The flashing Brownian ratchet

Using the ratchet and pawl machine as a basis for a Brownian ratchet ...
...several ideas have been used to get directed movement from Brownian particles.

A common mechanism is the flashing ratchet.

The mechanism:

Consider a system where there exists two one-dimensional potentials, U_on and U_off.
The asymmetry of the potential U_on is determined by a, where 0 < a < 1.
Having a = 1/2 creates a triangular symmetric potential;
otherwise the potential is asymmetrical (e.g., in the figure a < 1/2).

No macroscopic gradient
Net movement of particles in the forward direction
(direction of the arrow)

a slight gradient present
Causes the particles to drift backwards while U_off is acting -
thus, the net flow of particles in the forward direction is reduced.

Let there be Brownian particles existing in the potential diffusing to a position of least energy.

When Uon is applied, particles are trapped in the minima of the potential - so the concentration of the particles is peaked.
Switching the potential off, allows the particles to diffuse freely - so the concentration is a set of Gaussian curves centered around the minima.
When Uon is switched on again, there is a probability P _fwd that is proportional to the green area of the curve that some particles are to the right of aL. These particles move forwards to the minima located at L. Similarly there is a probability P _bck for particles that are to the left of (1-a)L. Since a < 1/2 then P _fwd>P _bck the net motion of the particles is to the right.

Thus we have directed motion!!

Here is a Java applet that shows a flashing BR working.

A physical implementation of the flashing ratchet Brownian motor

A charged particle moving over an array of interdigitated electrodes

When a voltage V is applied to interdigitated electrodes deposited on a glass slide with anisotropically positioned "teeth", the resulting potential is spatially periodic but anisotropic. It is possible to create L as small as 10^-5 m or less (with photolithography)

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