Transport and AW ex

Transport and AW ex - Transport You are on a train to NYC You are stirring the milk into your coffee The train and everything in it are moving

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Transport You are on a train to NYC. You are stirring the milk into your coffee. The train and everything in it are moving toward NYC via directed or advective transport As you stir, the milk is moving via turbulent diffusion. This is a random process.
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Flux ( 29 A B B A B A C C v F - - = / / Flux: mass per unit area per unit time (ng/m 2 -day) transfer or exchange velocity (m/day) aka mass transfer coefficient Concentration gradient (ng/m 3 ) Gradient flux law:
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Fick’s First Law One example of a gradient flux law is Fick’s First Law: x C D F x d d - = Relates the diffusive flux (F x ) of a chemical to its concentration gradient (dC/dx) and its molecular diffusion coefficient (D)
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Fick’s Second Law 2 2 x C D t C = The local concentration change with time (dC/dt) due to a diffusive transport process is proportional to the second spatial derivative of the concentration (concentration gradient)
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Turbulent diffusion In contrast to molecular diffusion, which arises due to thermal molecular motions, turbulent diffusion is based on the irregular patterns of currents in water and air. Turbulent vs. laminar flow is defined by the Reynold’s number: d = spatial dimension of the flow system or objects around which the flow occurs (m) v = typical flow velocity η f = dynamic viscosity of the fluid (kg/m-s) ρ f = density of the fluid (kg/m 3 ) For laminar flow Re < 0.1 f f / Re ρ η dv =
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Turbulent diffusion the effect of the turbulent velocity component on the transport of a dissolved substance can be described by an expression which has the same form as Fick’s first law: x C E F x x d d - = the molecular diffusivity (D) is now replaced by the turbulent or eddy diffusion coefficient, E E >>> D
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anisotropy in natural systems, turbulent diffusion is usually anisotropic, meaning that the magnitude of E depends on the direction. horizontal diffusion is usually much greater than vertical diffusion because: 1. natural systems extend horizontally 2. often the system (ocean, atmosphere) is density stratified
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Transport through boundaries (Chapter 19) What is a boundary = surface at which properties of a system change extensively or, discontinuously (interface) air-water interface sediment-water interface epilimnion - hypolimnion (thermocline) stratosphere – troposphere (tropopause) What to boundaries do? 1. control the transport of energy and matter 2. control chemical process triggered by the contact of two systems with different chemical composition
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What is the boundary condition? may be defined by a
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This document was uploaded on 10/25/2011.

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Transport and AW ex - Transport You are on a train to NYC You are stirring the milk into your coffee The train and everything in it are moving

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