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Hydrodynamics of an ideal aggregate with quadratically increasing permeability
1Civil and Environmental Engineering, University of Hawaii at Manoa, 2540 Dole Street, Honolulu, HI 96822, USA. albertsk@hawaii.edu
Journal of Colloid and Interface Science
|April 20, 2005
Summary
This study reveals hydrodynamic similarity between ideal porous aggregates and solid spheres. Key properties like settling velocity depend solely on permeability prefactor k2, offering insights into diffusion-limited-cluster-aggregation (DLCA) structures.
Area of Science:
- Fluid dynamics
- Porous media physics
- Aggregate science
Background:
- Porous aggregates exhibit complex hydrodynamic behaviors.
- Understanding these behaviors is crucial for various scientific and industrial applications.
- Existing models often simplify aggregate structures and properties.
Purpose of the Study:
- To derive an analytical expression for the stream function in an ideal porous aggregate.
- To investigate the hydrodynamic properties (radius, settling velocity, collection efficiency) of such aggregates.
- To establish hydrodynamic similarity between ideal aggregates and solid spheres.
Main Methods:
- Incorporation of Brinkman and continuity equations.
- Analytical derivation of the stream function.
- Analysis of hydrodynamic properties based on permeability and fractal dimension.
Main Results:
- An analytical expression for the stream function was derived.
- Hydrodynamic properties were found to depend solely on the permeability prefactor k2.
- Hydrodynamic similarity was discovered between ideal aggregates and impermeable solid spheres.
- The fractal dimension (Df) and prefactor (k2) were determined as 5/3 and 0.20, respectively.
Conclusions:
- The study provides a comprehensive understanding of the hydrodynamics of ideal porous aggregates.
- The findings are applicable to aggregates formed in the diffusion-limited-cluster-aggregation (DLCA) regime.
- Hydrodynamic similarity simplifies the prediction of aggregate behavior, analogous to solid spheres.
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