Fractal structure of asphaltene aggregates

A photographic technique coupled with image analysis was used to measure the size and fractal dimension of asphaltene aggregates formed in toluene-heptane solvent mixtures. First, asphaltene aggregates were examined in a Couette device and the fractal-like aggregate structures were quantified using boundary fractal dimension. The evolution of the floc structure with time was monitored. The relative rates of shear-induced aggregation and fragmentation/restructuring determine the steady-state floc structure. The average floc structure became more compact or more organized as the floc size distribution attained steady state. Moreover, the higher the shear rate is, the more compact the floc structure is at steady state. Second, the fractal dimensions of asphaltene aggregates were also determined in a free-settling test. The experimentally determined terminal settling velocities and characteristic lengths of the aggregates were utilized to estimate the 2D and 3D fractal dimensions. The size-density fractal dimension (D(3)) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This relatively low fractal dimension suggests that the asphaltene aggregates are highly porous and very tenuous. The aggregates have a structure with extremely low space-filling capacity.     

Evidence of Shear Rate Dependence on Restructuring and Breakup of Latex Aggregates

Small-angle static light scattering has been used to probe the evolution of aggregate size and structure in the shear-induced aggregation of latex particles. The size of aggregates obtained from the particle-sizing instrument (Coulter LS230) was compared with the size of those obtained with another approach utilizing the Guinier equation on the scattering data. Comparison of the two methods for studying the effects of mixing on the evolution of the aggregate size with time revealed similar trends. The aggregate structures were quantified in terms of their fractal dimensions on the grounds of the validity of Rayleigh-Gans-Debye scattering theory for the fractal aggregates. Analysis of the scattering patterns of aggregates verified that restructuring of the aggregates occurred as the aggregates were exposed to certain shear environments, resulting in a scale-dependent structure that could not be quantified by a fractal dimension. The effect of restructuring on aggregate size was particularly noticeable when the aggregates were exposed to average shear rates of 40 to 80 s(-1), whereas no significant restructuring occurred at lower shear rates. At 100 s(-1), the fragmentation of aggregates appeared to be more significant than aggregate compac-tion. Copyright 2001 Academic Press.     

Investigation of Asphaltene Aggregate Size Distribution Under Aggregation and Breakage Phenomena Using Monte Carlo Simulation

In this article, the aggregation and breakage processes are simulated through Monte Carlo method for asphaltene aggregates under shear-induced petroleum mixtures. The simulation results are verified by the aggregate size distributions of two types of asphaltenes having different fractal dimensions extracted from Iranian crude oil types. The obtained aggregate size distributions are affected by shear rate, toluene to heptane ratios and the oil type. The dynamic evolution of asphaltene aggregates shows an ascendant trend with time until they reach a maximum average diameter and then descent to a steady-state size. The asphaltene fractal dimension affects the aggregation process.     

剪应力下弱作用势胶体颗粒聚团的特点

探讨了不同剪应力下，具有Ｌｅｎｎａｒｄ－Ｊｏｎｅｓ势的胶体颗粒聚团的结构特性，包括簇团的大小分布，径向分布函数，分形维数和原子配位数。研究表明，在弱作用力下，胶体簇团的分布随剪应力的增加而趋向小簇团一边；径向分布函数曲线随剪应力的增加而降低，胡在近程距离内降低得最多；分形维数随剪应力的增加表现为先增加后减小的趋势，其值随模拟条件的不同而在１．９－２．４之间变动。剪应力“场”对分形维数的大小没有太大     

Analysis of the structure of very large bacterial aggregates by small-angle multiple light scattering and confocal image analysis

This work aims at developing a more accurate measurement of the physical parameters of fractal dimension and the size distribution of large fractal aggregates by small-angle light scattering. The theory of multiple scattering has been of particular interest in the case of fractal aggregates for which Rayleigh theory is no longer valid. The introduction of multiple scattering theory into the interpretation of scattering by large bacterial aggregates has been used to calculate the fractal dimension and size distribution. The fractal dimension is calculated from the form factor F(q) at large scattering angles. At large angles the fractal dimension can also be computed by considering only the influence of the very local environment on the optical contrast around a subunit. The fractal dimensions of E. coli strains flocculated with two different cationic polymers have been computed by two techniques: static light scattering and confocal image analysis. The fractal dimensions calculated with both techniques at different flocculation times are very similar: between 1.90 and 2.19. The comparison between two completely independent techniques confirms the theoretical approach of multiple scattering of large flocs using the Mie theory. Size distributions have been calculated from light-scattering data taking into account the linear independence of the structure factor S(q) relative to each size class and using the fractal dimension measured from F(q) in the large-angle range or from confocal image analysis. The results are very different from calculations made using hard-sphere particle models. The size distribution is displaced toward the larger sizes when multiple scattering is considered. Using this new approach to the analysis of very large fractal aggregates by static light multiple scattering, the fractal dimension and size distribution can be calculated using two independent parts of the scattering curve.     

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.     

Estimation of the dynamic size of fractal aggregates

A model is presented for an aggregation act occurring between two aggregates of any mass and fractal dimension. The kinetics of aggregation is also analyzed, as well as some previous works concerning the structure of fractal aggregates. As a result, a generalized curve is derived describing the normalized dynamic radius of clusters of spherical character as dependent on both the aggregate fractal dimension and the space dimension. It is shown how the curve may be utilized to determine the dynamic size of anisotropic aggregates. The obtained dependence can be used to estimate the dynamic size of fractal aggregates, to evaluate the prefactor in mass–radius relation and to model the aggregation kinetics.     

Fractal Morphology and Breakage of DLCA and RLCA Aggregates

Latex aggregates, formed in 1 M McIlvaine buffer solution and 0.2 M NaCl solution, have been characterized in terms of aggregate size distribution and fractal morphology. This was achieved using three sizing techniques (image analysis, laser scattering, and electrical sensing) in which size distributions and fractal properties of the aggregates were measured. Estimates of fractal dimensions were made using the two-slope method based on dimensional analysis and the small-angle light scattering method. Aggregate suspensions were prepared using both water and a mixture of heavy water/ water as the solvent. The latter essentially eliminated sedimentation, which was observed after one day of aggregation when water alone was used as a solvent. Latex aggregates formed by diffusion-limited colloid aggregation (DLCA) and reaction-limited colloid aggregation (RLCA) had fractal dimensions close to 1.8 and 2.1, respectively. As observed through image analysis, DLCA aggregates possessed a loose tenuous structure, whereas RLCA aggregates were more compact. Disruption of both DLCA and RLCA aggregates has been investigated in laminar flow and turbulent capillary flow. The shear forces introduced by a laminar shear device with a shear rate up to 1711 s(-1) were unable to bring about aggregate breakup; shearing facilitates aggregate growth in the case of DLCA. However, latex aggregates were significantly disrupted after passage through a turbulent capillary tube at 95209 s(-1). Copyright 2000 Academic Press.     

Experimental and modeling study of breakage and restructuring of open and dense colloidal aggregates

In this work we present experimental and simulation analysis of the breakage and restructuring of colloidal aggregates in dilute conditions under shear. In order to cover a broad range of hydrodynamic and interparticle forces, aggregates composed of primary particles with two sizes, d(p) = 90 and 810 nm, were generated. Moreover, to understand the dependence of breakage and restructuring on the cluster structure, aggregates grown under stagnant and turbulent conditions, having substantially different initial internal structures with fractal dimension d(f) equal to 1.7 and 2.7, respectively, were used. The aggregates were broken by exposing them to a well-defined elongational flow produced in a nozzle positioned between two syringes. To investigate the evolution of aggregate size and morphology, respectively, the mean radius of gyration, , and d(f) were monitored during the breakup process using light scattering and confocal laser scanning microscopy. It was found that the evolution of aggregates' fractal dimension during breakage is solely controlled by their initial structure and is independent of the primary particles size. Similarly, the scaling of the steady-state vs the applied hydrodynamic stress is independent of primary particle size, however, depends on the history of aggregate structure. To quantitatively explain these observations, the breakage process was modeled using stokesian dynamics simulations incorporating DLVO and contact interactions among particles. The required flow-field for these simulations was obtained from computational fluid dynamics. The complex flow pattern was simplified by considering a characteristic stream line passing through the zone with the highest hydrodynamic stress inside the nozzle, this being the most critical flow condition experienced by the clusters. As the flow-field along this streamline was found to be neither pure simple shear nor pure extensional flow, the real flow was approximated as an elongational flow followed by a simple shear flow, with a stepwise transition between them. Using this approach, very good agreement between the measured and simulated aggregate size values and structure evolution was obtained. The results of this study show that the process of cluster breakup is very complex and strongly depends on the initial aggregate structure and flow-field conditions.     

Layered droplet microstructures in sheared emulsions: finite-size effects

We investigate the influence of confinement on the steady state microstructure of emulsions sheared between parallel plates, in a regime where the average droplet dimension is comparable to the gap width between the confining walls. Utilizing droplet velocimetry, we find that the droplets can organize into discrete layers under the influence of shear. The number of layers decreases from two (at relatively higher shear rates) to one (at lower shear rates), as the drops grow slightly larger due to coalescence. We argue that the layering and overall composition profile may be controlled by the interplay of droplet collisions (which can cause separation of droplet centers in the velocity gradient direction), droplet migration toward the centerline (due to wall effects), and droplet packing constraints. We also study the effects of mixture composition on droplet microstructure, and summarize these results in the form of a morphology diagram in the parameter space of mass fraction and shear rate. We find that formation of strings of the suspended phase (reported earlier by our group in flow-visualization studies on confined emulsions) is observed over a broad composition window. We also find a stable (nontransient) morphology wherein the droplets are arranged in highly ordered pearl-necklace chain structures.     

Numerical simulation and experimental verification of particle coagulation dynamics for a pulsed input

Mathematical simulation of particle coagulation dynamics was carried out using improved sectional modeling techniques for a system with a pulsed input of primary particles. The methodological improvement included the modification of the size density function based on a realistic assumption of particle size distributions, the application of a new and comprehensive curvilinear collision model, and special adjustment for the mass transfer of a doublet of particles that were very different in size. The simulation results demonstrated that the rectilinear model over-predicted the rate of particle coagulation and that the degree of over-prediction increased as the particles increased in size and the system became more heterogeneous. The coagulation rate increased remarkably as the fractal dimension of the particle aggregates decreased. The curvilinear model and the fractal scaling relationship in place of the rectilinear model and the Euclidean sizing geometry are two important modifications to the conventional Smoluchowski modeling approach. However, both modifications, rather than only one of them, should be applied together to produce more accurate and realistic simulations of coagulation dynamics. As indicated by the simulation, the importance of fluid shear rate to particle coagulation is reduced according to the curvilinear model compared to that previously described with the rectilinear model. As particles increased in size, the role of shear rate in coagulation became even less significant according to the curvilinear view of particle collisions. The results of numerical simulations in terms of the evolution of particle size distributions compared reasonably well with the observations of the jar-test coagulation experiments, which suggested the applicability of the modeling system, including the modified curvilinear-fractal approach, established in the present study.     

The scaling behavior of a highly aggregated colloidal suspension microstructure and its change in shear flow

The nature of the network structure and the evolution of structural change in shear flow were investigated for metal particle dispersions in terms of fractal aggregation of colloidal particles. Polymer-stabilized metal particle inks were prepared via a polyvinyl chloride coating dispersed in solvent. The fractal dimension of 1.74 was calculated with the scaling model based on the power law relationship between the elastic modulus and volume fraction. This scaling behavior can be explained by considering the deformable network structure of soft materials. While the elastic property of the floc was dominant, the limit of linearity was found at the inter-floc link, which is relatively weak and brittle. The steady shear results reveal two mechanisms that contribute to the breakdown of the microstructure in metal particle inks at increasing shear rate. Scaling of steady shear viscosity shows that these mechanisms are related to both inter-floc interactions and the elasticity of the floc itself. Further, these results suggest that individual flocs deform with weak inter-floc interactions and rupture into smaller flocs or aggregates at high shear stress, which is associated with the increased shear rate.     

Flocculation kinetics and aggregate structure of kaolinite mixtures in laminar tube flow

Flocculation is commonly used in various solid-liquid separation processes in chemical and mineral industries to separate desired products or to treat waste streams. This paper presents an experimental technique to study flocculation processes in laminar tube flow. This approach allows for more realistic estimation of the shear rate to which an aggregate is exposed, as compared to more complicated shear fields (e.g. stirred tanks). A direct sampling method is used to minimize the effect of sampling on the aggregate structure. A combination of aggregate settling velocity and image analysis was used to quantify the structure of the aggregate. Aggregate size, density, and fractal dimension were found to be the most important aggregate structural parameters. The two methods used to determine aggregate fractal dimension were in good agreement. The effects of advective flow through an aggregate's porous structure and transition-regime drag coefficient on the evaluation of aggregate density were considered. The technique was applied to investigate the flocculation kinetics and the evolution of the aggregate structure of kaolin particles with an anionic flocculant under conditions similar to those of oil sands fine tailings. Aggregates were formed using a well controlled two-stage aggregation process. Detailed statistical analysis was performed to investigate the establishment of dynamic equilibrium condition in terms of aggregate size and density evolution. An equilibrium steady state condition was obtained within 90 s of the start of flocculation; after which no further change in aggregate structure was observed. Although longer flocculation times inside the shear field could conceivably cause aggregate structure conformation, statistical analysis indicated that this did not occur for the studied conditions. The results show that the technique and experimental conditions employed here produce aggregates having a well-defined, reproducible structure.     

Effect of floc structure on the rate of shear coagulation

We derived a mathematical expression for the temporal evolution of the number of particles due to shear coagulation, covering the later stage by expanding the initial stage approximation to take into account the formation of floc structure. In the derivation, it is assumed that flocculation proceeds through binary collisions between identical fractal flocs. The capture efficiency between flocs is calculated on the basis of trajectory analysis, which is determined by viscous hydrodynamic interaction between flocs and van der Waals attractive forces between two primary particles located at colliding points of flocs. The validity of the derived equation was tested by a coagulation experiment using polystyrene sulfate latex particles under conditions of rapid coagulation. The experiment was carried out in a laminar Couette flow generated in the gap between two concentric cylinders. Careful and direct observation of flocculation under microscopy provided the data on the fractal dimension as well as the temporal evolution of number concentration of flocs. The measured rate of coagulation gradually increases in accordance with the formation of the fractal structure of flocs. This behavior agreed very well with the prediction based on the derived equation.     

The effects of confinement on the behavior of water molecules between parallel Au plates of (001) planes

Molecular dynamics simulation is utilized to investigate the behavior of water molecules confined between two Au plates of (001) planes separated by gaps of 24.48, 16.32, 12.24, 11.22, and 10.20 A. The simulation results indicate that the arrangements of the water molecules are dependent on the gap size. For the largest gap size, adsorption of the Au surface creates two permanent water layers in the vicinity of each Au plate. Furthermore, in this case, the gap size is sufficiently large to permit the formation of a central region within which the water molecules are randomly oriented in a similar manner to bulk water molecules. The results indicate that the orientation of the first water layer directly absorbed by the plate surface does not change as the gap size between the two Au plates is reduced. However, the orientations of the O-H bonds in the second water layer parallel to the surface rearrange to form hydrogen bonds between the water layers as the separation between the plates is decreased. Finally, an inspection of the variation of the self-diffusion coefficients with the gap size suggests that the difference between the dynamic properties of the water molecules in the z direction and the x-y plane decreases as the distance between the two Au plates increases.     

具有多体效应的胶体聚团的特征

考察了多体效应（用Ｓｔｕｔｔｏｎ－Ｃｈｅｎ势，ＳＣ）对胶体聚团的影响并与双体（ＬＪ）势下的结果作了比较。研究表明，ＳＣ和ＬＪ势下簇团的性质有其相似的一面，如：随着剪应力的增加，系统里颗粒的平均势能增加，而每个簇团的颗粒数减少；在较强的剪应力场里，簇团沿剪应力方向（Ｘ轴）被明显拉长且其主轴偏离Ｘ轴等。但它们间的差异也是明显的，在剪应力下ＳＣ系统内颗粒排列得更合理，从而使得平均位能比ＬＪ系统低约１－３     

Characterization of fractal particles using acoustics, electroacoustics, light scattering, image analysis, and conductivity

Fractals are aggregates of primary particles organized with a certain symmetry defined essentially by one parameter-a fractal dimension. We have developed a model for the interpretation of acoustic data with respect to particle structure in aggregated fractal particles. We apply this model to the characterization of various properties of a fumed silica, being but one example of a fractal structure. Importantly, our model assumes that there is no liquid flow within the aggregates (no advection). For fractal dimensions of less than 2.5, we find that the size and density of aggregates, computed from the measured acoustic attenuation spectra, are quite independent of the assumed fractal dimension. This aggregate size agrees well with light-scattering measurements. We applied this model to the interpretation of electroacoustic data as well. A combination of electroacoustic and conductivity measurements yields sufficient data for comparing the fractal model of the particle organization with a simple model of the separate primary particles. Conductivity measurements provide information on particle surface conductivity reflected in terms of the Dukhin number (Du). Supporting information for the zeta potential and Du can also be provided by electroacoustic measurements assuming thin double-layer theory. In comparing values of Du from these two measurements, we find that the model of separate solid particles provides much more consistent results than a fractal model with zero advection. To explain this, we first need to explain an apparent contradiction in the acoustic and electroacoustic data for porous particles. Although not important for interpreting acoustic data, advection within the aggregate does turn out to be essential for interpreting electrokinetic and electroacoustic phenomena in dispersions of porous particles.     

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     

Colloidal Fouling of Ultrafiltration Membranes: Impact of Aggregate Structure and Size

A close coupling between the structure and size of hematite flocs formed in suspension and the permeability of the cake that accumulates on ultrafiltration membranes is observed. Specific resistances of cakes formed from flocs generated under diffusion-limited aggregation conditions are at least an order of magnitude lower than those of cakes formed from flocs generated under reaction-limited aggregation conditions. Similar effects are observed whether the aggregation regime is controlled by salt concentration, pH, or added organic anions. This dramatic difference in cake resistance is considered to arise from the size and fractal properties of the hematite assemblages. The ease of fluid flow through these assemblages will be influenced both by the fractal dimension of the aggregates and by their size relative to primary particle size (since, for fractal aggregates, porosity increases as the size of the aggregate increases). The size and strength of aggregates are also important determinants of the relative effects of permeation drag, shear-induced diffusion, and inertial lift and result, in the studies reported here, in relatively similar rates of particle deposition for both rapidly and slowly formed aggregates. The results presented here suggest that control of cake permeability (and mass) via control of aggregate size and structure is an area with scope for further development though the nature and extent of compaction effects in modifying the fractal properties of aggregates generated in suspension requires attention. Copyright 1999 Academic Press.     

Restructuring and break-up of two-dimensional aggregates in shear flow

We consider single two-dimensional aggregates, containing glass particles, placed at a water/air interface. We have investigated the critical shear rate for break-up of aggregates with different sizes in a simple shear flow. All aggregates break-up nearly at the same shear rate (1.8 +/- 0.2 s(-)(1)) independent of their size. The evolution of the aggregate structure before break-up was also investigated. With increasing shear rate, the aggregates adopt a more circular shape, and the particles order in a more dense, hexagonal structure. A simple theoretical model was developed to explain the experimentally observed break-up. In the model, the aggregate is considered as a solid circular disk that will break near its diameter. The capillary and drag force on the two parts of the aggregate were calculated, and from this force balance, the critical shear rate was found. The model shows a weak size dependence of the critical shear rate for the considered aggregates. This is consistent with the experimental observations.