Dispersive mass transfer

# Dispersive mass transfer

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Dispersive mass transfer, in fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

, is the spreading of mass from highly concentrated areas to less concentrated areas. It is one form of mass transfer
Mass transfer
Mass transfer is the net movement of mass from one location, usually meaning a stream, phase, fraction or component, to another. Mass transfer occurs in many processes, such as absorption, evaporation, adsorption, drying, precipitation, membrane filtration, and distillation. Mass transfer is used...

.

Dispersive mass flux is analogous to diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...

, and it can also be described using Fick's first law:

where c is mass concentration of the species being dispersed, E is the dispersion coefficient, and x is the position in the direction of the concentration gradient. Dispersion can be differentiated from diffusion in that it is caused by non-ideal flow patterns (i.e. deviations from plug flow
Plug flow
In fluid mechanics, plug flow is a simple model of the velocity profile of a fluid flowing in a pipe. In plug flow, the velocity of the fluid is assumed to be constant across any cross-section of the pipe perpendicular to the axis of the pipe...

) and is a macroscopic phenomenon, whereas diffusion is caused by random molecular motions (i.e. Brownian motion
Brownian motion
Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...

) and is a microscopic phenomenon. Dispersion is often more significant than diffusion in convection
Convection
Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....

-diffusion problems. The dispersion coefficient is frequently modeled as the product of the fluid velocity, U, and some characteristic length scale, α: