Interface Science in Drinking Water Treatment G. Newcombe and D. Dixon (editors) 9 2006 Elsevier Ltd. All rights reserved.
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Chapter 4" Practical application of fractal dimension
Bruce Jefferson and Peter R Jarvis
School of Water Sciences, Cranfield University, Bedfordshire, MK43 0AL
1. INTRODUCTION
An understanding of the physical characteristics of particles that exist or are generated in water treatment is important in determining the efficiency, operation and robustness of the separation processes used to remove them. Considerable attention has been traditionally placed on measuring and understanding the significance of particle size and to a lesser extent charge on these processes. However, consideration of aggregate structure has been less well explored due mainly to a lack of appropriate theories to describe complex random structures.
The major change occurred in the mid 1970s with the publication of Mandelbrot's [ 1 ] work on fractal geometry, which provided the required framework from which all the following fractal work is based. The key feature was the identification that aggregate structures exhibit a self similarity such that their character appears constant at different scales of magnification.
Many natural objects exhibit this property such as cauliflowers, trees and lungs. Perhaps the best known example of a natural fractal structure is the coastline of an island such as Great Britain. When the length of the coastline is measured with a fixed length stick a relationship is observed between the size of the measuring stick and the measured property (perimeter of the coastline). This occurs as smaller sized sticks can resolve details that the larger sticks will miss such as bays and inlets (Fig. 1).
~" ~ - 5 No.
i~ 5 ,1
31 N o . E_ 1 j
i ~ - 7
Fig. 1. Coastline of Britain measured by two different length measuring sticks
