- Email: [email protected]
Neutron, X-ray and light scattering rheo-optical techniques
450
Neutron, X-ray and light scattering rheo-optical techniques Bruce J Ackerson X-ray, neutron and light scattering techniques are used to elucidate the relation between suspension microstructure and macroscopic rheological properties. Refractive index matched samples are used with increasing frequency in a variety of experiments to study microstructure and flow homogeneity. The understanding of shear thickening, shear thinning and flow homogeneity has been advanced by both scattering and nonscattering techniques.
Addresses Department of Physics and Center for Laser Physics, Oklahoma State University, Stillwater, OK 74078, USA; e-mail: [email protected] Current Opinion in Colloid & Interface Science 1996, 1 :450-453
© Current Science Ltd ISSN 1359-0294 Abbreviations bee body centered cubic fcc face centered cubic LDV laser Doppler velocimetry NMRI nuclear magnetic resonance imaging
Introduction This review focuses on the use of scattering techniques to study the microstructure in complex fluid systems subject to shear flow and rheological measurement. The emphasis is primarily on particulate suspensions, but some block copolymer and surfactant systems which spontaneously form micellar or particle-like microstructures will be discussed. Furthermore, attention will be given to concentrated systems which evidence strong liquid-like (colloidal liquid) or crystal-like (colloidal crystal) ordering and can display unusual rheological behavior such as discontinuous shear thinning and shear thickening. Attention will not be given to dilute single particle orientation effects in shear flow nor to rheo-optical studies of fluid mixtures, liquid crystals, polymers, and many block copolymer or surfactant systems.
Colloidal liquids Colloidal liquids offer the best opportunity for a detailed theoretical understanding of microstructure and the relation of microstructure to rheology. The equilibrium microstructure evolves continuously with increasing shear rate and shear thinning is observed. Some theoreHcal approaches obtain qualitative agreement with microstructural data [1,2] by approximating hydrodynamic interactions at the pair level at small flow rates [1], or neglecting hydrodynamic interactions and predicting anomalous behavior in the vorticity direction [2]. Simulations either include hydrodynamics and are limited to small sample size [3], or neglect hydrodynamics and show a degree of particle ordering not yet confirmed by experiment [4].
In particular, Yan and Dhont [2] carefully determined the equilibrium order-disorder phase boundary and then performed scattering measurements under shear flow for an equilibrium disordered phase near the phase boundary. Significantly, they found no shear-induced ordering into layers or strings of particles, as seen in a variety [4] but not all [3] simulations. It may be argued that the experimental Peclet number [2] was not sufficiently large, although large values should not be necessary near the phase boundary. Brady revisits this topic in more depth later in this issue. While steady shear fails to induce long range orientational order, shear oscillations have been used to induce fcc crystal or layer ordering in colloidal liquids with long ranged particle interactions [5], similar to earlier work on hard spheres [6]. Oscillations appear to be quite effective in ordering the samples, but simultaneous settling introduces the possibility that the samples are concentrated by settling and then ordered by the shear flow. This, however, may be an advantage in making large dense colloidal crystals by shear processing. A light scattering cell with access to the shear gradient-velocity plane is reported [7]. This cell is similar to those used in the study of e1ectrorheological fluids described below, but insufficient data analysis is given to judge the success of this effort. The two-dimensional small angle detection is similar to earlier works [1,2] and should allow further testing for singular behavior of the long range structure [2]. A stress-optical relation for colloidal suspensions is proposed [8··] which connects the thermodynamic stress to optical dichroism measurements. While this calculation approximates the hydrodynamic and direct particle interactions, experimental results are promising and its potential usefulness should not be underestimated.
Colloidal crystals Rheo-optic studies of equilibrium colloidal crystals were made for colloidal suspensions [9-11,12·], block copolymer melts [13,14] and micellar solutions [15-17,18·,19]. The shear orienting and melting phenomenology of the equilibrium bee and fcc crystal structures was similar to that observed" In earlier cited work for very dilute but strongly interacting dispersions, where particles are arranged to provide the least resistance to the shear flow. This similarity is remarkable given the hydrodynamically dense nature of these systems, especially the melts which have no intervening solvent. Differences observed between the melts and dispersions were attributed to use of oscillatory, rather than steady, shear flow and the transformation of bee spherical micelles to hexagonally packed cylinders with increasing strain amplitude.
Neutron, X-ray and light scattering rheo-optical techniques Ackerson
In dense dispersions a partially oriented (tumbling) polycrystalline structure, observed at the lowest shear rates [10,18-], transforms into a sliding layer structure at larger shear rates. Careful rheological measurements [9,10] indicate this to be accompanied by a discontinuous shear thinning. Further increase in shear rate leads to scattering patterns which may be interpreted as shear melting either via a partial disordering of layers (as proposed for concentrated suspensions) or ordered layers translating with some correlation relative to neighboring layers (as proposed for more dilute suspensions), [20]. This is a distinction which can be checked with more careful scattering studies. 'Even higher shear rates produce an amorphous or shear melted state.
Shear thickening Much of the current work on the connection of microstructure with rheological properties may be traced to the seminal work of Hoffman [21,22], who demonstrated by light diffraction and rheological measurements the correlation between the loss of close packed layer ordering and the onset of shear thickening. This shear thickening transition remains an area of active study. In the work of Chow and Zukoski [23-] a nonequilibrium 'phase diagram' shows the correlation bur not coincidence of the loss of orientationally ordered microstructures with . the onset of stress fluctuations. They hypothesize that these fluctuations are caused by transient cell spanning clusters associated with the ollset of shear thickening at shear rates well above the 'shear melting' transition, as .noted above. Similarly, dichroism studies [24] observed a marked increase in. the time scale of relaxation when samples are sheared above the discontinuous shear thickening transition (bur not at all in continuous shear thickening transitions). This is attributed to the formation of large anisotropic clusters that relax both by disorientation and disintegration. Recent computer simulations [25] suggested that such cluster formation produces a heterogeneous collective microstructure, which should enhance small angle scattering. Bender and Wagner [26] observed such an enhanced small angle scattering in sheared suspensions compared [0 a quiescent sample, and especially for shear rates corresponding to thickening. The work of Chow and Zukoski [27--] further demonstrated the reality of clusters by observing the onset of unstable flow as cell gap size is reduced, with no observable shear thickening at large gap sizes. Presumably, clusters cannot dissipate quickly enough in small gaps compared to the rate of shear-induced formation to avoid jamming the gap. These experiments suggest a connection to recent work-in tribology on the flow of molecules in confined geometries [28].
Nonhomogeneous shear flow A number of recent papers demonstrated nonhomogeneous panicle concentration, spatial variations of microstructure or nonhomogeneous flow in suspensions [29-31,32-,33-40]. Thus one should not assume that the
451
colloidal crystals discussed previously deform homogeneously; indeed some samples appeared heterogeneous during flow [10,31,33]. The scattering techniques discussed above are not suitable for characterizing flow homogeneity but other optical methods revealed nonhomogeneous flow with shear localized in internal slip layers [33,40]. The rheological properties were similar [0 those from other studies [9,10,23-] but were either not detailed enough to disclose discontinuous shear thinning [40] or imposed constant shear rate rather than constant shear stress [33]. For these systems where the shear stress increased weakly, while the shear rate increased by orders of magnitude, the shear viscosity is roughly proportional to the inverse of the shear rate, suggesting unstable flow profiles. These studies point out the importance of equilibrium stress properties, either elastic modulus [23-], osmotic pressure [40], or high frequency storage modulus [33], in obtaining a volume fraction-independent or ionic strength-independent scaling of dynamical (yield) suspension properties. A strong argument for inhomogeneous flow is suggested by this scaling [40]. Clearly more information concerning flow homogeneity needs to be combined with scattering measurements. Recent measurements of homogeneity, some with long histories, include the invasive doping technique to visualize slip zones [40], polarization microscopy [33], ultrasound [34], nuclear magnetic resonance imaging (NMRI) [36,39] and laser Doppler velocity (LOV) [35,37] to quantify homogeneity of flow and particle concentration. Koh er 0/. [35] note that ultrasound cannot distinguish between particle and fluid velocities or give particle concentrations, and that N!\IRI has more limited spatial and temporal resolution than LOV and that NMRI has yet to be shown consistent with other measurement methods. These criticisms must be weighed against the need for index matched samples with LOY. Other methods directly observe microstructure inhomogeneities induced near the cell walls in sheared systems [29,30]. Finally, another study [31] observed nonhomogeneous stick-slip flow of colloidal crystals, while monitoring elastic excitations of the crystals and correlating them with the expected boundary conditions during a stick-slip process. This work is a delightful example of what can be done with these model mesoscopic systems.
Aggregation and shear flow Particle aggregatjon, iriduced either by external fields [41,42-,43-46] or attractive interparticle interactions [47-49], is investigated by scattering in the presence of shear flow. Another study exploited scattering to understand the rheological behavior as albumin colloids collapse into a close packed structure with increasing concentration [50]. Here we will concentrate on field-induced aggregation. When electric fields are activated and particles form chains as in electrorheological suspensions, light scattering studies show a 'two-dimensional' spinodal-like
452
Rheology and rheological techniques
decomposition in the absence of shear [43]. In steady shear, chain size and the chain orientation angle with respect to the field direction increase with shear rate [43]. This is consistent with earlier fragmenting droplet models that also explain power-law behavior of the shear viscosity [44]. Large amplitude oscillatory shear shows extreme nonlinear behavior of field-induced structures as captured serniquantiratively with a simple fragmentation/aggregation model [42"]. While fragmentation is an essential feature in the theoretical explanation of the data (in the absence of slip), others argued that small strain amplitudes lead to nonlinearities based on slight structural rearrangements [45,46], which may not be observable by scattering techniques.
2.
Yan YD, Dhont JKG: Shear-induced structure distortion in nonaqueous dispersions of charged colloidal spheres via light scattering. Physica A 1993, 198:78-107.
3.
Phung T, Brady JF: Structure, diffusion and rheology of colloidal dispersions. Am Inst Phys ConI Proc 1992, 256:391.
4.
Mitchell PJ, Heyes DM, Melrose JR: Brownian-dynamics simulations of model stabilized colloidal dispersions under shear. J Chern Soc Faraday Trans 1995, 91:1975-1989.
5.
Yan YD, Dhont JKG, Smits C, Lekkerker HNW: Oscillatory-shearinduced order In nonaqueous dispersions of charged colloidal spheres. Physica A 1994, 202:68-80.
6.
Ackerson BJ, Pusey PN: Shear-induced order in suspensions of hard spheres. Phys Rev Lett 1988, 61:1033-1036.
7.
Clarke SM, Ottewill RH, Rennie AR: light scattering studies of dispersion under shear. Adv Colloid Interface Sci 1995, 60:95-118.
8.
Conclusions While scattering techniques are valuable for elucidating the connection between suspension microstructure and macroscopic rheological properties, the resolution afforded by neutron scattering must be improved and a greater range of reciprocal space must be investigated to keep pace with theoretical progress. Proposed mechanisms of shear melting have not been examined with sufficient care [IS"], for example, the interdigitated and disordered layer models [20] have similar. scattering patterns in the vorticity-velocity plane. The increased small angle scattering produced by the shear thickening transition [26] is only beginning to be investigated. Light scattering may augment neutron scattering to ascertain whether a preferred length scale exists for these fluctuations, as indicated by the variable cell gap measurements [27""]. Flow in concentrated suspensions can be quite complex and inhomogeneous. Work on inhomogeneous flow emphasizes the necessity of multiple measurements of microstructure, concentration, and velocity profiles [32"] in order to properly characterize and understand the flow process. Furthermore, order induced by cell walls, by' shear-induced diffusion, and by wall slip need to be characterized to avoid misinterpreting scattering and rheological data. While experiments have not demonstrated shear-induced order from an amorphous state, as indicated in simulations, higher shear rates must be used to guarantee their absence. Clearly, theories need to include hydrodynamic interactions and simulations may require more particles to capture the complex behaviors seen in concentrated suspensions at low shear rates. Much remains to be done.
References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: " •"
1.
Bender JW, Wagner NJ: Optical measurement of the contributions of colloidal forces to the rheology of concentrated suspensions. J Colloid Interface Sci 1995, 172:171-184. Optical dichroism is used to distinguish between thermodynamic and hydrodynamic contributions to the stress tensor using a new stress-optical relationship. While the stress-optical relation is 'exact' in the limit of low shear, this paper argues that it is more generally valid. 9.
Chen LB, Ackerson BJ, Zukoski CF: Rheological consequences of microstructural transitions in colloidal crystals. J Rheo/1994, 38:193-215.
10.
Chen LB, Chow MK, Ackerson BJ, Zukoski CF: Rheological and microstructural transitions in colloidal crystals. Langmuir 1994, 10:2817-2829..
11.
Dux C, Versmold H, Reus V, Zemb T, Lindner P: Neutron diffraction from shear ordered colloidal dispersions. J Chem Phys 1996, 104:6369-6374.
Wuerth M, Schwarz J, Culis F, Leiderer P, Palberg T: Growth kinetics of body centered cubic colloidal crystals. Phys Rev E 1995, 52:6415-6423. This is a very clean measurement of crystal growth velocity with well characterized samples, crystals oriented by shear, and measurement made noninvasivelyby light scattering. 12.
13.
Koppi KA, Tirrell M, Bates FS: Epitaxial growth and shearing of the body centered cubic phase in diblock copolymer melts. J
14.
Almdal K, Koppi KA, Bates FS: Dynamically sheared body-centered-cubic ordered diblock copolymer mell Macromolecules 1993, 26:4058-4060.
15.
Linemann R, Lauger J, Schmidt G, Kratzat K, Richtering W: Linear and nonlinear rheology of micellar solutions in the isotropic, cubic and hexagonal phase probed by rheo-small-angle light scattering. Rheol Acta 1995, 34:440-449.
16.
Mortensen K, Talmon Y: Cryo-TEM and SANS microstructural study of pluronic polymer solutions. Macromolecules 1995, 28:8829-8834.
17.
Okamoto S, Saijo K, Hashimoto T: Dynamic SAXS studies of sphere-forming block copolymers under large oscillatory shear deformation. Macromolecules 1994, 27:3753-3758.
Rheo/1994, 38:999-10n
18.
McConnell GA, Lin MY, Gast AP: long range order in polymeric micelles under steady shear. Macromolecules 1995, 28:6754-6764. The scattering results obtained for these hydrodynamically dense suspensions are remarkably similar to those observed for dilute colloidal solids undergoing shear flow. As referee of the paper, I should have pointed out that the bcc sample data presented prior to shear melting is consistent with either a model having interlayer centering or degradation of order within a layer. 19.
Raspaud E, Adam M, Lairez L: Dilute and semi-dilute properties of triblock copolymers in a selective solvenl Polym Prepr 1994, 30:580.
20.
Hoffman RL: Interrelationships of particle structure and flow in concentrated suspensions. MRS Bull 1991, 16:32-37.
21.
Hoffman RL: Discontinuous and dilatant viscosity behavior in concentrated suspensions. I. Observations of a flow instability. Trans Soc Rheo/1972, 16:155-173.
of special interest of outstanding interest Wagner NJ, Russel WS: Nonequilibrium statistical mechanics of concentrated colloidal dispersions: hard spheres in weak flows with many-body thermodynamic interactions. Physica A 1989, 155:475-518.
Neutron, X-ray and light scattering rheo-optical techniques Ackerson
22.
Hoffman RL: Discontinuous and dilatant viscos ity behavior in concentrated suspensions. II. Theory and experimental tests. J Collo id Interface Sci 1974, 46:491-506.
23.
Chow MK, Zukoski CF: Nonequilibrium behavior of dense suspensions of uniform particles: volume fraction and size dependence ·of rheology and microstructure. J Rheo/1995, 39:33-59. This paper summarizesprevious work on discontinuous shear thinning and the scaling of properties on the elastic modulus, and extends the work to include shear thickening, a nonequilibrium phase diagram, and a scaling of the shear rate by the equilibrium modulus divided by the continuous phase viscosity. . 24.
D'Haene P, Mewis J, Fuller GG : Scattering dichroism measurements of f1ow·induced structure of a shear thickening suspension. J Colloid Interface Sci 1993, 56:350-358.
25.
Boersma WH, Laven J, Stein HN: Computer simulations of shear tl)ickeningof concentrated dispersions. J Rheo/1995, 39:841-860.
26.
Bender JW, Wagner NJ: Structure and rheology relations in colloidal suspensions: shear thinning and shear thickening properties of dense suspensions [pre print]. AIChE Int Part Tech Forum, Denver, 1994.
27. ••
Chow MK, Zukoski CF: Gap size and shear history dependencies in shear thickening of a suspension ordered at rest J Rheo/1995, 39:15-32. This paper demonstrates that reducing shear cell gap size can produce shear thickening as well as a reduction in the shear rate for the onset of the thickening transition. The thickening results from particle aggregates which span the cell gap and transfer momentum before dissipating. 28.
Idziak SHJ, Safinya CR, Sirota EB, Bruinsma RF, Liang KS, Israelachvili IN: Structure of complex fluids under flow and confinement X-ray couette shear cell and the X-ray surface forces apparatus. ACS Symp Ser 1994,587:288-299.
29.
Brown ABD, Ball RC, Clarke SM, Melrose J, Rennie AR: Model hard sphere systems under flow, a novel experimental approach. Trends Colloid Interface Sci 1995, 98:99-102.
30.
Hamilton WA, Butler PD, Baker SM, Smith GS, Hayter JB, Magid U, Pynn R: Shear Induced helli!lgonal ordering observed in an Ionic viscoelastic fluid in flow past a surface. Phys Rev Lett 1994,72:2219-2222.
31.
Palberg T, Streicher K: Resonant stick-slip motion In a colloidal crystal. Nature 1994, 367:51-54.
32.
Palberg T, Wurth M: Multiphase coexistence and non·linear rheology of colloidai 'dispersions as observed in a model capilJary viscometer. J Phys 11996,6:237-244 . This paper presents a wealth of data for the nonhomogeneousflow of a well characterized sample. Much is to be leamed by a detailed analysis of these data
453
35.
Koh CJ, Hookham P, leal lG: An experimental investigation of concentrated suspension flows in a rectangular channel. J Fluid Mech 1994, 266:1-32.
36.
Corbell AM, Phillips RJ, Kauten RJ, McCarthy KL: Magnetic resonance imaging of concentration and velocitY profiles of pure fluids and solid suspensions In rota ting geometries. J Rheo/1995, 39:907-924.
37.
Jana SC, Kapoor B, Acrivos A: Apparent wall slip velocity coefficients In concentrated suspensions of noncolloidal particles. J Rheo/1995, 39:1123-1132.
38.
Mills P, Snabre P: Rheology and structure of concentrated suspensions of hard spheres: shear induced particle migration. J Phys 111995, 5:1597-1608.
39.
Mondy LA, Brenner H, Altobelli SA, Abbott JR, Graham AL: Shearinduced particle migration in suspensions of rods. J Rheol 1994, 38:444-452.
40 .
Persello J, Magnin A, Chang J, Piau JM, Cabane B: Aow of colloidal aqueous silica dispersions. J Rheo/1994, 38:1845-1870.
41.
Dikanskii YI, Achkasova EA, Polikhronidi NG: Diffraction lightscattering by structured magnetic liquids in sheaf flow. Colloid J 1995, 57:113-116.
42.
Martin JE, Odinek J: A light·scattering study of the nonlinear dynamics ~f electrorheological fluids in oscillatory shear. J Rheo/1995, 39:995-1009. A simple fragmentation/aggregation model is used to give a semiquantitative explanation of large amplitude shear oscillation measurements on an alectrorheological fluid. A stress-optical connection is suggested. 43.
Martin JE, Odinek J: Light scattering stud ies of the electrorheological transition. J Non'Cryst Solids 1994, 172-174:1135-1141.
44.
Martin JE, Odinek J, Halsey TC: Structure and electrorheological fluid in steady shear. Phys Rev E 1994, 50:3263-3266.
45 .
Parthasarathy M, Klingenberg DJ: A microstructural investigation of the nonlinear response of electrorheological suspensions. I. Start-up of steadyshear flow. Rheol Acra 1995,34:417-429.
46.
Parthasarathy M, Klingenberg DJ: A microstructural investigation of the nonlinear response of eleetrorheological suspensions. II. Oscillatory shear flow. Rheol Acta 1995, 34:430-439. .
47.
Hamano K, Ishii T, Ozawa M, Senqers N, Krall AH: Critical·point rheology of a sheared phase-separating micellar solution. Phys Rev E 1994, 51:1254-1262.
48.
Dhont JKG, Verduin H: The effect of shear·f1ow on critical correlations In colloidal systems; microstructure, turbidity and dichroism. J Chern Phys 1994, 101:6 193- 6205.
33.
Imhof A, Van Blaaderen A, Dhont JKG: Shear melting of colloidal crystals of charged spheres studied with rheology and polarizing microscopy. Langmuir 1994, 10:3477-3484.
49.
Muzny CD, Hansen D, Straly GC, Evans DJ, Hanley HJM: Simulation and sans studies of gelation under shear. Int J Thermophys 1995, 16:337-346.
34.
Kytomaa HK, Corrington SW: Ultrasonic imaging velocimetry of transient liquefaction of coheslonless part iculate med ia. Int J Multiphase FlolV 1994, 20:915-926.
50.
Inoue H, Matsumoto T: Viscoelastic and SAXS studies of the structural transition in concentrated aqueous colloids of ovalbumin and serum albumins. J Rheo/1994, 38 :973-984.
Neutron, X-ray and light scattering rheo-optical techniques Bruce J Ackerson X-ray, neutron and light scattering techniques are used to elucidate the relation between suspension microstructure and macroscopic rheological properties. Refractive index matched samples are used with increasing frequency in a variety of experiments to study microstructure and flow homogeneity. The understanding of shear thickening, shear thinning and flow homogeneity has been advanced by both scattering and nonscattering techniques.
Addresses Department of Physics and Center for Laser Physics, Oklahoma State University, Stillwater, OK 74078, USA; e-mail: [email protected] Current Opinion in Colloid & Interface Science 1996, 1 :450-453
© Current Science Ltd ISSN 1359-0294 Abbreviations bee body centered cubic fcc face centered cubic LDV laser Doppler velocimetry NMRI nuclear magnetic resonance imaging
Introduction This review focuses on the use of scattering techniques to study the microstructure in complex fluid systems subject to shear flow and rheological measurement. The emphasis is primarily on particulate suspensions, but some block copolymer and surfactant systems which spontaneously form micellar or particle-like microstructures will be discussed. Furthermore, attention will be given to concentrated systems which evidence strong liquid-like (colloidal liquid) or crystal-like (colloidal crystal) ordering and can display unusual rheological behavior such as discontinuous shear thinning and shear thickening. Attention will not be given to dilute single particle orientation effects in shear flow nor to rheo-optical studies of fluid mixtures, liquid crystals, polymers, and many block copolymer or surfactant systems.
Colloidal liquids Colloidal liquids offer the best opportunity for a detailed theoretical understanding of microstructure and the relation of microstructure to rheology. The equilibrium microstructure evolves continuously with increasing shear rate and shear thinning is observed. Some theoreHcal approaches obtain qualitative agreement with microstructural data [1,2] by approximating hydrodynamic interactions at the pair level at small flow rates [1], or neglecting hydrodynamic interactions and predicting anomalous behavior in the vorticity direction [2]. Simulations either include hydrodynamics and are limited to small sample size [3], or neglect hydrodynamics and show a degree of particle ordering not yet confirmed by experiment [4].
In particular, Yan and Dhont [2] carefully determined the equilibrium order-disorder phase boundary and then performed scattering measurements under shear flow for an equilibrium disordered phase near the phase boundary. Significantly, they found no shear-induced ordering into layers or strings of particles, as seen in a variety [4] but not all [3] simulations. It may be argued that the experimental Peclet number [2] was not sufficiently large, although large values should not be necessary near the phase boundary. Brady revisits this topic in more depth later in this issue. While steady shear fails to induce long range orientational order, shear oscillations have been used to induce fcc crystal or layer ordering in colloidal liquids with long ranged particle interactions [5], similar to earlier work on hard spheres [6]. Oscillations appear to be quite effective in ordering the samples, but simultaneous settling introduces the possibility that the samples are concentrated by settling and then ordered by the shear flow. This, however, may be an advantage in making large dense colloidal crystals by shear processing. A light scattering cell with access to the shear gradient-velocity plane is reported [7]. This cell is similar to those used in the study of e1ectrorheological fluids described below, but insufficient data analysis is given to judge the success of this effort. The two-dimensional small angle detection is similar to earlier works [1,2] and should allow further testing for singular behavior of the long range structure [2]. A stress-optical relation for colloidal suspensions is proposed [8··] which connects the thermodynamic stress to optical dichroism measurements. While this calculation approximates the hydrodynamic and direct particle interactions, experimental results are promising and its potential usefulness should not be underestimated.
Colloidal crystals Rheo-optic studies of equilibrium colloidal crystals were made for colloidal suspensions [9-11,12·], block copolymer melts [13,14] and micellar solutions [15-17,18·,19]. The shear orienting and melting phenomenology of the equilibrium bee and fcc crystal structures was similar to that observed" In earlier cited work for very dilute but strongly interacting dispersions, where particles are arranged to provide the least resistance to the shear flow. This similarity is remarkable given the hydrodynamically dense nature of these systems, especially the melts which have no intervening solvent. Differences observed between the melts and dispersions were attributed to use of oscillatory, rather than steady, shear flow and the transformation of bee spherical micelles to hexagonally packed cylinders with increasing strain amplitude.
Neutron, X-ray and light scattering rheo-optical techniques Ackerson
In dense dispersions a partially oriented (tumbling) polycrystalline structure, observed at the lowest shear rates [10,18-], transforms into a sliding layer structure at larger shear rates. Careful rheological measurements [9,10] indicate this to be accompanied by a discontinuous shear thinning. Further increase in shear rate leads to scattering patterns which may be interpreted as shear melting either via a partial disordering of layers (as proposed for concentrated suspensions) or ordered layers translating with some correlation relative to neighboring layers (as proposed for more dilute suspensions), [20]. This is a distinction which can be checked with more careful scattering studies. 'Even higher shear rates produce an amorphous or shear melted state.
Shear thickening Much of the current work on the connection of microstructure with rheological properties may be traced to the seminal work of Hoffman [21,22], who demonstrated by light diffraction and rheological measurements the correlation between the loss of close packed layer ordering and the onset of shear thickening. This shear thickening transition remains an area of active study. In the work of Chow and Zukoski [23-] a nonequilibrium 'phase diagram' shows the correlation bur not coincidence of the loss of orientationally ordered microstructures with . the onset of stress fluctuations. They hypothesize that these fluctuations are caused by transient cell spanning clusters associated with the ollset of shear thickening at shear rates well above the 'shear melting' transition, as .noted above. Similarly, dichroism studies [24] observed a marked increase in. the time scale of relaxation when samples are sheared above the discontinuous shear thickening transition (bur not at all in continuous shear thickening transitions). This is attributed to the formation of large anisotropic clusters that relax both by disorientation and disintegration. Recent computer simulations [25] suggested that such cluster formation produces a heterogeneous collective microstructure, which should enhance small angle scattering. Bender and Wagner [26] observed such an enhanced small angle scattering in sheared suspensions compared [0 a quiescent sample, and especially for shear rates corresponding to thickening. The work of Chow and Zukoski [27--] further demonstrated the reality of clusters by observing the onset of unstable flow as cell gap size is reduced, with no observable shear thickening at large gap sizes. Presumably, clusters cannot dissipate quickly enough in small gaps compared to the rate of shear-induced formation to avoid jamming the gap. These experiments suggest a connection to recent work-in tribology on the flow of molecules in confined geometries [28].
Nonhomogeneous shear flow A number of recent papers demonstrated nonhomogeneous panicle concentration, spatial variations of microstructure or nonhomogeneous flow in suspensions [29-31,32-,33-40]. Thus one should not assume that the
451
colloidal crystals discussed previously deform homogeneously; indeed some samples appeared heterogeneous during flow [10,31,33]. The scattering techniques discussed above are not suitable for characterizing flow homogeneity but other optical methods revealed nonhomogeneous flow with shear localized in internal slip layers [33,40]. The rheological properties were similar [0 those from other studies [9,10,23-] but were either not detailed enough to disclose discontinuous shear thinning [40] or imposed constant shear rate rather than constant shear stress [33]. For these systems where the shear stress increased weakly, while the shear rate increased by orders of magnitude, the shear viscosity is roughly proportional to the inverse of the shear rate, suggesting unstable flow profiles. These studies point out the importance of equilibrium stress properties, either elastic modulus [23-], osmotic pressure [40], or high frequency storage modulus [33], in obtaining a volume fraction-independent or ionic strength-independent scaling of dynamical (yield) suspension properties. A strong argument for inhomogeneous flow is suggested by this scaling [40]. Clearly more information concerning flow homogeneity needs to be combined with scattering measurements. Recent measurements of homogeneity, some with long histories, include the invasive doping technique to visualize slip zones [40], polarization microscopy [33], ultrasound [34], nuclear magnetic resonance imaging (NMRI) [36,39] and laser Doppler velocity (LOV) [35,37] to quantify homogeneity of flow and particle concentration. Koh er 0/. [35] note that ultrasound cannot distinguish between particle and fluid velocities or give particle concentrations, and that N!\IRI has more limited spatial and temporal resolution than LOV and that NMRI has yet to be shown consistent with other measurement methods. These criticisms must be weighed against the need for index matched samples with LOY. Other methods directly observe microstructure inhomogeneities induced near the cell walls in sheared systems [29,30]. Finally, another study [31] observed nonhomogeneous stick-slip flow of colloidal crystals, while monitoring elastic excitations of the crystals and correlating them with the expected boundary conditions during a stick-slip process. This work is a delightful example of what can be done with these model mesoscopic systems.
Aggregation and shear flow Particle aggregatjon, iriduced either by external fields [41,42-,43-46] or attractive interparticle interactions [47-49], is investigated by scattering in the presence of shear flow. Another study exploited scattering to understand the rheological behavior as albumin colloids collapse into a close packed structure with increasing concentration [50]. Here we will concentrate on field-induced aggregation. When electric fields are activated and particles form chains as in electrorheological suspensions, light scattering studies show a 'two-dimensional' spinodal-like
452
Rheology and rheological techniques
decomposition in the absence of shear [43]. In steady shear, chain size and the chain orientation angle with respect to the field direction increase with shear rate [43]. This is consistent with earlier fragmenting droplet models that also explain power-law behavior of the shear viscosity [44]. Large amplitude oscillatory shear shows extreme nonlinear behavior of field-induced structures as captured serniquantiratively with a simple fragmentation/aggregation model [42"]. While fragmentation is an essential feature in the theoretical explanation of the data (in the absence of slip), others argued that small strain amplitudes lead to nonlinearities based on slight structural rearrangements [45,46], which may not be observable by scattering techniques.
2.
Yan YD, Dhont JKG: Shear-induced structure distortion in nonaqueous dispersions of charged colloidal spheres via light scattering. Physica A 1993, 198:78-107.
3.
Phung T, Brady JF: Structure, diffusion and rheology of colloidal dispersions. Am Inst Phys ConI Proc 1992, 256:391.
4.
Mitchell PJ, Heyes DM, Melrose JR: Brownian-dynamics simulations of model stabilized colloidal dispersions under shear. J Chern Soc Faraday Trans 1995, 91:1975-1989.
5.
Yan YD, Dhont JKG, Smits C, Lekkerker HNW: Oscillatory-shearinduced order In nonaqueous dispersions of charged colloidal spheres. Physica A 1994, 202:68-80.
6.
Ackerson BJ, Pusey PN: Shear-induced order in suspensions of hard spheres. Phys Rev Lett 1988, 61:1033-1036.
7.
Clarke SM, Ottewill RH, Rennie AR: light scattering studies of dispersion under shear. Adv Colloid Interface Sci 1995, 60:95-118.
8.
Conclusions While scattering techniques are valuable for elucidating the connection between suspension microstructure and macroscopic rheological properties, the resolution afforded by neutron scattering must be improved and a greater range of reciprocal space must be investigated to keep pace with theoretical progress. Proposed mechanisms of shear melting have not been examined with sufficient care [IS"], for example, the interdigitated and disordered layer models [20] have similar. scattering patterns in the vorticity-velocity plane. The increased small angle scattering produced by the shear thickening transition [26] is only beginning to be investigated. Light scattering may augment neutron scattering to ascertain whether a preferred length scale exists for these fluctuations, as indicated by the variable cell gap measurements [27""]. Flow in concentrated suspensions can be quite complex and inhomogeneous. Work on inhomogeneous flow emphasizes the necessity of multiple measurements of microstructure, concentration, and velocity profiles [32"] in order to properly characterize and understand the flow process. Furthermore, order induced by cell walls, by' shear-induced diffusion, and by wall slip need to be characterized to avoid misinterpreting scattering and rheological data. While experiments have not demonstrated shear-induced order from an amorphous state, as indicated in simulations, higher shear rates must be used to guarantee their absence. Clearly, theories need to include hydrodynamic interactions and simulations may require more particles to capture the complex behaviors seen in concentrated suspensions at low shear rates. Much remains to be done.
References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: " •"
1.
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13.
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18.
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27. ••
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41.
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42.
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