Study of fractal flow of inhomogeneous fluids over smooth inclined surfaces and determination of their fractal dimension and university classes

Abstract

Patterns formed by the flow of an inhomogeneous fluid (suspension) over a smooth inclined surface were studied. It was observed that fractal patterns formed. There exists a threshold angle for the inclination above which, global fractal patterns are formed. This angle depends on the particle size of the suspension. We observed that there are two fractal dimensions for these patterns, depending on the area from which the pattern is extracted. If the pattern is taken from the top which only consists of the beginning stages of the pattern forming, one finds two fractal dimensions i.e. 1.35-1.45 and 1.6-1.7, in which the first one is dominant. And if the entire pattern is taken, then fractal dimension 1.6-1.7 is observed. The first fractal dimension belongs to the class of flow of water over an inhomogeneous surface, and the second one corresponds to the river network. This may imply that both universality classes are present. However , disorder is present in the fluid and is transferred to the surface. We have also determined the fractal dimension of the patterns formed below the threshold angle. We find it to be between 1.57 to 1.7.

Keywords

• fractal patterns
• fractal dimension
• universal class
• inhomogeneous fluids