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Chaotic Advection
The field of Chaotic Advection concerns itself with fluid flow, mixing, and turbulence. The two kinds of flows that we are concerned with here are laminar and turbulent flows. Laminar flow is characterized by steady particle motion in which fluid flows in parallel layers with little to no disruptions between the layers. This type of flow has relatively low velocities. Groundwater bears the most resemblance to this kind of flow. Contrary to laminar flow is turbulent flow, in which particles move erraticly in the general direction of the flow. Turbulent flow is more commonly observed in nature, such as in rivers, bodies of water, and wind currents. The problem with laminar flow is that particles mix poorly, and mixing is accomplished rather slowly by Brownian movement and molecular diffusion. Turbulence, in reference to the mixing of groundwater, is not particularly ideal either, for it can result in cellular damage to the organisms required for bioremediation.
Differentiating between these types of flows requires an understanding of viscosity and the Reynolds Number. Viscosity measures a particular fluid’s resistance to flow through a certain boundary. The point at which a fluid flows smoothly through its particular boundary, having relatively little frictional forces acting on it, would be a laminar flow, because fluid flows are viscous. Conversely, the point where a fluid has many frictional forces impeding its flow results in a turbulent flow. The concept of viscosity uses the assumption that in any type of flow there are different velocities present that cause a certain level of shear stress which occurs between the layers of the flow. This measure of shear stress is the viscosity of the flow.
The Reynolds number is the main determinant used in establishing whether a flow is laminar or turbulent. It calculates the ratio of the inertial forces to the viscous forces of a fluid flow. The Reynolds number is a non-dimensional number because it has no units of measurement. The difference between flows can be classified by certain ranges of the number. An Re less than 2000 results in a laminar flow, which means that there are enough viscous forces acting on the flow to cancel out the effects of the inertial forces. An Re between 2000 and 4000 results in a transitional flow, which has the properties of a laminar flow, but it exhibits slight instabilities, as seen in more pronounced turbulent flows. An Re greater than 4000 constitutes a turbulent flow, which means that the inertial forces acting on the flow are significantly greater than the viscous forces (Zoran Savovic).
Differentiating between these types of flows requires an understanding of viscosity and the Reynolds Number. Viscosity measures a particular fluid’s resistance to flow through a certain boundary. The point at which a fluid flows smoothly through its particular boundary, having relatively little frictional forces acting on it, would be a laminar flow, because fluid flows are viscous. Conversely, the point where a fluid has many frictional forces impeding its flow results in a turbulent flow. The concept of viscosity uses the assumption that in any type of flow there are different velocities present that cause a certain level of shear stress which occurs between the layers of the flow. This measure of shear stress is the viscosity of the flow.
The Reynolds number is the main determinant used in establishing whether a flow is laminar or turbulent. It calculates the ratio of the inertial forces to the viscous forces of a fluid flow. The Reynolds number is a non-dimensional number because it has no units of measurement. The difference between flows can be classified by certain ranges of the number. An Re less than 2000 results in a laminar flow, which means that there are enough viscous forces acting on the flow to cancel out the effects of the inertial forces. An Re between 2000 and 4000 results in a transitional flow, which has the properties of a laminar flow, but it exhibits slight instabilities, as seen in more pronounced turbulent flows. An Re greater than 4000 constitutes a turbulent flow, which means that the inertial forces acting on the flow are significantly greater than the viscous forces (Zoran Savovic).
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