Stokes force
Equation
The Stokes force is the force generated by the flow around a sphere immersed in it. In this case, the model of force proportional to velocity is used:
$ F = b v $ |
In this context, it can be shown that the constant $b$ is equal to:
$b = 6\pi r \eta$
where $r$ is the radius of the sphere and $\eta$ is the viscosity of the medium. Thus, the Stokes force is given by:
$ F =6 \pi \eta r v_c $ |
This force is primarily applicable in laminar flows.
ID:(4871, 0)
Particle velocity in electric field
Equation
A charged particle
$ F = q E $ |
This force is opposed by a force due to the effect of the medium that can be modeled by Stokes law
$ F =6 \pi \eta r v_c $ |
If both forces are equalized, it is obtained that the particle moves with a constant speed equal to
$ \vec{v} = \mu \vec{E} $ |
with mobility equal to
$ \mu =\displaystyle\frac{ q }{6 \pi \eta a }$ |
ID:(11997, 0)
Particle mobility in electric field
Equation
To equalize the force caused by the electric field
$ F = q E $ |
with the opposing force that is modeled with Stokes law
$ F =6 \pi \eta r v_c $ |
the relationship is obtained
$ \vec{v} = \mu \vec{E} $ |
with mobility equal to
$ \mu =\displaystyle\frac{ q }{6 \pi \eta a }$ |
ID:(11998, 0)