Nonlinear frictiophoresis
Nonlinear frictiophoresis is the unidirectional drift of a particle in a medium caused by periodic driving force with zero mean.
The effect is possible due to nonlinear dependence of the friction-drag force on the particle's velocity.
[2] At first glance, a periodic driving force with zero mean is able to entrain a particle into an oscillating movement without unidirectional drift, because integral momentum provided to the particle by the force is zero.
The possibility of unidirectional drift can be recognized if one takes into account that the particle itself loses momentum through transferring it further to the medium it moves in/at.
For this to happen, the driving force time-dependence must be more complicated than it is in a single sinusoidal harmonic.
The simplest case of friction-velocity dependence law is the Stokes's one:
The friction-velocity law (1) is observed for a slowly moving spherical particle in a Newtonian fluid.
The characteristic property of the law (1) is that any, even a very small driving force is able to get particle moving.
This kind of friction-velocity (dry friction) law has a jump discontinuity at
For the sake of simplicity, we consider here the physical situation when inertia may be neglected.
The latter can be achieved if particle's mass is small, velocity is low and friction is high.
In this situation, the particle driven with force (4) immediately starts moving with constant velocity
[1] The dimensionless equation of motion for a particle driven by periodic force
Another type of analysis,[4] based on symmetry breaking suggests as well that a zero mean driving force is able to generate a directed drift.
for a standard DNA ladder up to 1500 bp long in 1.5% agarose gel.
In the DNA fragments separation, zero mean periodic electric field is used in zero-integrated-field electrophoresis (ZIFE),[6] where the field time dependence similar to that shown in Fig.
This allows to separate long fragments in agarose gel, nonseparable by standard constant field electrophoresis.
The long DNA geometry and its manner of movement in a gel, known as reptation do not allow to apply directly the consideration based on Eq.
It was observed, [7] that under certain physical conditions the mechanism described in Mathematical analysis section, above, can be used for separation with respect to specific mass, like particles made of isotopes of the same material.
The idea of organizing directed drift with zero mean periodic drive have obtained further development for other configurations and other physical mechanism of nonlinearity.
-axis in a medium with nonlinear friction can be manipulated by applying electromagnetic wave polarized circularly along
[8] [9] A small detuning between the first and second harmonic in (6) results in continuous rotational drift.
[9] If a particle undergoes a directed drift while moving freely in accordance with Eq.
This kind of behavior, as rigorous mathematical analysis shows, [10] results in modification of
qualitatively, by, e.g. changing the number of equilibrium points, see Fig.
The effect may be essential during high frequency electric field acting on biopolymers.
[11] For electrophoresis of colloid particles under a small strength electric field, the force
For a high strength, the linearity is broken due to nonlinear polarization.
may happen to have a constant component that can cause a directed drift.
This same effect for a liquid in a tube may serve in electroosmotic pump driven with zero mean electric field.
