Paul Meakin

Effect of aggregation on thermal conduction in colloidal nanofluids

Using effective medium theory the authors demonstrate that the thermal conductivity of nanofluids can be significantly enhanced by the aggregation of nanoparticles into clusters. Predictions of the effective medium theory are in excellent agreement with detailed numerical calculation on model nanofluids involving fractal clusters and show the importance of cluster morphology on thermal conductivity enhancements.

A Simulation Model for Meandering Rivers

A computer model for the dynamics of meandering rivers has been used to study the interplay between the migrating river and the changing sedimentary environment created by the meandering river itself. The model is based on the theory of Ikeda et al. [1981] and is closely related to that proposed by Howard [1983]. Coarser sands, which are often associated with high credibility, are deposited in the point bars formed when the river migrates away from its former bank. Fine-grained material eventually fills the oxbow lakes created by cutoff processes and forms erosion-resistant plugs. In the simulations, geometric forms of individual meanders observed in different natural sedimentary environments have been reproduced by changing the credibility of the corresponding sedimentary materials, such as point bar deposits, flood plain deposits, and oxbow lake deposits. The simulations indicate that the typical meander wavelength is determined mainly by hydraulic factors such as the flow in the channel and the inclination of the underlying flood plain and is independent of the difference in the credibilities of sedimentary deposits. The computational approach permits exploration of long-term changes in the floodplain geology, mediated by the meandering river. As an initial demonstration, the formation of meander belts is investigated using the model. The results suggest that a meander belt will be formed by a rivers own cutoff loops only if the characteristic time of deposition and solidification of an oxbow lake is longer than the typical time that it takes the river to migrate downstream over the distance of a meander-loop wavelength.

Simulations of reactive transport and precipitation with smoothed particle hydrodynamics

A numerical model based on smoothed particle hydrodynamics (SPH) was developed for reactive transport and mineral precipitation in fractured and porous materials. Because of its Lagrangian particle nature, SPH has several advantages for modeling Navier-Stokes flow and reactive transport including: (1) in a Lagrangian framework there is no non-linear term in the momentum conservation equation, so that accurate solutions can be obtained for momentum dominated flows and; (2) complicated physical and chemical processes such as surface growth due to precipitation/dissolution and chemical reactions are easy to implement. In addition, SPH simulations explicitly conserve mass and linear momentum. The SPH solution of the diffusion equation with fixed and moving reactive solid-fluid boundaries was compared with analytical solutions, Lattice Boltzmann [Q. Kang, D. Zhang, P. Lichtner, I. Tsimpanogiannis, Lattice Boltzmann model for crystal growth from supersaturated solution, Geophysical Research Letters, 31 (2004) L21604] simulations and diffusion limited aggregation (DLA) [P. Meakin, Fractals, scaling and far from equilibrium. Cambridge University Press, Cambridge, UK, 1998] model simulations. To illustrate the capabilities of the model, coupled three-dimensional flow, reactive transport and precipitation in a fracture aperture with a complex geometry were simulated.

The structure of fractal colloidal aggregates of finite extent

Abstract The structure of fractal colloid aggregates formed in both the diffusion- and the reaction-limited regimes is studied by static light scattering experiments. The crossover region of the structure factor of the clusters is measured, and the effects of the finite extent of the fractal structure on the scattering are investigated. The polydispersity of the cluster mass distribution markedly changes the shape of the measured scattering intensity. A form for the structure factor obtained from computer-generated clusters is found to describe the colloidal aggregates very well, for both regimes. Other available models for the crossover region are also discussed. In addition, the effects of the optical plasma resonance in the case of metallic colloids and the effects of cluster restructuring on the static scattering are discussed.

The effects of restructuring on the geometry of clusters formed by diffusion-limited, ballistic, and reaction-limited cluster-cluster aggregation.

The effects of simple restructuring mechanisms on the geometry of clusters formed by diffusion‐limited, ballistic, and reaction‐limited cluster–cluster aggregation have been investigated using three‐dimensional off‐lattice models. In these models restructuring is allowed to take place immediately after two clusters have contacted each other, but no subsequent restructuring is allowed. Restructuring takes place in three distinct stages and the process can be stopped after each stage. In the case of diffusion‐limited cluster–cluster aggregation, the fractal dimensionality is increased from about 1.8 to about 2.1 after the first stage. Complete restructuring increases the fractal dimensionality to about 2.2. Similar but somewhat smaller increases in the fractal dimensionality are found for ballistic and reaction‐limited aggregation.

Simple models for heterogeneous catalysis: Phase transition‐like behavior in nonequilibrium systems

A simple model for heterogeneous catalysis, recently introduced by Ziff, Gulari, and Barshad (ZGB), has been explored using computer simulation. This is a nonequilibrium model which exhibits phase transition‐like behavior. The only parameter in this model (Y) sets the ratio with which two reactive species (A and B2) are fed to the surface (lattice). On the square lattice, ZGB found a range of values of this parameter for which steady states with nonzero A and B concentrations occur. Outside of this range, the surface becomes completely covered with A or B sites. The range of Y values corresponding to steady state with nonzero A and B concentrations is bounded by two ‘‘critical’’ values Y1 and Y2. For values of Y close to but above Y1 we have obtained approximate values for the exponents which describe the dependence of the steady‐state densities of A and B sites on (Y−Y1). These exponents both seem to have the same value independent of lattice details. We have extended the work of ZGB to the hexagonal lat...

A Historical Introduction to Computer Models for Fractal Aggregates

It has been known for a century that small particles dispersed in liquids and gases can form aggregates with extraordinarily low densities, and a variety of studies in the 1960s and 1970s, based on conceptual models and computer models, suggested that “anomalous” scaling relationships were associated with the structures of these aggregates. However, the lack of a suitable theoretical framework and the limits of computer technology inhibited the development of a coherent understanding of the structures of these aggregates and the kinetics of their formation. In the 1980s, the popularization of fractal geometry and rapid advances in computer technology removed these barriers to progress. In this review, the early work on fractal aggregates is discussed and the basic particle-cluster and cluster-cluster aggregation models introduced in the 1980s are described. During the 1990s, interest has been focused on the subtle relationships between aggregation, gelation and spinodal decomposition and on the physical behavior of systems containing fractal aggregates. The following papers in this special issue of the Journal of Sol-Gel Science and Technology on “Computer simulations of aggregation and sol-gel processes” describe recent advances in these directions. They are previewed in this introductory contribution.

Universality of fractal aggregates as probed by light scattering

Fractal colloid aggregates are studied with both static and dynamic light scattering. The dynamic light scattering data are scaled onto a single master curve, whose shape is sensitive to the structure of the aggregates and their mass distribution. By using the structure factor determined from computer-simulated aggregates, and including the effects of rotational diffusion, we predict the shape of the master curve for different cluster distributions. Excellent agreement is found between our predictions and the data for the two limiting régimes, diffusion-limited and reaction-limited colloid aggregation. Furthermore, using data from several completely different colloids, we find that the shapes of the master curves are identical for each régime. In addition, the cluster fractal dimensions and the aggregation kinetics are identical in each régime. This provides convincing experimental evidence of the universality of these two régimes of colloid aggregation.

Diffusion-limited aggregation in three dimensions: results from a new cluster-cluster aggregation model

Abstract Diffusion-limited aggregation has been investigated using three-dimensional lattice models in which both particles and clusters can move and stick together. The final state consists of a single cluster or network of occupied lattice sites with a fractal dimensionality of about 1.75. Two versions of the model have been investigated. In Model 1, the cluster diffusion coefficient is independent of cluster size, and in Model 2, only the smallest clusters are allowed to “diffuse.” Both models give final states which are identical within the accuracy of the simulations. However, the cluster size dispersion at intermediate stages is distinctly different for Model 1 and Model 2. The results taken together with more extensive simulations in two dimensions indicate that a fractal dimensionality of ≈ 1.75 will be obtained for all versions of the model in which the diffusion coefficient of small clusters is equal to or greater than the diffusion coefficient for larger clusters. A number of the geometric properties which characterize final state and intermediate clusters are analyzed. Some of these properties should be amenable to measurement in real systems. The results of the simulations are in good agreement with measurements of the fractal dimensionality of metal particle aggregates.

A new model for biological pattern formation

Various non-equilibrium growth models have been used to explore the development of morphology in biological systems. Here we review a class of biological growth models which exhibit fractal structures and discuss the relationship of these models to a variety of other phenomena.