Fragmentation and erosion of two-dimensional aggregates in shear flow

We consider single two-dimensional aggregates containing glass particles trapped at a water/oil or water/air interface. Two modes for aggregate break-up are observed: break-up by fragmentation into a few parts and break-up by erosion of single particles. We have studied the critical shear rate for these modes as a function of the aggregate size. Two different particle sizes were used. The smaller particles, with a radius of 65 microm, form aggregates that break up predominantly by erosion at a shear rate between 0.5 and 0.7 s(-1). This value hardly depends on the size of the aggregates. The larger particles, with a radius of 115 microm, form aggregates that break by erosion or by fragmentation. In both modes, the critical shear rate again depends only weakly on the size of the aggregates and ranges between 1.6 and 2.2 s(-1). Also the structural changes inside the aggregate before break-up were studied. The aggregate behavior at the water/air and water/oil interfaces is quite similar. The critical shear rate for break up was also modeled. The model shows in both modes a weak dependence of the critical shear rate on the aggregate size, which is consistent with the experimental observations. The kinetics of the erosion process was also modeled and compared with the experimentally obtained time dependence of the aggregate size. The differences in the large and small particle systems can be attributed to the occurrence of friction forces between the particles, which one expects to be much larger for the large particle system, due to the stronger two-particle interaction.     

Hydrodynamic forces and critical stresses in low-density aggregates under shear flow

The distribution of stresses in rigid colloidal aggregates under a shear flow was investigated numerically for particle-cluster and cluster-cluster aggregates with fractal dimensions ranging from 1.7 to 2.3. stokesian dynamics was used to calculate the hydrodynamic force on each monomer, while the internal intermonomer interactions were calculated by applying force and torque balances on each primary particle. Although the hydrodynamic forces act mainly on the periphery of the clusters, their filamentous structure propagates and accumulates internal stresses toward the inner region of the aggregates, where consequently the most loaded intermonomer bonds are located. The spatial stress distribution, when scaled by the proper power of the radius of gyration, is independent of aggregate size and fractal dimension. This feature has made it possible to identify the most probable locations of bond failure in the structure and to estimate the relationship between shear rate and particle size for the occurrence of restructuring and of breakage.     

Breakage rate of colloidal aggregates in shear flow through stokesian dynamics

We study the first breakage event of colloidal aggregates exposed to shear flow by detailed numerical analysis of the process. We have formulated a model, which uses stokesian dynamics to estimate the hydrodynamic interactions among the particles in a cluster, van der Waals interactions and Born repulsion to describe the normal interparticle interactions, and the tangential interactions through discrete element method to account for contact forces. Fractal clusters composed of monodisperse spherical particles were generated using different Monte Carlo methods, covering a wide range of cluster masses (N(sphere) = 30-215) and fractal dimensions (d(f) = 1.8-3.0). The breakup process of these clusters was quantified for various flow magnitudes (γ), under both simple shear and extensional flow conditions, in terms of breakage rate constant (K(B)), mass distribution of the produced fragments (FMD, f(m,k)), and critical stable aggregate mass (N(c)), defined as the largest cluster mass that does not break under defined flow conditions. The breakage rate K(B) showed a power law dependence on the product of the aggregate size and the applied stress, with values of the corresponding exponents depending only on the aggregate fractal dimension and the type of flow field, whereas the prefactor of the power law relation also depends on the size of the primary particles comprising a cluster. The FMD was fitted by Schultz-Zimm distribution, and the parameter values showed an analogous dependence on the product of the aggregate size and the applied stress similar to the rate constant. Finally, a power law relation between the applied stress and corresponding largest stable aggregate mass was found, with an exponent value depending on the aggregate fractal dimension. This unique and detailed analysis of the breakage process can be directly utilized to formulate a breakage kernel used in solving population balance equations.     

Aggregation of break-up of clay flocs in turbulent flow

Flocculated clay particles make up the suspended matter found in the waters of river estuaries, and their properties are strongly influenced by the flow field in which they find themselves. The size distribution of the clay flocs is determined by an equilibrium between the general tendency of the flow to enhance aggregation and break-up are investigated and expressions for the size distribution of the flocs are obtained.     

Proteins in a shear flow

The conformational dynamics of a single protein molecule in a shear flow is investigated using Brownian dynamics simulations. A structure-based coarse grained model of a protein is used. We consider two proteins, ubiquitin and integrin, and find that at moderate shear rates they unfold through a sequence of metastable states-a pattern which is distinct from a smooth unraveling found in homopolymers. Full unfolding occurs only at very large shear rates. Furthermore, the hydrodynamic interactions between the amino acids are shown to hinder the shear flow unfolding. The characteristics of the unfolding process depend on whether a protein is anchored or not, and if it is, on the choice of an anchoring point.     

Disruption of polystyrene latex aggregates in capillary flow

 Disruption of polystyrene latex aggregates, formed in 1 M citric acid/phosphate buffer solution at pH 3.8 through diffusion-limited colloid aggregation (DLCA) and in 0.2 M NaCl solution at pH 5.5 through reaction-limited colloid aggregation (RLCA), was studied with respect to aggregate size and fractal nature. This was achieved using small-angle laser scattering in conjunction with a specially designed sampling method, which brought about the elimination of the disruption of the aggregates caused by a commercial stirrer sample unit. Aggregations were carried out in a mixture of deuterium oxide and water instead of water alone as a solvent to minimise sedimentation resulting from the differences in density between the latex particles and the electrolytes. An initial “steady state” in terms of aggregate size and fractal dimension was found to occur after around 20 min and 2 days for DLCA and RLCA aggregates, respectively, at 25 °C. No aggregate disruption was detected for DLCA and RLCA aggregates after their passing through a capillary tube for shear rates up to 1584 and 2694 s⁻¹, respectively. At higher shear rates, significant decreases in the aggregate volume-mean diameter, D[4, 3], occurred after shearing. The degree of reduction in D[4, 3] was larger for DLCA aggregates in comparison to RLCA aggregates. The results would suggest that DLCA aggregates were more subject to disruption during shearing. A high degree of disruption was observed in turbulent flow for both aggregates. Received: 30 June 1999 Accepted in revised form: 11 November 1999     

Dynamics of attractive vesicles in shear flow

A nonequilibrium molecular dynamics (NEMD) method is employed to study the dynamics of two identical vesicles with attractive interactions immersed in shear flow. The dynamics behaviors of attractive vesicles depend on the attractive interactions and the shear rates simultaneously. There are four motion types for attractive vesicles in shear flow: a coupled-tumbling (CTB) motion, a coupled-trembling (CTR) motion, a collision/rotation mixture (CRM) motion and a separated-tank-treading (STT) motion, which are determined by the competition between the shear flow and the attractive interactions. Furthermore, the dynamics behavior of an individual vesicle shows three main motion types such as tumbling, trembling and tank-treading motions, and relies mainly on the shear rates. Meanwhile, comparisons with rigid vesicles for the dynamics behaviors are made, and the collision/rotation mixture (M) motion isn’t observed for rigid vesicles.     

Perturbation expansion of polymers in shear flow

The effect of shear flow on the excluded volume properties of bead spring chains is calculated via the perturbation expansion of the mean-square end-to-end distance with respect to the excluded volume parameter z. The coefficient of the series 〈R²〉/〈R²〉₀ = 1 + C₁ · z − … vanishes for large flow rates but shows a strong dependence on the shear rate in the intermediate regime.     

Normal stress and shear stress in a viscoelastic liquid under oscillatory shear flow

Normal stress and shear stress of concentrated polystyrene solutions in a chlorinated diphenyl were measured under steady flow and oscillatory shear flow in a Weissenberg rheogoniometer. The normal stress difference was observed to oscillate at double the frequency of the applied shear strain with amplitude proportional to the square of the applied amplitude, while the shear stress was found to oscillate at the same frequency with amplitude proportional to the applied amplitude. A theoretical relation between the displacement of the oscillatory normal stress difference from zero level and the dynamic modulus derived by Lodge and other investigators was confirmed experimentally, and the theoretical predictions of Coleman and Markovitz concerning the relation among steady-flow normal stress difference and dynamic modulus were also confirmed. However, the theoretical predictions of Lodge, of Spriggs, Huppler and Bird, and of Williams on the relation between the amplitude and phase of oscillatory normal stress and those of oscillatory shear stress did not agree with experimental results.     

Stability of two-dimensional crystalline aggregates of a protein studied by molecular dynamics

Two-dimensional protein (ferritin) aggregates with a square lattice symmetry, which were formed within a thin liquid layer on a mercury surface, were studied by molecular dynamics (MD) simulation. For the simulation, the ferritin molecule was modeled by an assembly of 49 spheres, and the intermolecular interactions were given by simple formulae. During the simulation, molecules were confined within a layer, which corresponds to the thin liquid layer. An annealing MD simulation was done starting from a random molecular configuration within the layer, and aggregates with the square lattice symmetry were also obtained. To study the stability of aggregates, dissociation processes of the aggregates were analyzed using MD simulations at room temperature. Interactions between the nearest-neighbor molecules were regarded as bonds. Mean bond energies and correlation coefficients between the bond energies were calculated from the MD trajectories. A decay profile according to the dissociation was obtained, yielding a dissociation rate constant. Buried bonds were stronger than peripheral bonds. The larger the aggregate size, the stronger the bond for each of the buried and peripheral bonds. A simple theoretical account, which is applicable to a general bonded network, was introduced to analyze the dynamics of the aggregates. © 1994 by John Wiley & Sons, Inc.     

Oscillatory shear flow of polymeric systems

On the basis of the Leonov viscoelastic constitutive equation, oscillatory shear flow of elastic fluids in the linear and nonlinear regimes has been considered. The Fourier components and associated phase angles of the shear and normal components of the elastic strain tensor have been found as functions of frequency and deformation amplitude in the range usually employed in experiment, and are presented in a form convenient for further rheological applications. In the linear case, the results correspond to many known theories. In the nonlinear case, the theoretical results have been compared with experiments, on different polymeric systems, with very good agreement being obtained for the shear stress in polymeric solutions but only qualitative agreement for the shear stress and first normal-stress difference in polymer melts.     

Prediction of three-dimensional fractal dimensions using the two-dimensional properties of fractal aggregates

Fractal dimension analysis using an optical imaging analysis technique is a powerful tool in obtaining morphological information of particulate aggregates formed in coagulation processes. However, as image analysis uses two-dimensional projected images of the aggregates, it is only applicable to one and two-dimensional fractal analyses. In this study, three-dimensional fractal dimensions are estimated from image analysis by characterizing relationships between three-dimensional fractal dimensions (D(3)) and one (D(1)) and two-dimensional fractal dimensions (D(2) and D(pf)). The characterization of these fractal dimensions were achieved by creating populations of aggregates based on the pre-defined radius of gyration while varying the number of primary particles in an aggregate and three-dimensional fractal dimensions. Approximately 2000 simulated aggregates were grouped into 33 populations based on the radius of gyration of each aggregate class. Each population included from 15 to 115 aggregates and the number of primary particles in an aggregate varied from 10 to 1000. Characterization of the fractal dimensions demonstrated that the one-dimensional fractal dimensions could not be used to estimate two- and three-dimensional fractal dimensions. However, two-dimensional fractal dimensions obtained statistically, well-characterized relationships with aggregates of a three-dimensional fractal characterization. Three-dimensional fractal dimensions obtained in this study were compared with previously published experimental values where both two-dimensional fractal and three-dimensional fractal data were given. In the case of inorganic aggregates, when experimentally obtained three-dimensional fractal dimensions were 1.75, 1.86, 1.83+/-0.07, 2.24+/-0.22, and 1.72+/-0.13, computed three-dimensional fractal dimensions using two-dimensional fractal dimensions were 1.75, 1.76, 1.77+/-0.04, 2.11+/-0.09, and 1.76+/-0.03, respectively. However, when primary particles were biological colloids, experimentally obtained three-dimensional fractal dimensions were 1.99+/-0.08 and 2.14+/-0.04, and computed values were both 1.79+/-0.08. Analysis of the three-dimensional fractal dimensions with the imaging analysis technique was comparable to the conventional methods of both light scattering and electrical sensing when primary particles are inorganic colloids.     

Modelling of shear flow in liquid crystalline materials

The flow behaviour of liquid crystalline polymers (LCPs) is quite complex and these materials exhibit varied and complicated textural patterns when subject to a flow field. The complexity arises from two general factors, the first that they are long chained and thus have long relaxation times, and second that they are liquid crystalline, and thus there is co-operative motion of the molecules. In both thermotropic and lyotropic LCPs subject to low shear flows, it is known that defects and disclinations influence the microstructure and rheology, but it is not clear by what mechanisms these distortions shrink or multiply during flow. In this work, a model is developed to examine the behaviour of defects in shear flows. The simulations based on the model show a spectrum of microstrucural development as a function of applied shear rate: reorientation of domains of different alignment associated with disclinations at low shear strains; the multiplication of wall type defects and the orientation of these normal to the shear gradient axis at intermediate shear rates, and the tendency towards disclination annihilation; the generation of a flow-aligned monodomain at higher shear rates.     

Kinetic analyses of colloidal crystallization in shear flow

Colloidal crystallization kinetics is studied in the shear flow of a suspension of colloidal silica spheres (110 nm in diameter), using a continuously-circulating type of stopped flow cell system. The crystallization rate from a suspension containing a small amount of nuclei and/or single crystals is high compared with that from a suspension containing no nuclei and/or single crystals. Crystal growth takes place at shear rates smaller than 3.4 s^–1 and at sphere concentrations higher than a volume fraction of 0.004.     

Structure parameter of electrorheological fluids in shear flow

A structure parameter, Sn = η(c)γ/τ(E), is proposed to represent the increase of effective viscosity due to the introduction of particles into a viscous liquid and to analyze the shear behavior of electrorheological (ER) fluids. Sn can divide the shear curves of ER fluids, τ/E(2) versus Sn, into three regimes, with two critical values Sn(c) of about 10(-4) and 10(-2), respectively. The two critical Sn(c) are applicable to ER fluids with different particle volume fractions φ in a wide range of shear rate γ and electric field E. When Sn < 10(-4), the shear behavior of ER fluids is mainly dominated by E and by shear rate when Sn > 10(-2). The electric current of ER fluids under E varied with shear stress in the same or the opposite trend in different shear rate ranges. Sn(c) also separates the conductivity variation of ER fluids into three regimes, corresponding to different structure evolutions. The change of Sn with particle volume fraction and E has also been discussed. The shear thickening in ER fluids can be characterized by Sn(c)(L) and Sn(c)(H) with a critical value about 10(-6). As an analogy to friction, the correspondence between τ/E(2) and friction coefficient, Sn and bearing numbers, as well as the similarity between the shear curve of ER fluids and the Stribeck curve of friction, indicate a possible friction origin in ER effect.     

Modelling of shear flow in liquid crystalline materials

The flow behaviour of liquid crystalline polymers (LCPs) is quite complex and these materials exhibit varied and complicated textural patterns when subject to a flow field. The complexity arises from two general factors, the first that they are long chained and thus have long relaxation times, and second that they are liquid crystalline, and thus there is co-operative motion of the molecules. In both thermotropic and lyotropic LCPs subject to low shear flows, it is known that defects and disclinations influence the microstructure and rheology, but it is not clear by what mechanisms these distortions shrink or multiply during flow. In this work, a model is developed to examine the behaviour of defects in shear flows. The simulations based on the model show a spectrum of microstrucural development as a function of applied shear rate: reorientation of domains of different alignment associated with disclinations at low shear strains; the multiplication of wall type defects and the orientation of these normal to the shear gradient axis at intermediate shear rates, and the tendency towards disclination annihilation; the generation of a flow-aligned monodomain at higher shear rates.