Velocity in Response To A Force
In some cases, the average velocity field exists because of a force; for example, the equation might describe the flow of ions dissolved in a liquid, with an electric field pulling the ions in some direction (as in gel electrophoresis). In this situation, it is usually called the drift-diffusion equation or the Smoluchowski equation, after Marian Smoluchowski who described it in 1915 (not to be confused with the Einstein–Smoluchowski relation or Smoluchowski coagulation equation).
Typically, the average velocity is directly proportional to the applied force, giving the equation:
where is the force, and characterizes the friction or viscous drag. (The inverse is called mobility.)
Read more about this topic: Generic Scalar Transport Equation
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