 1.9 g I-’ hydroxyethylcellulose. Volume fraction, @,versus height of column (mm).
130 0.8 -
07-
0.6 -
8 E‘ 0.5 .g
-
8 .e $
0.4 -
>”
0
I
I
20
1 40
1 60
1
SO
1 100
1 120
1 140
180
180
1
1
1
1
200
220
240
260
Height/mm
Fig. 3. Consolidation of a 40% v/v column of flocculated suspension of cyanazine containing 21 g 1-l hydroxyethylcellulose. No dilatant sediment at cell base. Volume fraction, 9, as a function of height of column (mm).
ture (small uniaxial compression modulus), to permit compression of the floe to the packing limit of the particles. Figure 3 shows consolidation of a flocculated suspension containing 21 g 1-l HEC, a polymer concentration well into the semidilute regime. The rate of consolidation is attenuated, but the final packing fraction is expected to approach the close-packed limit given sufficient time. Floe consolidation rates Taking the maximum packing fraction &,, as that obtained at the base of the cell containing the stable suspension with no added polymer, we have expressed the rate of accumulation and consolidation of particles in terms of changes in volume fraction #, at a fixed low level above the cell base. We did not choose the very base of the cell to avoid difficulty in experimental determination of volume fraction values, but we selected a region where the volume fraction undergoes a high rate of change, i.e., 10 mm above the base. The empirical rate equation is expressed as kt= -log(@,,,-@)
(1)
131
where k is an assumed first-order rate for the consolidation of particles. We refer to k as a consolidation rate constant. Figure 4 shows some typical plots of log (g,,, - $) versus time for different polymer concentrations and the fit (linear least squares) is reasonable over quite long time periods, in excess of 100 days. Figure 5 shows a plot of the resultant first-order rate constants as a function of polymer concentration. It can be seen that for concentrations from 1.9 to 26.5 mg ml-’ there is a single power law, determined by geometric regression analysis, describing the relationship between consolidation rate constant and polymer concentration, which goes in inverse proportions to the polymer concentration to the power 3/2. Discontinuities in this power-law relationship are only apparent at polymer concentrations below - 1.9 mg ml-‘, where the consolidation rates become constant. Polymer concentrations below 1.9 g 1-l were not used in the fitting procedure, but are shown in Fig. 5 for completeness. The reason that concentrations of polymer below 1.9 mg ml-’ were not used in the fitting procedure was that observations of the sedimentation velocity of the boundary with the supernatant (tangents to the height/time plot) showed that there was an initial increase in the sedimentation velocity with increasing polymer concentration which maximised and then decreased at concentrations of free polymer - 1.9 mg ml-’ upwards. The sedimentation velocity was measured as the tangent to the boundary movement line after 5 days, and the resultant sedimentation velocities as a function of free polymer concentration
1.0
1
0
I
1
1
25
50
75
I
100 Time
Fig. 4. Determination
of consolidation
1
125
I
150
I
175
I 200
Idays)
rate constants for two levels of added hydroxyethylcellulose.
132
Fig. 5. Consolidation rate constant versus hydroxyethylcellulose 40% v/v cyanazine suspensions.
concentration.
Suspensions were
are shown in Fig. 6. The effect is ascribed to the formation of floes, at low polymer concentration, with no significant self-hindering connectivity, such that the overall effect is to increase the sedimentation velocity in a Stokesian manner for the initial increments in polymer concentration. At higher polymer concentrations the greater degree of flocculation reduces the sedimentation velocity as expected, suggesting that the polymer concentration giving the maximum sedimentation velocity might correspond to a balance between two opposing effects, namely increasing floe size assisting sedimentation and increasing suspension viscosity causing retardation of sedimentation. Our results do not show any obvious critical discontinuities in the consolidation rate constant at any free-polymer concentration, rather a continuous increase in the degree of flocculation from the lowest polymer additions upwards, but we feel that this is not necessarily inconsistent with previous reports [ 121, the time scale of our experiments being very long term compared to the time scale of the microscopic observations. Since the degree of depletion flocculation is a polymer concentration dependent phenomenon [ 171, the consolidation rate constants reflecting the attractive force between the particles, then at low polymer concentrations the rate of assembly and the extent of the connectivity of the floes that result is sufficiently limited that it requires longer time scales to become manifest. Our longer time scales of observation can appreciate this.
0.0
1
0
I
I
I
I
I
I
5
10
15
20
25
30
Polymer
concentration
mglml
Fig. 6. Sedimentation velocity of a 40% v/v cyanazine suspension ethylcellulose. Rate determined after 5 days.
as a function of added hydroxy-
CONCLUSION
We have demonstrated that it is possible to quantify a rate of sediment formation or floe consolidation for polydisperse industrial suspensions by direct observations on the sediment using ultrasound velocity measurements. Observations on the boundary between the suspension and the supernatant continuous phase give only limited insight into the most significant changes. The first-order rate constant that we determined for floe consolidation is in inverse proportion to the added nonadsorbing polymer concentration to the power 3/2. The rate of boundary subsidence goes approximately with the inverse of the square root of polymer concentration in the same free-polymer concentration range. The functions describing both processes do not appear to have critical discontinuities at any polymer concentration. The above findings mean that it should be possible to predict the likely rate and extent of dilatant sediment formation in long term stored polydisperse suspensions from ultrasound scanning experiments. Direct observation of freeliquid formation in concentrated suspensions is probably a poor guide to dilatant sediment formation.
134 REFERENCES
2 3 4 5 6
8 9 10 11 12 13 14 15 16 17
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