The Effect of Polydispersity in Primary Particle Size on Measurement of the Fractal Dimension of Aggregates

The use of the mass fractal dimension has become a popular method of characterising the structure of aggregates of fine particles. This parameter is often inferred from scattering experiments that exhibit a power law correlation between scattered intensity and the scattering vector. In this paper we demonstrate deviations from this behaviour that occur when the particles making up the aggregate are not monodisperse, even though the aggregate maintains the same fractal structure as observed in the monodisperse case. We have performed light scattering experiments with aggregating colloidal haematite and performed DLCA computer simulations to explain the observed behaviour. The behaviour can influence the determination of the mass fractal dimension, as can other factors such as scattering effects from primary particles.     

A model to describe the settling behavior of fractal aggregates

A model to predict fractal dimension from sedimentating fractal aggregates has been successfully developed. This model was developed using the settling rate and size data of fractal aggregates. In order to test the validity of the model, a purpose-built settling rig, equipped with lens with magnification of 1200x, which can capture images of particles/flocs down to 2 microm in diameter was used. The performance and technique of the settling rig were validated by comparing the measured settling rates of 30- and 50.7-microm standard particles with their theoretical settling rates calculated using Stokes' law. The measured settling rates were within 10% agreement with the calculated Stokes' velocities. The settling rates and sizes of the particles/flocs were analyzed using image analysis software called WiT 5.3. The maximum temperature gradient across the settling column was 0.1 degrees C, which effectively eliminated convective currents due to temperature differences in the settling column. A total of 1000 calcium phosphate flocs were analyzed. Calcium phosphate flocs with fractal dimensions varying from 2.3 to 2.8 were generated via orthokinetic aggregation. Measurements of fractal dimensions, using light scattering, were done simultaneously with the settling experiments and they were found to be constant. The fractal dimensions calculated using the model agreed with those obtained by light scattering to within 12%.     

Evaluation of an empirical traction equation for forestry tires

Variable load test data were used to evaluate the applicability of an existing forestry tire traction model for a new forestry tire and a worn tire of the same size with and without tire chains in a range of soil conditions. The clay and sandy soils ranged in moisture content from 17 to 28%. Soil bulk density varied between 1.1 and 1.4g cm⁻³ with cone index values between 297 and 1418 kPa for a depth of 140 mm. Two of the clay soils had surface cover or vegetation, the other clay soil and the sandy soil had no surface cover. Tractive performance data were collected in soil bins using a single tire test vehicle with the tire running at 20% slip. A non-linear curve fitting technique was used to optimize the model by fitting it to collected input torque data by modifying the coefficients of the traction model equations. Generally, this procedure resulted in improved prediction of input torque, gross traction ratio and net traction ratio. The predicted tractive performance using the optimized coefficients showed that the model worked reasonably well on bare, uniform soils with the new tire. The model was flexible and could be modified to predict tractive performance of the worn tire with and without chains on the bare homogeneous soils. The model was not adequate for predicting tractive performance on less uniform soils with a surface cover for any of the tire treatments.     

Solitary wave solutions to nonlinear evolution equations in mathematical physics

This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.     

Arsen, Antimon, Zinn,

Ohne Zusammenfassung     

The Use of Small Angle Light Scattering to Study Structure of Flocs

In this paper, a new approach using small angle light scattering to study the structure of large micron sized flocs is described. The flocs were made up from uniformly sized, approximately spherical hematite particles, induced to aggregate using 250 mM KCl to ensure that growth was governed by diffusion limited aggregation alone. The fractal dimensions of the hematite aggregates changed from 1.73 to 2.23 ± 0.05 as the aggregation proceeded, indicating that restructuring occurred during aggregation. The fractal dimensions obtained from the small angle light scattering technique are compared with those obtained from the combination of volume fraction and floc size measurement. The steady state fractal dimensions (2.23 ± 0.05) obtained by small angle light scattering are comparable to the fractal dimensions obtained from determining the slope of the relationship between floc volume fraction and floc size (2.09 and 2.14 ± 0.05). The discrepancy between the fractal dimensions obtained by these techniques during the initial stages of aggregation is due to the fact that the latter method measures the average fractal dimensions, whilst the former method measures the fractal dimensions at any particular instant.     

Measurement of Aggregate Fractal Dimensions Using Static Light Scattering

Aggregates formed from colloidal particles will vary in shape according to the aggregation regime prevalent. Compact structures are formed when the aggregation is slow, whilst loose tenuous structures are formed when rapid (or diffusion limited) aggregation prevails. These structures can be fractal in nature, that is, there is a relationship between porosity and the number of primary particles making up the aggregate, and is described by the fractal dimension, d_F. Fractal dimensions of hematite aggregates have been measured experimentally using the static light scattering technique. Fractal dimensions varied with aggregation regimes; for the rapid aggregation regime, d_F was found to be 2.8, whilst for conditions in which aggregation was slow (retardation forces prevail), d_F's of 2.3 were measured. For conditions which lead to aggregation in which both diffusion and retardation forces play a part, structures with fractal dimensions such that 2.3 < d_F < 2.8 were found. The effects of adsorbed fulvic acid, a naturally occuring organic acid, on the kinetics of hematite aggregation and on the resulting structure of hematite aggregates were also investigated. The study of aggregate structure shows that the fractal dimensions of hematite aggregates which are partially coated with fulvic acid molecules are higher than those obtained with no adsorbed fulvic acid. The scattering exponents obtained from static light scattering experiments of these aggregates range from 2.83 ± 0.08 to 3.42 ± 0.1. The scattering exponents of greater than 3 indicate that the scattering is the result of objects that contains pores which are bounded by surfaces with a fractal structure, and can be related only to surface fractal dimension. The high fractal dimensions are due to restructuring within the aggregates, which only occured at low coverage by the organic acid.