Academic literature on the topic 'Flocculated suspension'

<p>A mathematical model for a consolidation process of a highlyconcentrated, flocculated suspension is developed.Thesuspension is treated as a mixture of a fluid and solidparticles by an Eulerian two-phase fluid model.W e characterizethe suspension by constitutive relations correlating thestresses, interaction forces, and inter-particle forces toconcentration and velocity gradients.This results in threeempirically determined material functions: a hystereticpermeability, a non-Newtonian viscosity and a non-reversibleparticle interaction pressure.P arameters in the models arefitted to experimental data.</p><p>A simulation program using finite difference methods both intime and space is applied to one and two dimensional testcases.Numer ical experiments are performed to study the effectof different viscosity and permeability models. The effect ofshear on consolidation rate is studied and it is significantwhen the permeability hysteresis model is employed.</p>

Batch sedimentation is a method that enables us to understand the mechanism of compaction and compression of sedimenting slurry. However, batch settling behaviour is a very complex phenomenon that is not easily described fully by a mathematical model. This causes unrealistically large empirical calculations when the thickener size estimations are required. Channelling, reverse concentration gradients and the initial concentration of the slurry have large effects on batch settling. Existing procedures do not provide clear relationships involving these three significant variables. In this study, batch sedimentation phenomena are examined in detail and possible explanations are given to clarify the complex behaviour using recent theories. Modern research has shown that channelling is an unwanted formation because channels can change the concentration at the bottom and top of the bed by carrying a great amount of flocs upwards. Batch sedimentation tests were performed using flocculated slurry of Calcium Carbonate at various initial concentrations such as 250 g/l, 500 g/l, 750 g/l and 1000 g/l to observe channelling and reverse concentration gradients. Flux plots for the batch system reveal behaviour which can be attributed to the upward flow of solids. In addition, photographic methods were used to observe settling processes, channelling mechanisms and flocs in the channels. One of the purposes of this work was to examine the phenomenological solid-liquid separation theory of Buscall and White (1987), which employs the material properties of the local volume fraction, compressive yield stress Py ()ö and hindered settling function R()ö to identify the material behaviour in batch sedimentation. Stepped-pressure filtration and batch settling tests were used to measure the material characteristics for the flocculated CaCO3 suspension. Experimental data were demonstrated using Height versus Time and Height versus Concentration graphs and displayed the possible region of reverse concentration gradients and channelling in the settling bed. Mathematical predictions adopted from Usher (2002) were performed employing material characteristics of the material and graphical documentations were presented. The results of mathematical predictions were compared to the experimental results and the modes of sedimentation explained by Lester et al. (2005). Fundamental theoretical models and experimental observations highlight that the main driving force for channelling is the high-pressure gradient at the bottom of the bed and the most important factors that cause channelling are high initial concentration of slurry and settling time. The predictions also show that the material and flocculant used for the batch settling tests demonstrate important effect on the settling process. The knowledge and information gained from this study is valuable to maximize the thickening process.

The ability to separate a suspension into its respective solid and liquid constituents is an important requirement in the chemical, wastewater and mineral industries. Typically, separation occurs in open, large diameter tanks known variously as thickeners, settlers or clarifiers. The design and operation of these devices have been based, until recently, on kinematic models and macroscopic mass balances. The problem with these approaches is that consolidation in the bed is not described accurately and consequently, the area required for thickening is often grossly overestimated. Recently, Buscall and White [24] proposed a 1−D phenomenological theory of dewatering that encompasses both sedimentation and consolidation, providing a more solid grounding for understanding, simulating and optimising dewatering in a range of devices, including thickeners. This theory identifies two important rheological parameters; a concentration dependent yield stress, Py (φ) and hindered settling function, R(φ).<br>Despite representing a significant improvement over a kinematical approach, Buscall and White’s dewatering theory involves a number of simplifications so that in practise, simulations often underestimate dewatering in full sized thickeners [97, 153]. One aspect of thickening that is poorly understood is the effect of raking. At the base of the thickener, a rake transports the thickened sediment to the outlet. An additional effect from raking is to increase the average solid concentration in the underflow [33, 46]. Raking introduces normal and shear stresses, which cannot be described within a one-dimensional framework. Therefore, observed differences between predicted and measured thickener underflow concentrations are attributed to the action of the rake.<br>The aim of this thesis is to develop a better understanding of how shear stresses effect compressional dewatering in both pilot and full scale thickening operations. Before attempting to quantify the effect of shear on dewatering, it was considered necessary to first establish that the 1-D model was capable of predicting dewatering in the absence of shear. Up until now, no known studies have been undertaken to validate the model under controlled conditions. To approximate one-dimensional flow with no shear, a tall narrow column with no moving parts was used. Two solid fluxes and several bed heights were studied, and the outputs from the column were compared with the 1-D model predictions. The results show that under ideal conditions, the model predicted the underflow solid concentration to within 10 %.<br>The effect of shear on dewatering was investigated using a Couette shear device. Couette geometry was chosen to provide uniform shear. Since in Couette flow, no normal stresses act in the direction of rotation, the mechanism behind dewatering can investigated. These experiments showed that shear caused dewaterability to improve up to a critical shear rate, beyond which dewaterability was adversely affected. The relationship between this critical shear rate and flocculation conditions was investigated by using different flocculant dosages. The shear modified Py (φ,γ) and R(φ,γ) can be input to the 1−D model, thereby incorporating shear indirectly. As a result, the model predicted an order of magnitude increase in solids flux.<br>The above procedure was used to characterise the dewaterability of a real thickener feed as a function of shear rate. The optimum shear rate was determined by finding the minimum R(φ,γ). Then, Py(φ) and R(φ) were input into the thickener model. The predicted underflow concentration could then be compared against plant data.<br>Even when shear is taken into account, the model still under predicts the performance of the thickener. To understand this result, the pilot column work was revisited since the control over experimental conditions was far greater. To introduce shear, concentric cylinders were installed in the column and rotated at a fixed speed. Thus, the effect of shear and bed height on underflow density were determined at different rates of shear. This showed that the underflow concentration increased with bed height; a result not expected based on the model prediction. The effects of shear on underflow density were secondary to bed height.<br>The bed height dependence can only be explained if dewatering is not steady but changes over time. For a four metre bed height the residence time is eight times longer than a one metre bed. Improvements in dewatering could be related to time dependent restructuring of aggregates which would result in an associated change in R(φ). By fluidizing suspensions for times corresponding to the residence times in the tall column, R(φ) and Py(φ) could be determined, as functions of volume fraction and time. Aggregate properties including structure and density were measured before and after fluidization using focussed beam reflectance measurement (FBRM) and floc density analysis (FDA).

In day to day life we encounter many different materials which are intermediate between crystalline solids and simple liquids that include paints , glues , suspensions, polymers, surfactants, food and cosmetic products and so on. ‘Soft condensed matter’ is an emerging field of science that aims to generalize the flow and various deformation mechanisms in this apparent diverse class of materials from a ‘mesoscopic’ point of view (important length scales for these systems is usually 10nm-1μm) where the actual atomic and molecular details governed by various quantum mechanical laws are not very important. These soft systems are held together by weaken tropic forces and therefore can be perturbed easily (the typical elastic modulus of these materials is many orders of magnitude lower compared to metallic solids). Moreover, very long relaxation times in these systems(∼10−3 to 1 s) have made them ideal candidates to study non-equilibrium physics. The present Thesis is an endeavor to understand linear and non-linear flow behavior and low Reynolds number instabilities in various soft matter systems like suspensions of flocculated carbon nanotubes and carbon black, surfactant gels, colloidal glasses, Langmuir monolayers etc probed mainly by bulk and interfacial rheology, in-situ light scattering, particle image velocimetry(PIV) techniques and Fourier transform rheology. We also use dynamic light scattering techniques for particle sizing and characterization of Brownian systems. Chapter 1 gives a general introduction to soft condensed matter, particularly, the important length and time scales, various interactions and the rich phase behavior emerged from the delicate balance between energy and entropy in these systems. In this context, We describe the detailed phase behavior of two such systems studied in this thesis. We next describe briefly a few important concepts which motivate the main problems studied in the present thesis like the shear-thickening in suspensions of Brownian and non-Brownian particles, non-equilibrium steady state fluctuation relations in driven systems, elasticity driven instabilities in complex fluids, jamming transitions and aging behavior. This is followed by a discussion of the experimental techniques like linear and nonlinear rheology, including the Fourier transform rheology. Chapter 2 discusses the experimental techniques used by us in detail. We first describe the different components and mode of operations of the MCR-300 stress-controlled rheometer (Paar Physica, Germany) and various experimental geometries. Next we discuss the set up for two dimensional rheological measurements. The homebuilt imaging set up for in-situ polarized light scattering and direct imaging studies is described along with the in-situ particle image velocimetry (PIV) to map out the exact spatially resolved velocity profiles in 2D systems. We give a brief account of the techniques of Fourier transform rheology. At the end of this chapter, we briefly describe the angle resolved dynamic light scattering (DLS) set up (Brookhaven Instruments, USA). In Chapter 3, we study colossal discontinuous shear-thickening transition in confined suspensions of fractal clusters formed by multi-wall carbon nanotubes (MWNT) by rheology and in-situ imaging experiments. Monotonic decrease in viscosity with increasing shear stress, known as shear thinning, is a known rheological response to shear flow in complex fluids in general and for flocculated suspensions in particular. In the present experiments we demonstrate a discontinuous shear thickening transition where the viscosity jumps sharply above a critical shear stress by four to six orders of magnitude in flocculated suspensions of MWNT even at very low weight fractions(∼0.5%). Rheo-optical observations reveal the shear-thickened state as a percolated structure of MWNT flocs spanning the system size. We present a dynamic phase diagram of the non-Brownian MWNT dispersions revealing a starting jammed state followed by shear-thinning and shear-thickened states. The present study further suggests that the shear-thickened state obtained as a function of shear stress is likely to be a generic feature of fractal clusters under flow, albeit under confinement. An understanding of the shear thickening phenomena in confined geometries is pertinent for flow controlled fabrication techniques in enhancing the mechanical strength and transport properties of thin films and wires of nanostructured composites as well as in lubrication issues. We try to understand the flow of jammed and shear-thickened states under constant applied strain rate by studying the building up and relaxation of individual stress fluctuation events similar to the flow in dense granular materials. We also characterize the metastable shear thickened states by superposing a small sinusoidal stress component on a steady applied stress as well as by studying the a thermal entropy consuming fluctuations which are also observed for other jammed systems under an applied steady shear stress as described in the next chapter. Chapter 4 reports the study of non-equilibrium fluctuations in concentrated gels and glassy systems(in jammed state), the nature of fluctuations and their systemsize dependence in the framework of fluctuation relation and Generalized Gumbel distribution. In the first part, we show that the shear rate at a fixed shear stress in a micellar gel in a jammed state exhibits large fluctuations, showing positive and negative values, with the mean shear rate being positive. The resulting probability distribution functions (PDFs) of the global power flux to the system vary from Gaussian to non-Gaussian, depending on the driving stress and in all cases show similar symmetry properties as predicted by Gallavotti-Cohen steady state fluctuation relation. The fluctuation relation allows us to determine an effective temperature related to the structural constraints of the jammed state. We have measured the stress dependence of the effective temperature. Further, experiments reveal that the effective temperature and the standard deviation of the shear rate fluctuations increase with the decrease of the systemsize. In the second part of this chapter, we report a universal large deviation behavior of spatially averaged global injected power just before the rejuvenation of the jammed state formed by an aging suspension of laponite clay under an applied stress. The probability distribution function (PDF) of these entropy consuming strongly non-Gaussian fluctuations follow an universal large deviation functional form described by the Generalized Gumbel (GG) distribution like many other equilibrium and non-equilibrium systems with high degree of correlations but do not obey Gallavotti-Cohen Steady State Fluctuation Relation (SSFR). However, far from the unjamming transition (for smaller applied stresses) SSFR is satisfied for both Gaussian as well as non-Gaussian PDF. The observed slow variation of the mean shear rate with system size supports a recent theoretical prediction for observing GG distribution. We also establish the universality of the observations reported in this chapter in the light of other jammed systems under shear. We examine in the first part of Chapter 5, the shear-thinning behavior of a two dimensional yield stress bearing monolayer of sorbitan tristearate at air/water interface. The flow curve (stress vs shear rate) consists of a linear region at low shear stresses/shear rates, followed by a stress plateau at higher values. The velocity profile obtained from particle imaging velocimetry indicates that shear banding occurs showing coexistence of fluidized region near the rotor and solid region with vanishing shear-rate away from the rotor. In the fluidized region, the velocity profile which is linear at low shear rates becomes exponential at the onset of shear-thinning, followed by a time varying velocity profile in the plateau region. At low values of constant applied shear rates, the viscosity of the film increases with time, thus showing aging behavior like in soft glassy three-dimensional (3D) systems. Further, at the low values of the applied stress in the yield stress regime, the shear-rate fluctuations in time show both positive and negative values, similar to that observed in sheared 3D jammed systems. By carrying out a statistical analysis of these shear-rate fluctuations, we estimate the effective temperature of the soft glassy monolayer using the Galavatti-Cohen steady state fluctuation relation. In the second part of this chapter, we study in detail the non-linear viscoelastic behavior of Langmuir monolayers. Under oscillatory shear usually observed in many 3D metastable complex fluids with large structural relaxation times. At large strain amplitudes(γ), the storage modulus (G”) decreases monotonically whereas the loss modulus (G”) exhibits a peak above a critical strain amplitude before it decreases at higher strain amplitudes. The power law decay exponents of G” and G” are in the ratio 2:1. The peak in G” is absent at high temperatures and low concentration of sorbitan tristearate. Strain-rate frequency sweep measurements on the monolayers do indicate a strain-rate dependence of the structural relaxation time. The present study on sorbitan tristearate monolayers clearly indicates that the nonlinear viscoelastic behavior in 2D Langmuir monolayers is very general and exhibits many of the features observed in 3D complex fluids. We report in the first part of Chapter 6 scattering dichroism experiments to quantify the spatio-temporal nematodynamics of shear-thinning worm like micellar gels of surfactant Cetyltrimethylammonium Tosylate (CTAT) in the presence of salt sodium chloride (NaCl) enroute to rheochaos. For shear rates past the plateau onset, we observe a presence of alternating bright and dark‘ intertwined’ birefringent structures along the vorticity direction. The orientational order corresponding to these structures are predominantly oriented at +45deg and−45deg to the flow (v) in the (v,∇v) plane. The orientational dynamics of the nematics especially at the interface between the structures, has a one-to-one correspondence with the temporal behavior of the stress. Experiments show that the spatial motion of the vorticity structures depend on the gap thickness of the Couette cell. We next discuss the random temporal flow behavior of this system at high values of applied shear rate/stress in the framework of elastic turbulence in the second part of this chapter. Here, we study the statistical properties of spatially averaged global injected power fluctuations for the worm-like micellar system described above. At sufficiently high Weissenberg numbers (Wi) the shear rate and hence the injected power p(t) at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (PDF) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian pdf scan be well described by an universal large deviation functional form given by the Generalized Gumbel (GG) distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in-situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence. In Chapter 7, we study the vorticity banding under large amplitude oscillatory shear (LAOS) in a dilute worm-like micellar gel formed by surfactant CTAT by Fourier transform rheology and in-situ polarized light scattering. Under LAOS we found the signature of a non-trivial order-disorder transition of Taylor vortices. In the non-linear regime, higher harmonicde composition of the resulting stress signal reveals that the third harmonic I3 shows a very prominent maximum at the strain value where the number density (nv) of the Taylor vortices is maximum for a wide range of angular frequencies both above and below the linear crossover point. Subsequent increase in applied strain results in distortions of the vortices and a concomitant decrease in nv when I3 also drops very sharply and acts like an order parameter for this order-disorder transition. We further quantify the transition by defining an independent order parameter like quantity from the spatial correlation function of the scattered intensity and equivalently its Fourier transform which essentially captures the non monotonous third harmonic behavior. Lissajous plots indicate an intra-cycle strain hardening for the values of γ corresponding to the peak of I3 similar to that observed for hard-sphere glasses. Our study is an important step forward to correlating the structures developed in the system under LAOS to the appearances of the higher harmonics in the non-linear regime. The Thesis concludes with a summary of the main results and a brief account on the scope of future work as described in Chapter 8.