A magnetic gradient induced force in NMR restricted diffusion experiments

We predict that the phase cancellation of a precessing magnetisation field carried by a diffusing species in a bounded geometry under certain nuclear magnetic resonance pulsed magnetic field gradient sequences results in a small force over typically micrometre length scales. Our calculations reveal that the total magnetisation energy in a pore under the influence of a pulsed gradient will be distance-dependent thus resulting in a force acting on the boundary. It is shown that this effect of the magnetisation of diffusing particles will appear as either an attractive or repulsive force depending on the geometry of the pore and magnetic properties of the material. A detailed analysis is performed for the case of a pulsed gradient spin-echo experiment on parallel planes. It is shown that the force decays exponentially in terms of the spin-spin relaxation. The proof is based on classical electrodynamics. An application of this effect to soft matter is suggested.