complex fluids
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Agitation of Complex Fluids in Cylindrical Vessels by Newly Designed Anchor Impellers
The fluid flows and power consumption in a vessel stirred by anchor impellers are investigated in this paper. The case of rheologically complex fluids modeled by the Bingham-Papanastasiou model is considered. New modifications in the design of the classical anchor impeller are introduced. A horizontal blade is added to the standard geometry of the anchor, and the effect of its inclination angle (α) is explored. Four geometrical configurations are realized, namely: α = 0°, 20°, 40°, and 60°. The effects of the number of added horizontal blades, Reynolds number, and Bingham number are also examined. The obtained findings reveal that the most efficient impeller design is that with (case 4) arm blades inclined by 60°.This case allowed the most expansive cavern size with enhanced shearing in the whole vessel volume. The effect of adding second horizontal arm blades (with 60°) gave better hydrodynamic performance only with a slight increase in power consumption. A significant impact of Bingham number (Bn) was observed, where Bn = 5 allowed obtaining the lowest power input and most expansive well-stirred region.
<p>A flow phenomena called ‘shear banding’ is often observed for a certain class of complex fluids, namely wormlike micellar solutions. Wormlike micelles are elongated flexible self-assembly structures formed by the aggregation of amphiphiles, which may entangle into a dynamic network above a certain concentration threshold. The entanglement results in the sample having both solid-like (elastic) and liquid-like (viscous) properties, an ambiguity commonly found in complex fluids. Under certain shear conditions, the flow couples with the structure of the micellar network, leading to the formation of (shear) bands with differing viscosity. The principle goal of this work is to address open questions regarding the temporal and spatial stability of shear banded flow. Shear banding is often studied in cylindrical Couette cells, where the fluid is sheared in a gap between differentially rotating concentric cylinders. For the sake of an accurate description of the flow in such a shear cell, the methodology for a 2D Nuclear Magnetic Resonance (NMR) velocimetry technique (known as PGSE-RARE), which offers high temporal and spatial resolution, is improved and refined. Two main challenges are identified and overcome. The first concerns the fact that the velocity imaging process operates on a Cartesian grid, whereas the flow in the Couette cell is of cylindrical symmetry. Numerical calculations and NMR simulations based on the Bloch equations, as well as experimental evidence, give insight on the appropriate selection of the fluid volume over which velocity information is accumulated and the preferred scheme through which the NMR image is acquired in the so-called k-space. The small extent of the fluid gap for the cells in use is the second challenge. In this respect, a variant of the velocimetry technique is developed, which offers ultra high resolution in the gap direction, necessary for a detailed description of the flow profile in the banded state. The refined methodology is applied in a thorough study of a certain wormlike micellar solution (‘10% CPCl’), which is known to exhibit spatiotemporal fluctuations and has been subject of numerous studies over the past 20 years. NMR results are supported by a recently developed 2D Rheo-USV (Ultrasonic Speckle Velocimetry) method, which offers an even higher temporal resolution. The two complementary methods show good agreement for averaged velocity profiles. In line with previous studies the fluid is found to follow a standard anomalous lever rule, which is characterized by a constant shear rate in the high viscosity band and a varying shear rate and proportion of the high shear rate band. In particular, the high resolution NMR variant allows a refined picture on the dynamics of the interface between the two bands. Furthermore, slip is observed for all investigated shear rates. The amount of slip, however, is found to strongly depend on the specifities of the Couette cells in use. Spatially and temporally resolved flow maps reveal various flow instabilities. Ultrasound measurements show vorticity structures in the order of the gap width. In the NMR case no such structures are observed due to the lower resolution in the axial direction. For higher shear rates the occurrence of turbulent bursts is detected for USV. No direct evidence of similar flow instabilities is found in the NMR case. Finally, broad distributions dominate the high shear rate band in temporally and spatially resolved velocity profiles, showing the fluctuative nature of the flow.</p>
<p>A flow phenomena called ‘shear banding’ is often observed for a certain class of complex fluids, namely wormlike micellar solutions. Wormlike micelles are elongated flexible self-assembly structures formed by the aggregation of amphiphiles, which may entangle into a dynamic network above a certain concentration threshold. The entanglement results in the sample having both solid-like (elastic) and liquid-like (viscous) properties, an ambiguity commonly found in complex fluids. Under certain shear conditions, the flow couples with the structure of the micellar network, leading to the formation of (shear) bands with differing viscosity. The principle goal of this work is to address open questions regarding the temporal and spatial stability of shear banded flow. Shear banding is often studied in cylindrical Couette cells, where the fluid is sheared in a gap between differentially rotating concentric cylinders. For the sake of an accurate description of the flow in such a shear cell, the methodology for a 2D Nuclear Magnetic Resonance (NMR) velocimetry technique (known as PGSE-RARE), which offers high temporal and spatial resolution, is improved and refined. Two main challenges are identified and overcome. The first concerns the fact that the velocity imaging process operates on a Cartesian grid, whereas the flow in the Couette cell is of cylindrical symmetry. Numerical calculations and NMR simulations based on the Bloch equations, as well as experimental evidence, give insight on the appropriate selection of the fluid volume over which velocity information is accumulated and the preferred scheme through which the NMR image is acquired in the so-called k-space. The small extent of the fluid gap for the cells in use is the second challenge. In this respect, a variant of the velocimetry technique is developed, which offers ultra high resolution in the gap direction, necessary for a detailed description of the flow profile in the banded state. The refined methodology is applied in a thorough study of a certain wormlike micellar solution (‘10% CPCl’), which is known to exhibit spatiotemporal fluctuations and has been subject of numerous studies over the past 20 years. NMR results are supported by a recently developed 2D Rheo-USV (Ultrasonic Speckle Velocimetry) method, which offers an even higher temporal resolution. The two complementary methods show good agreement for averaged velocity profiles. In line with previous studies the fluid is found to follow a standard anomalous lever rule, which is characterized by a constant shear rate in the high viscosity band and a varying shear rate and proportion of the high shear rate band. In particular, the high resolution NMR variant allows a refined picture on the dynamics of the interface between the two bands. Furthermore, slip is observed for all investigated shear rates. The amount of slip, however, is found to strongly depend on the specifities of the Couette cells in use. Spatially and temporally resolved flow maps reveal various flow instabilities. Ultrasound measurements show vorticity structures in the order of the gap width. In the NMR case no such structures are observed due to the lower resolution in the axial direction. For higher shear rates the occurrence of turbulent bursts is detected for USV. No direct evidence of similar flow instabilities is found in the NMR case. Finally, broad distributions dominate the high shear rate band in temporally and spatially resolved velocity profiles, showing the fluctuative nature of the flow.</p>
<p>Flow properties of a complex fluid depend on not only the characterizations of the components that make up the system but also the interactions between the phases. One of the most significant factors that affect these interactions is the length scale of the dispersed phase. According to Stokes law, the root of complex fluid rheological models, the velocity of a moving particle in a fluid is a function of the viscosity of the fluid and also the size of the moving droplet. The main aim of this research is to understand the crucial elements that define and control the rheological behaviour of complex fluids and thereby provide evidence for proposed modifications of the available rheological models to include parameters that capture the deduced crucial elements. In particular, by adjusting different aspects of Stokes law. The modified models can then be applied to a wider range of complex fluid systems, including emulsions, regardless of the chemicals that form the system. The complex fluids used in this research to develop the above are emulsions with droplets ranging over four orders of magnitude, 10 nm to 100 µm. Within a single base chemical system microemulsions, nanoemulsions and macroemulsions could be formed. The length scale and flow properties of each group were examined and the effect of length scale on rheological properties was investigated. Critical elements there were identified include: • Use of the appropriate viscosity value for the fluid through which the dispersed phase diffuses. It is often assumed that the viscosity of the pure continuous phase fluid can be used as the reference viscosity in the Stokes equation. In a real system the viscosity of the continuous phase can be strongly affected, and thereby defined by, the presence of the dispersed phase itself and the interfacial layer. Hence it is paramount that the appropriate reference viscosity is used. It is noted that the standard assumption is often applicable for highly diluted suspensions that are composed of rigid spheres. However, the research undertaken here demonstrates that this assumption must be reconsidered for more concentrated systems and particularly for emulsions. We recommend that for such systems the viscosity of the pure continuous phase is replaced by the constant viscosity of the sample at a zero shear rate. • Consideration of structural factors that also affect the viscosity. In particular it is often assumed that: 1- the droplets/particles are spherical and non-deformable; and 2- the dispersed phase presents as a single length scale, i.e. the system is a monodisperse system. The inclusion of these assumptions limits dramatically the applicability of the available models to fit and describe the real flow behaviour and thereby does not allow for predictability of behaviours. Typically models have been modified by adding experimental factors rather than explicitly incorporating the above factors into the development of a model. In this work the deviation from these rheological models are explained and correlated to the deviation from spherical structure and monodispersity. • Defining the relative viscosity as the ratio between the sample viscosity and the reference viscosity is common practice in the application of most rheological models. The viscosity of water tends to be taken as the reference viscosity. This leads to no agreement between the well-known rheological models and the experimental data, especially when applied to analysis of microemulsion rheology. In this work, we show that by taking the viscosity of the relevant ternary surfactant solution as the reference viscosity, the existing models can be applicable to microemulsions. This work sheds light on the relationship between the non-Newtonian behaviour of nanoemulsions and their underlying thermodynamic instability. In these systems the Newtonian behaviour is not evident till a shear rate of 100/s is reached. On the other hand the Newtonian viscosity is observed in thermodynamically stable systems, e.g. surfactant solutions and microemulsions, beyond a shear rate of 5/s or less. The Newtonian region also was observed in normal emulsions with narrow size distributions, dilute monodisperse coarse emulsions or dilute normal emulsions prepared in a Warring blender while a short chain alcohol is added to the system. By adding the short chain alcohol to the system not only the densities of the two phases are made similar and the emulsification is eased but also the polydispersity of the final emulsion is decreased. Finally a single model to be applicable to different types of emulsions with droplet sizes over five orders of magnitude was proposed. However the relationship is applicable to the systems with a low degree of polydispersity and once polydispersity is introduced the flow behaviour becomes complicated and the proposed model is not applicable.</p>
<p>Flow properties of a complex fluid depend on not only the characterizations of the components that make up the system but also the interactions between the phases. One of the most significant factors that affect these interactions is the length scale of the dispersed phase. According to Stokes law, the root of complex fluid rheological models, the velocity of a moving particle in a fluid is a function of the viscosity of the fluid and also the size of the moving droplet. The main aim of this research is to understand the crucial elements that define and control the rheological behaviour of complex fluids and thereby provide evidence for proposed modifications of the available rheological models to include parameters that capture the deduced crucial elements. In particular, by adjusting different aspects of Stokes law. The modified models can then be applied to a wider range of complex fluid systems, including emulsions, regardless of the chemicals that form the system. The complex fluids used in this research to develop the above are emulsions with droplets ranging over four orders of magnitude, 10 nm to 100 µm. Within a single base chemical system microemulsions, nanoemulsions and macroemulsions could be formed. The length scale and flow properties of each group were examined and the effect of length scale on rheological properties was investigated. Critical elements there were identified include: • Use of the appropriate viscosity value for the fluid through which the dispersed phase diffuses. It is often assumed that the viscosity of the pure continuous phase fluid can be used as the reference viscosity in the Stokes equation. In a real system the viscosity of the continuous phase can be strongly affected, and thereby defined by, the presence of the dispersed phase itself and the interfacial layer. Hence it is paramount that the appropriate reference viscosity is used. It is noted that the standard assumption is often applicable for highly diluted suspensions that are composed of rigid spheres. However, the research undertaken here demonstrates that this assumption must be reconsidered for more concentrated systems and particularly for emulsions. We recommend that for such systems the viscosity of the pure continuous phase is replaced by the constant viscosity of the sample at a zero shear rate. • Consideration of structural factors that also affect the viscosity. In particular it is often assumed that: 1- the droplets/particles are spherical and non-deformable; and 2- the dispersed phase presents as a single length scale, i.e. the system is a monodisperse system. The inclusion of these assumptions limits dramatically the applicability of the available models to fit and describe the real flow behaviour and thereby does not allow for predictability of behaviours. Typically models have been modified by adding experimental factors rather than explicitly incorporating the above factors into the development of a model. In this work the deviation from these rheological models are explained and correlated to the deviation from spherical structure and monodispersity. • Defining the relative viscosity as the ratio between the sample viscosity and the reference viscosity is common practice in the application of most rheological models. The viscosity of water tends to be taken as the reference viscosity. This leads to no agreement between the well-known rheological models and the experimental data, especially when applied to analysis of microemulsion rheology. In this work, we show that by taking the viscosity of the relevant ternary surfactant solution as the reference viscosity, the existing models can be applicable to microemulsions. This work sheds light on the relationship between the non-Newtonian behaviour of nanoemulsions and their underlying thermodynamic instability. In these systems the Newtonian behaviour is not evident till a shear rate of 100/s is reached. On the other hand the Newtonian viscosity is observed in thermodynamically stable systems, e.g. surfactant solutions and microemulsions, beyond a shear rate of 5/s or less. The Newtonian region also was observed in normal emulsions with narrow size distributions, dilute monodisperse coarse emulsions or dilute normal emulsions prepared in a Warring blender while a short chain alcohol is added to the system. By adding the short chain alcohol to the system not only the densities of the two phases are made similar and the emulsification is eased but also the polydispersity of the final emulsion is decreased. Finally a single model to be applicable to different types of emulsions with droplet sizes over five orders of magnitude was proposed. However the relationship is applicable to the systems with a low degree of polydispersity and once polydispersity is introduced the flow behaviour becomes complicated and the proposed model is not applicable.</p>
<p>This thesis reports the use of Rheo-NMR, that is, a class of techniques within the realm of magnetic resonance which are both confirmatory and complementary to rheometric experiments on materials which can best be classified as complex fluids. The physical properties of such fluids are both hybrid and, in general, vaguely defined. In displaying characteristics attributable to both ideal fluids and elastic solids, the term `complex fluid', in a very real sense, epitomises all the fluids with which every human deals with (and is comprised of) daily. With a multitude of potential candidates for further research then, here we confine ourselves to fluids of molecules and aggregates which are either linear polymers or at least maintain the curvilinear one-dimensional topology of linear polymers. Magnetic resonance is an ideal research tool in this regard, as it is in many respects a rather statistical and insensitive tool from a signal-to-samplevolume perspective, precisely the regime in which the dynamics of a macroscopic collection of macromolecules is relevant. Material deformation is the mechanism upon which rheological measurement depends, and the first research presented here reports on a numerical simulation of the NMR signal of sheared polymer melts. Proton NMR relaxation times of such melts have previously been measured experimentally and found to depend on the shear rate applied by a horizontal Couette geometry, presumably due to the alignment of the mean-field boundaries of the space in which the polymer may reside, known as the polymer tube. The restrictions forming the tube are the other polymers in the bulk, around which an exemplar polymer molecule must meander. In diffusing through this tube, whose direction between entanglements is random in equilibrium, at any time, the return-to-origin correlation for a single spin returning to its locally anisotropic environment generates the least NMR transverse relaxation, as the sum contribution from all tube segments is random. When a deformation-related transformation matrix is applied to the coordinates of entanglements in the polymer, tube segments are no longer isotropically distributed, and an enhanced relaxation process results. Here we present the results of a numerical simulation of this procedure, based on the earlier model of Ball, Callaghan and Samulski, in addition to measurements of the transverse NMR relaxation by Cormier. Not only does it demonstrate qualitative agreement, the NMR signal can be simulated quantitavely or conversely, the size of several key polymer physics parameters can be found through fitting to the NMR signal. Proton NMR spectroscopy is inherently simpler than deuteron NMR spectroscopy, in which the nucleus of interest is quadrupolar. However, a large section of this thesis deals with the structures and response of worm-like micellar structures in solution, for which alignment data cannot reasonably be measured with the proton alone. The most used sample in this thesis is that of the BASF nonionic block copolymer Pluronic P105 in aqueous solution (5% w/w), and a small amount of 1-phenylethanol is required to stabilise cylindrical micellar structures. 1-phenylethanol is a small molecule perfectly suited to act also as a deuterated probe molecule to observe alignment, as it resides in the core of the micelle. By using a variety of Rheo-NMR techniques, such as velocimetry, spatially resolved spectroscopy, and diffusometry, many different flow and alignment behaviours were observed for this solution in Couette flow. Following the measured temperature-dependent viscosity of the P105 solution, which shows an elevated viscosity in a temperature region 15K wide centred at 297 K, we use temperature and applied shear rate as independent variables in our experiments, first identifying spectral features through diffusometry, and then observing a range of behaviours including shear-banding and quadrupolar splitting indicating alignment. Finally we present some experimental work performed in the extensional flow geometry known as the semi-hyperbolic converging die. Extensional flow, inherently, is a transient and nite procedure, and such a geometry is designed to produce a constant extension rate along the axis of its constricting pipe, which, compared to the mill geometries, improves the volume and time over which extension occurs. We investigate the flow and alignment measuring capabilities of Rheo-NMR in this geometry.</p>
<p>This thesis reports the use of Rheo-NMR, that is, a class of techniques within the realm of magnetic resonance which are both confirmatory and complementary to rheometric experiments on materials which can best be classified as complex fluids. The physical properties of such fluids are both hybrid and, in general, vaguely defined. In displaying characteristics attributable to both ideal fluids and elastic solids, the term `complex fluid', in a very real sense, epitomises all the fluids with which every human deals with (and is comprised of) daily. With a multitude of potential candidates for further research then, here we confine ourselves to fluids of molecules and aggregates which are either linear polymers or at least maintain the curvilinear one-dimensional topology of linear polymers. Magnetic resonance is an ideal research tool in this regard, as it is in many respects a rather statistical and insensitive tool from a signal-to-samplevolume perspective, precisely the regime in which the dynamics of a macroscopic collection of macromolecules is relevant. Material deformation is the mechanism upon which rheological measurement depends, and the first research presented here reports on a numerical simulation of the NMR signal of sheared polymer melts. Proton NMR relaxation times of such melts have previously been measured experimentally and found to depend on the shear rate applied by a horizontal Couette geometry, presumably due to the alignment of the mean-field boundaries of the space in which the polymer may reside, known as the polymer tube. The restrictions forming the tube are the other polymers in the bulk, around which an exemplar polymer molecule must meander. In diffusing through this tube, whose direction between entanglements is random in equilibrium, at any time, the return-to-origin correlation for a single spin returning to its locally anisotropic environment generates the least NMR transverse relaxation, as the sum contribution from all tube segments is random. When a deformation-related transformation matrix is applied to the coordinates of entanglements in the polymer, tube segments are no longer isotropically distributed, and an enhanced relaxation process results. Here we present the results of a numerical simulation of this procedure, based on the earlier model of Ball, Callaghan and Samulski, in addition to measurements of the transverse NMR relaxation by Cormier. Not only does it demonstrate qualitative agreement, the NMR signal can be simulated quantitavely or conversely, the size of several key polymer physics parameters can be found through fitting to the NMR signal. Proton NMR spectroscopy is inherently simpler than deuteron NMR spectroscopy, in which the nucleus of interest is quadrupolar. However, a large section of this thesis deals with the structures and response of worm-like micellar structures in solution, for which alignment data cannot reasonably be measured with the proton alone. The most used sample in this thesis is that of the BASF nonionic block copolymer Pluronic P105 in aqueous solution (5% w/w), and a small amount of 1-phenylethanol is required to stabilise cylindrical micellar structures. 1-phenylethanol is a small molecule perfectly suited to act also as a deuterated probe molecule to observe alignment, as it resides in the core of the micelle. By using a variety of Rheo-NMR techniques, such as velocimetry, spatially resolved spectroscopy, and diffusometry, many different flow and alignment behaviours were observed for this solution in Couette flow. Following the measured temperature-dependent viscosity of the P105 solution, which shows an elevated viscosity in a temperature region 15K wide centred at 297 K, we use temperature and applied shear rate as independent variables in our experiments, first identifying spectral features through diffusometry, and then observing a range of behaviours including shear-banding and quadrupolar splitting indicating alignment. Finally we present some experimental work performed in the extensional flow geometry known as the semi-hyperbolic converging die. Extensional flow, inherently, is a transient and nite procedure, and such a geometry is designed to produce a constant extension rate along the axis of its constricting pipe, which, compared to the mill geometries, improves the volume and time over which extension occurs. We investigate the flow and alignment measuring capabilities of Rheo-NMR in this geometry.</p>
<p>Shear banding, where a fluid spatially partitions into strain rate or shear bands in steadystate simple shear flow conditions, was first observed in wormlike micelles solutions and has since been observed in many other complex fluids. These solutions have been used extensively to explore the relationship between shear (or stress) banding and microstructure in complex fluids. This relationship is difficult to study because of its dynamic nature and there is still no clear consensus as to how banding relates to microstructural changes in wormlike micelles solutions. In this thesis, the rheology of a number of wormlike micelles solutions is examined using both conventional and novel techniques with the view to developing a better understanding of this relationship. The rheology of three wormlike micelles solutions composed of a surfactant cetylpyridinium chloride (CPCl) and counterion sodium salicylate in water with or without the salt sodium chloride were examined using mechanical rheometry and the rheo-optical techniques: homodyne photo-correlation spectroscopy (PCS), diffusing wave spectroscopy (DWS) and ellipsometry. Rheo-mechanical measurements were largely consistent with the predictions of the reptation-reaction model. While signi cant stress fluctuations were noted in one particular flow geometry, they were generally not observed in most rheomechanical measurements presented here, indicating that these fluctuations are not universal and that they are geometry dependent. Shear induced turbidity was directly observed in the cone-plate and parallel-plate geometries with turbid rings forming in samples that showed a stress plateau. The Poisson-renewal model, which extends the reptationreaction model to include the influence of high frequency modes on the linear rheology, was tested experimentally using mechanical rheometry, DWS microrheology and literature data. In most cases the data fitted the model behaviour quite well, giving a physically reasonable estimate of the average length of the micelles. DWS's spatial sensitivity to shear induced relative motion was then used to probe the flow behaviour of selected wormlike micelles solutions in the cylindrical-Couette, cone-plate and parallel-plate geometries. In the cylindrical-Couette, the 'flow-DWS' measurements were largely consistent with rheo-mechanical measurements and indicated that some wormlike micelles solutions were partitioning into apparently stable high and low strain rate bands in the vicinity of the stress plateau. While measurements in the cone-plate and parallel-plate geometries also suggested shear banding in samples that showed a stress plateau, the interpretation was less clear-cut. Homodyne PCS was combined with ellipsometry to examine the spatial relationship between strain rate and birefringence banding in selected wormlike micelles solutions in a cylindrical-Couette geometry. In contrast to the observations of previous workers, it was found here that the birefringence and strain rate bands did coincide. Furthermore, the high strain rate band was observed to be more turbid than the lower strain rate band suggesting a connection between strain rate, optical anisotropy and turbidity.</p>
